Greeks formula implementation, from Black-Scholes-Merton model.
Usage
bsmgreeks(
greeks = c("delta", "gamma", "vega", "rho", "theta"),
type,
spot,
strike,
time,
rate,
yield,
sigma
)
bsmdelta(type, spot, strike, time, rate, yield, sigma)
bsmvega(type, spot, strike, time, rate, yield, sigma)
bsmgamma(type, spot, strike, time, rate, yield, sigma)
bsmtheta(type, spot, strike, time, rate, yield, sigma)
bsmrho(type, spot, strike, time, rate, yield, sigma)Arguments
- greeks
desired greek letter: delta, gamma, vega, rho or theta.
- type
call for call option, any other value for put.
- spot
current stock price.
- strike
the strike price.
- time
time to option expiration in years.
- rate
the risk-free interest rate.
- yield
the dividends that are expected to be paid.
- sigma
volatility of the stock price.
Recycle rule
These arguments handle the recycle rule so vectors can be provided and once those vectors differs in length the recycle rule is applied.
bsmdelta
Delta greek letter measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price.
bsmgamma
Gamma greek letter measures the rate of change in the delta with respect to changes in the underlying price.
bsmrho
Rho measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate.
Examples
bsmgreeks("delta", "put", 20, 30, 0:2000 / 1000, 0.15, 0, 0.25)
#> [1] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [7] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [13] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [19] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [25] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [31] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [37] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [43] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [49] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [55] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [61] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [67] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [73] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [79] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [85] -1.0000000 -1.0000000 -0.9999999 -0.9999999 -0.9999999 -0.9999999
#> [91] -0.9999999 -0.9999999 -0.9999999 -0.9999998 -0.9999998 -0.9999998
#> [97] -0.9999997 -0.9999997 -0.9999996 -0.9999996 -0.9999995 -0.9999995
#> [103] -0.9999994 -0.9999993 -0.9999992 -0.9999991 -0.9999990 -0.9999988
#> [109] -0.9999987 -0.9999985 -0.9999983 -0.9999981 -0.9999979 -0.9999977
#> [115] -0.9999974 -0.9999971 -0.9999968 -0.9999965 -0.9999961 -0.9999957
#> [121] -0.9999953 -0.9999948 -0.9999943 -0.9999938 -0.9999932 -0.9999926
#> [127] -0.9999919 -0.9999912 -0.9999904 -0.9999896 -0.9999887 -0.9999877
#> [133] -0.9999867 -0.9999856 -0.9999844 -0.9999832 -0.9999819 -0.9999805
#> [139] -0.9999790 -0.9999775 -0.9999758 -0.9999741 -0.9999722 -0.9999702
#> [145] -0.9999682 -0.9999660 -0.9999637 -0.9999613 -0.9999587 -0.9999561
#> [151] -0.9999532 -0.9999503 -0.9999472 -0.9999439 -0.9999405 -0.9999370
#> [157] -0.9999333 -0.9999294 -0.9999253 -0.9999210 -0.9999166 -0.9999120
#> [163] -0.9999072 -0.9999021 -0.9998969 -0.9998915 -0.9998858 -0.9998799
#> [169] -0.9998738 -0.9998674 -0.9998608 -0.9998540 -0.9998469 -0.9998395
#> [175] -0.9998319 -0.9998240 -0.9998158 -0.9998074 -0.9997986 -0.9997896
#> [181] -0.9997803 -0.9997706 -0.9997607 -0.9997504 -0.9997398 -0.9997288
#> [187] -0.9997175 -0.9997059 -0.9996939 -0.9996816 -0.9996689 -0.9996559
#> [193] -0.9996424 -0.9996286 -0.9996144 -0.9995998 -0.9995848 -0.9995694
#> [199] -0.9995535 -0.9995373 -0.9995206 -0.9995035 -0.9994860 -0.9994680
#> [205] -0.9994496 -0.9994307 -0.9994114 -0.9993915 -0.9993713 -0.9993505
#> [211] -0.9993293 -0.9993075 -0.9992853 -0.9992625 -0.9992393 -0.9992155
#> [217] -0.9991913 -0.9991665 -0.9991411 -0.9991153 -0.9990889 -0.9990619
#> [223] -0.9990344 -0.9990063 -0.9989777 -0.9989485 -0.9989187 -0.9988884
#> [229] -0.9988574 -0.9988259 -0.9987938 -0.9987611 -0.9987277 -0.9986938
#> [235] -0.9986593 -0.9986241 -0.9985883 -0.9985519 -0.9985149 -0.9984772
#> [241] -0.9984388 -0.9983999 -0.9983602 -0.9983200 -0.9982790 -0.9982374
#> [247] -0.9981952 -0.9981522 -0.9981086 -0.9980643 -0.9980193 -0.9979736
#> [253] -0.9979273 -0.9978802 -0.9978325 -0.9977840 -0.9977348 -0.9976849
#> [259] -0.9976343 -0.9975830 -0.9975310 -0.9974782 -0.9974248 -0.9973705
#> [265] -0.9973156 -0.9972599 -0.9972035 -0.9971463 -0.9970884 -0.9970297
#> [271] -0.9969703 -0.9969101 -0.9968492 -0.9967875 -0.9967251 -0.9966618
#> [277] -0.9965979 -0.9965331 -0.9964676 -0.9964013 -0.9963342 -0.9962663
#> [283] -0.9961977 -0.9961283 -0.9960581 -0.9959871 -0.9959153 -0.9958427
#> [289] -0.9957693 -0.9956951 -0.9956202 -0.9955444 -0.9954678 -0.9953905
#> [295] -0.9953123 -0.9952333 -0.9951535 -0.9950730 -0.9949916 -0.9949093
#> [301] -0.9948263 -0.9947425 -0.9946578 -0.9945724 -0.9944861 -0.9943990
#> [307] -0.9943111 -0.9942223 -0.9941328 -0.9940424 -0.9939512 -0.9938592
#> [313] -0.9937663 -0.9936727 -0.9935782 -0.9934829 -0.9933867 -0.9932897
#> [319] -0.9931919 -0.9930933 -0.9929939 -0.9928936 -0.9927925 -0.9926906
#> [325] -0.9925878 -0.9924842 -0.9923798 -0.9922746 -0.9921685 -0.9920616
#> [331] -0.9919539 -0.9918453 -0.9917359 -0.9916257 -0.9915147 -0.9914028
#> [337] -0.9912901 -0.9911766 -0.9910622 -0.9909470 -0.9908310 -0.9907142
#> [343] -0.9905966 -0.9904781 -0.9903588 -0.9902387 -0.9901177 -0.9899960
#> [349] -0.9898734 -0.9897499 -0.9896257 -0.9895007 -0.9893748 -0.9892481
#> [355] -0.9891206 -0.9889923 -0.9888631 -0.9887332 -0.9886024 -0.9884709
#> [361] -0.9883385 -0.9882053 -0.9880713 -0.9879364 -0.9878008 -0.9876644
#> [367] -0.9875272 -0.9873891 -0.9872503 -0.9871106 -0.9869702 -0.9868289
#> [373] -0.9866869 -0.9865441 -0.9864004 -0.9862560 -0.9861108 -0.9859648
#> [379] -0.9858180 -0.9856704 -0.9855220 -0.9853728 -0.9852229 -0.9850722
#> [385] -0.9849207 -0.9847684 -0.9846153 -0.9844615 -0.9843068 -0.9841514
#> [391] -0.9839953 -0.9838384 -0.9836806 -0.9835222 -0.9833629 -0.9832030
#> [397] -0.9830422 -0.9828807 -0.9827184 -0.9825554 -0.9823916 -0.9822270
#> [403] -0.9820617 -0.9818957 -0.9817289 -0.9815614 -0.9813931 -0.9812241
#> [409] -0.9810543 -0.9808838 -0.9807126 -0.9805406 -0.9803679 -0.9801945
#> [415] -0.9800203 -0.9798454 -0.9796698 -0.9794935 -0.9793164 -0.9791387
#> [421] -0.9789602 -0.9787810 -0.9786010 -0.9784204 -0.9782391 -0.9780570
#> [427] -0.9778743 -0.9776908 -0.9775066 -0.9773218 -0.9771362 -0.9769500
#> [433] -0.9767630 -0.9765754 -0.9763871 -0.9761981 -0.9760084 -0.9758180
#> [439] -0.9756270 -0.9754352 -0.9752428 -0.9750498 -0.9748560 -0.9746616
#> [445] -0.9744665 -0.9742707 -0.9740743 -0.9738773 -0.9736795 -0.9734811
#> [451] -0.9732821 -0.9730824 -0.9728820 -0.9726810 -0.9724794 -0.9722771
#> [457] -0.9720742 -0.9718706 -0.9716664 -0.9714616 -0.9712561 -0.9710500
#> [463] -0.9708433 -0.9706359 -0.9704280 -0.9702194 -0.9700102 -0.9698003
#> [469] -0.9695899 -0.9693788 -0.9691671 -0.9689549 -0.9687420 -0.9685285
#> [475] -0.9683144 -0.9680997 -0.9678844 -0.9676685 -0.9674521 -0.9672350
#> [481] -0.9670173 -0.9667991 -0.9665803 -0.9663609 -0.9661409 -0.9659203
#> [487] -0.9656992 -0.9654775 -0.9652552 -0.9650323 -0.9648089 -0.9645850
#> [493] -0.9643604 -0.9641353 -0.9639097 -0.9636835 -0.9634567 -0.9632294
#> [499] -0.9630015 -0.9627731 -0.9625442 -0.9623147 -0.9620846 -0.9618541
#> [505] -0.9616229 -0.9613913 -0.9611591 -0.9609264 -0.9606932 -0.9604595
#> [511] -0.9602252 -0.9599904 -0.9597551 -0.9595193 -0.9592829 -0.9590461
#> [517] -0.9588087 -0.9585709 -0.9583325 -0.9580936 -0.9578542 -0.9576144
#> [523] -0.9573740 -0.9571331 -0.9568918 -0.9566500 -0.9564076 -0.9561648
#> [529] -0.9559215 -0.9556777 -0.9554335 -0.9551887 -0.9549435 -0.9546978
#> [535] -0.9544517 -0.9542051 -0.9539580 -0.9537104 -0.9534624 -0.9532139
#> [541] -0.9529650 -0.9527156 -0.9524658 -0.9522155 -0.9519647 -0.9517135
#> [547] -0.9514619 -0.9512098 -0.9509573 -0.9507043 -0.9504509 -0.9501971
#> [553] -0.9499428 -0.9496881 -0.9494330 -0.9491775 -0.9489215 -0.9486651
#> [559] -0.9484082 -0.9481510 -0.9478933 -0.9476353 -0.9473768 -0.9471179
#> [565] -0.9468586 -0.9465988 -0.9463387 -0.9460782 -0.9458173 -0.9455559
#> [571] -0.9452942 -0.9450321 -0.9447696 -0.9445067 -0.9442434 -0.9439797
#> [577] -0.9437156 -0.9434512 -0.9431864 -0.9429211 -0.9426555 -0.9423896
#> [583] -0.9421232 -0.9418565 -0.9415894 -0.9413220 -0.9410542 -0.9407860
#> [589] -0.9405174 -0.9402485 -0.9399792 -0.9397096 -0.9394396 -0.9391693
#> [595] -0.9388986 -0.9386276 -0.9383562 -0.9380844 -0.9378124 -0.9375399
#> [601] -0.9372672 -0.9369941 -0.9367206 -0.9364469 -0.9361728 -0.9358983
#> [607] -0.9356235 -0.9353484 -0.9350730 -0.9347973 -0.9345212 -0.9342448
#> [613] -0.9339681 -0.9336910 -0.9334137 -0.9331360 -0.9328581 -0.9325798
#> [619] -0.9323012 -0.9320223 -0.9317430 -0.9314635 -0.9311837 -0.9309036
#> [625] -0.9306232 -0.9303425 -0.9300614 -0.9297801 -0.9294985 -0.9292166
#> [631] -0.9289345 -0.9286520 -0.9283692 -0.9280862 -0.9278029 -0.9275193
#> [637] -0.9272354 -0.9269512 -0.9266668 -0.9263821 -0.9260971 -0.9258119
#> [643] -0.9255263 -0.9252405 -0.9249545 -0.9246682 -0.9243816 -0.9240947
#> [649] -0.9238076 -0.9235202 -0.9232326 -0.9229447 -0.9226566 -0.9223682
#> [655] -0.9220796 -0.9217907 -0.9215015 -0.9212122 -0.9209225 -0.9206327
#> [661] -0.9203425 -0.9200522 -0.9197616 -0.9194708 -0.9191797 -0.9188884
#> [667] -0.9185969 -0.9183051 -0.9180131 -0.9177209 -0.9174284 -0.9171357
#> [673] -0.9168428 -0.9165497 -0.9162563 -0.9159628 -0.9156690 -0.9153750
#> [679] -0.9150808 -0.9147863 -0.9144917 -0.9141968 -0.9139017 -0.9136065
#> [685] -0.9133110 -0.9130153 -0.9127194 -0.9124233 -0.9121270 -0.9118305
#> [691] -0.9115337 -0.9112368 -0.9109397 -0.9106424 -0.9103450 -0.9100473
#> [697] -0.9097494 -0.9094513 -0.9091531 -0.9088546 -0.9085560 -0.9082572
#> [703] -0.9079582 -0.9076590 -0.9073597 -0.9070601 -0.9067604 -0.9064605
#> [709] -0.9061605 -0.9058602 -0.9055598 -0.9052592 -0.9049584 -0.9046575
#> [715] -0.9043564 -0.9040551 -0.9037537 -0.9034521 -0.9031504 -0.9028484
#> [721] -0.9025464 -0.9022441 -0.9019417 -0.9016391 -0.9013364 -0.9010336
#> [727] -0.9007305 -0.9004274 -0.9001240 -0.8998205 -0.8995169 -0.8992131
#> [733] -0.8989092 -0.8986051 -0.8983009 -0.8979966 -0.8976921 -0.8973874
#> [739] -0.8970827 -0.8967777 -0.8964727 -0.8961675 -0.8958622 -0.8955567
#> [745] -0.8952511 -0.8949454 -0.8946395 -0.8943335 -0.8940274 -0.8937211
#> [751] -0.8934148 -0.8931083 -0.8928016 -0.8924949 -0.8921880 -0.8918810
#> [757] -0.8915739 -0.8912667 -0.8909593 -0.8906519 -0.8903443 -0.8900366
#> [763] -0.8897288 -0.8894209 -0.8891128 -0.8888047 -0.8884964 -0.8881880
#> [769] -0.8878796 -0.8875710 -0.8872623 -0.8869535 -0.8866446 -0.8863356
#> [775] -0.8860265 -0.8857173 -0.8854080 -0.8850986 -0.8847891 -0.8844795
#> [781] -0.8841698 -0.8838600 -0.8835501 -0.8832401 -0.8829301 -0.8826199
#> [787] -0.8823097 -0.8819993 -0.8816889 -0.8813784 -0.8810678 -0.8807571
#> [793] -0.8804463 -0.8801355 -0.8798245 -0.8795135 -0.8792024 -0.8788912
#> [799] -0.8785799 -0.8782686 -0.8779572 -0.8776457 -0.8773341 -0.8770225
#> [805] -0.8767107 -0.8763989 -0.8760871 -0.8757751 -0.8754631 -0.8751511
#> [811] -0.8748389 -0.8745267 -0.8742144 -0.8739021 -0.8735896 -0.8732772
#> [817] -0.8729646 -0.8726520 -0.8723393 -0.8720266 -0.8717138 -0.8714010
#> [823] -0.8710880 -0.8707751 -0.8704621 -0.8701490 -0.8698358 -0.8695226
#> [829] -0.8692094 -0.8688961 -0.8685827 -0.8682693 -0.8679559 -0.8676424
#> [835] -0.8673288 -0.8670152 -0.8667016 -0.8663879 -0.8660741 -0.8657603
#> [841] -0.8654465 -0.8651326 -0.8648187 -0.8645047 -0.8641907 -0.8638767
#> [847] -0.8635626 -0.8632484 -0.8629343 -0.8626201 -0.8623058 -0.8619916
#> [853] -0.8616772 -0.8613629 -0.8610485 -0.8607341 -0.8604196 -0.8601051
#> [859] -0.8597906 -0.8594761 -0.8591615 -0.8588469 -0.8585323 -0.8582176
#> [865] -0.8579029 -0.8575882 -0.8572734 -0.8569587 -0.8566439 -0.8563290
#> [871] -0.8560142 -0.8556993 -0.8553844 -0.8550695 -0.8547546 -0.8544397
#> [877] -0.8541247 -0.8538097 -0.8534947 -0.8531797 -0.8528646 -0.8525496
#> [883] -0.8522345 -0.8519194 -0.8516043 -0.8512892 -0.8509740 -0.8506589
#> [889] -0.8503437 -0.8500286 -0.8497134 -0.8493982 -0.8490830 -0.8487678
#> [895] -0.8484526 -0.8481374 -0.8478222 -0.8475069 -0.8471917 -0.8468764
#> [901] -0.8465612 -0.8462459 -0.8459307 -0.8456154 -0.8453001 -0.8449849
#> [907] -0.8446696 -0.8443543 -0.8440391 -0.8437238 -0.8434085 -0.8430933
#> [913] -0.8427780 -0.8424628 -0.8421475 -0.8418322 -0.8415170 -0.8412018
#> [919] -0.8408865 -0.8405713 -0.8402561 -0.8399408 -0.8396256 -0.8393104
#> [925] -0.8389952 -0.8386801 -0.8383649 -0.8380497 -0.8377346 -0.8374194
#> [931] -0.8371043 -0.8367892 -0.8364741 -0.8361590 -0.8358439 -0.8355288
#> [937] -0.8352138 -0.8348988 -0.8345837 -0.8342687 -0.8339538 -0.8336388
#> [943] -0.8333238 -0.8330089 -0.8326940 -0.8323791 -0.8320642 -0.8317494
#> [949] -0.8314346 -0.8311198 -0.8308050 -0.8304902 -0.8301755 -0.8298607
#> [955] -0.8295460 -0.8292314 -0.8289167 -0.8286021 -0.8282875 -0.8279729
#> [961] -0.8276584 -0.8273439 -0.8270294 -0.8267149 -0.8264005 -0.8260861
#> [967] -0.8257717 -0.8254574 -0.8251431 -0.8248288 -0.8245145 -0.8242003
#> [973] -0.8238861 -0.8235719 -0.8232578 -0.8229437 -0.8226297 -0.8223156
#> [979] -0.8220016 -0.8216877 -0.8213738 -0.8210599 -0.8207460 -0.8204322
#> [985] -0.8201184 -0.8198047 -0.8194910 -0.8191773 -0.8188637 -0.8185501
#> [991] -0.8182366 -0.8179230 -0.8176096 -0.8172961 -0.8169828 -0.8166694
#> [997] -0.8163561 -0.8160428 -0.8157296 -0.8154164 -0.8151033 -0.8147902
#> [1003] -0.8144772 -0.8141642 -0.8138512 -0.8135383 -0.8132254 -0.8129126
#> [1009] -0.8125998 -0.8122871 -0.8119744 -0.8116618 -0.8113492 -0.8110366
#> [1015] -0.8107241 -0.8104117 -0.8100993 -0.8097869 -0.8094746 -0.8091624
#> [1021] -0.8088502 -0.8085380 -0.8082259 -0.8079139 -0.8076019 -0.8072900
#> [1027] -0.8069781 -0.8066662 -0.8063545 -0.8060427 -0.8057311 -0.8054194
#> [1033] -0.8051079 -0.8047963 -0.8044849 -0.8041735 -0.8038621 -0.8035508
#> [1039] -0.8032396 -0.8029284 -0.8026173 -0.8023063 -0.8019952 -0.8016843
#> [1045] -0.8013734 -0.8010626 -0.8007518 -0.8004411 -0.8001304 -0.7998198
#> [1051] -0.7995093 -0.7991988 -0.7988884 -0.7985781 -0.7982678 -0.7979575
#> [1057] -0.7976474 -0.7973373 -0.7970272 -0.7967172 -0.7964073 -0.7960975
#> [1063] -0.7957877 -0.7954779 -0.7951683 -0.7948587 -0.7945491 -0.7942397
#> [1069] -0.7939303 -0.7936209 -0.7933117 -0.7930024 -0.7926933 -0.7923842
#> [1075] -0.7920752 -0.7917663 -0.7914574 -0.7911486 -0.7908399 -0.7905312
#> [1081] -0.7902226 -0.7899141 -0.7896056 -0.7892972 -0.7889889 -0.7886806
#> [1087] -0.7883724 -0.7880643 -0.7877563 -0.7874483 -0.7871404 -0.7868326
#> [1093] -0.7865248 -0.7862171 -0.7859095 -0.7856020 -0.7852945 -0.7849871
#> [1099] -0.7846798 -0.7843725 -0.7840653 -0.7837582 -0.7834512 -0.7831442
#> [1105] -0.7828374 -0.7825305 -0.7822238 -0.7819171 -0.7816106 -0.7813041
#> [1111] -0.7809976 -0.7806913 -0.7803850 -0.7800788 -0.7797727 -0.7794666
#> [1117] -0.7791606 -0.7788547 -0.7785489 -0.7782432 -0.7779375 -0.7776319
#> [1123] -0.7773264 -0.7770210 -0.7767156 -0.7764104 -0.7761052 -0.7758001
#> [1129] -0.7754950 -0.7751901 -0.7748852 -0.7745804 -0.7742757 -0.7739711
#> [1135] -0.7736665 -0.7733621 -0.7730577 -0.7727534 -0.7724492 -0.7721450
#> [1141] -0.7718410 -0.7715370 -0.7712331 -0.7709293 -0.7706255 -0.7703219
#> [1147] -0.7700183 -0.7697148 -0.7694114 -0.7691081 -0.7688049 -0.7685018
#> [1153] -0.7681987 -0.7678957 -0.7675928 -0.7672900 -0.7669873 -0.7666847
#> [1159] -0.7663821 -0.7660797 -0.7657773 -0.7654750 -0.7651728 -0.7648706
#> [1165] -0.7645686 -0.7642667 -0.7639648 -0.7636630 -0.7633613 -0.7630597
#> [1171] -0.7627582 -0.7624568 -0.7621555 -0.7618542 -0.7615530 -0.7612520
#> [1177] -0.7609510 -0.7606501 -0.7603493 -0.7600486 -0.7597479 -0.7594474
#> [1183] -0.7591469 -0.7588466 -0.7585463 -0.7582461 -0.7579460 -0.7576460
#> [1189] -0.7573461 -0.7570463 -0.7567466 -0.7564469 -0.7561474 -0.7558479
#> [1195] -0.7555486 -0.7552493 -0.7549501 -0.7546510 -0.7543520 -0.7540531
#> [1201] -0.7537543 -0.7534555 -0.7531569 -0.7528584 -0.7525599 -0.7522616
#> [1207] -0.7519633 -0.7516651 -0.7513671 -0.7510691 -0.7507712 -0.7504734
#> [1213] -0.7501757 -0.7498781 -0.7495806 -0.7492832 -0.7489858 -0.7486886
#> [1219] -0.7483915 -0.7480944 -0.7477975 -0.7475006 -0.7472039 -0.7469072
#> [1225] -0.7466106 -0.7463142 -0.7460178 -0.7457215 -0.7454253 -0.7451292
#> [1231] -0.7448332 -0.7445373 -0.7442415 -0.7439458 -0.7436502 -0.7433547
#> [1237] -0.7430593 -0.7427640 -0.7424687 -0.7421736 -0.7418786 -0.7415837
#> [1243] -0.7412888 -0.7409941 -0.7406994 -0.7404049 -0.7401105 -0.7398161
#> [1249] -0.7395219 -0.7392277 -0.7389337 -0.7386397 -0.7383459 -0.7380521
#> [1255] -0.7377584 -0.7374649 -0.7371714 -0.7368781 -0.7365848 -0.7362916
#> [1261] -0.7359986 -0.7357056 -0.7354127 -0.7351200 -0.7348273 -0.7345348
#> [1267] -0.7342423 -0.7339499 -0.7336577 -0.7333655 -0.7330734 -0.7327815
#> [1273] -0.7324896 -0.7321978 -0.7319062 -0.7316146 -0.7313231 -0.7310318
#> [1279] -0.7307405 -0.7304493 -0.7301583 -0.7298673 -0.7295765 -0.7292857
#> [1285] -0.7289951 -0.7287045 -0.7284141 -0.7281237 -0.7278335 -0.7275433
#> [1291] -0.7272533 -0.7269633 -0.7266735 -0.7263837 -0.7260941 -0.7258046
#> [1297] -0.7255151 -0.7252258 -0.7249366 -0.7246475 -0.7243584 -0.7240695
#> [1303] -0.7237807 -0.7234920 -0.7232034 -0.7229149 -0.7226265 -0.7223382
#> [1309] -0.7220500 -0.7217619 -0.7214739 -0.7211860 -0.7208982 -0.7206106
#> [1315] -0.7203230 -0.7200355 -0.7197481 -0.7194609 -0.7191737 -0.7188867
#> [1321] -0.7185997 -0.7183129 -0.7180261 -0.7177395 -0.7174530 -0.7171665
#> [1327] -0.7168802 -0.7165940 -0.7163079 -0.7160219 -0.7157359 -0.7154501
#> [1333] -0.7151644 -0.7148789 -0.7145934 -0.7143080 -0.7140227 -0.7137375
#> [1339] -0.7134525 -0.7131675 -0.7128827 -0.7125979 -0.7123133 -0.7120287
#> [1345] -0.7117443 -0.7114600 -0.7111757 -0.7108916 -0.7106076 -0.7103237
#> [1351] -0.7100399 -0.7097562 -0.7094726 -0.7091892 -0.7089058 -0.7086225
#> [1357] -0.7083394 -0.7080563 -0.7077733 -0.7074905 -0.7072078 -0.7069251
#> [1363] -0.7066426 -0.7063602 -0.7060779 -0.7057957 -0.7055136 -0.7052316
#> [1369] -0.7049497 -0.7046679 -0.7043863 -0.7041047 -0.7038233 -0.7035419
#> [1375] -0.7032607 -0.7029795 -0.7026985 -0.7024176 -0.7021368 -0.7018561
#> [1381] -0.7015755 -0.7012950 -0.7010146 -0.7007343 -0.7004541 -0.7001741
#> [1387] -0.6998941 -0.6996143 -0.6993346 -0.6990549 -0.6987754 -0.6984960
#> [1393] -0.6982167 -0.6979375 -0.6976584 -0.6973794 -0.6971005 -0.6968218
#> [1399] -0.6965431 -0.6962645 -0.6959861 -0.6957078 -0.6954295 -0.6951514
#> [1405] -0.6948734 -0.6945955 -0.6943177 -0.6940400 -0.6937624 -0.6934850
#> [1411] -0.6932076 -0.6929304 -0.6926532 -0.6923762 -0.6920993 -0.6918224
#> [1417] -0.6915457 -0.6912691 -0.6909926 -0.6907162 -0.6904400 -0.6901638
#> [1423] -0.6898877 -0.6896118 -0.6893360 -0.6890602 -0.6887846 -0.6885091
#> [1429] -0.6882337 -0.6879584 -0.6876832 -0.6874081 -0.6871331 -0.6868583
#> [1435] -0.6865835 -0.6863089 -0.6860343 -0.6857599 -0.6854856 -0.6852114
#> [1441] -0.6849373 -0.6846633 -0.6843894 -0.6841157 -0.6838420 -0.6835684
#> [1447] -0.6832950 -0.6830217 -0.6827484 -0.6824753 -0.6822023 -0.6819294
#> [1453] -0.6816566 -0.6813840 -0.6811114 -0.6808389 -0.6805666 -0.6802944
#> [1459] -0.6800222 -0.6797502 -0.6794783 -0.6792065 -0.6789348 -0.6786632
#> [1465] -0.6783917 -0.6781204 -0.6778491 -0.6775780 -0.6773069 -0.6770360
#> [1471] -0.6767652 -0.6764945 -0.6762239 -0.6759534 -0.6756830 -0.6754128
#> [1477] -0.6751426 -0.6748725 -0.6746026 -0.6743328 -0.6740631 -0.6737935
#> [1483] -0.6735240 -0.6732546 -0.6729853 -0.6727161 -0.6724470 -0.6721781
#> [1489] -0.6719093 -0.6716405 -0.6713719 -0.6711034 -0.6708350 -0.6705667
#> [1495] -0.6702985 -0.6700304 -0.6697625 -0.6694946 -0.6692269 -0.6689592
#> [1501] -0.6686917 -0.6684243 -0.6681570 -0.6678898 -0.6676227 -0.6673557
#> [1507] -0.6670889 -0.6668221 -0.6665555 -0.6662889 -0.6660225 -0.6657562
#> [1513] -0.6654900 -0.6652239 -0.6649579 -0.6646920 -0.6644263 -0.6641606
#> [1519] -0.6638951 -0.6636296 -0.6633643 -0.6630991 -0.6628340 -0.6625690
#> [1525] -0.6623041 -0.6620393 -0.6617747 -0.6615101 -0.6612456 -0.6609813
#> [1531] -0.6607171 -0.6604530 -0.6601890 -0.6599251 -0.6596613 -0.6593976
#> [1537] -0.6591340 -0.6588706 -0.6586072 -0.6583440 -0.6580808 -0.6578178
#> [1543] -0.6575549 -0.6572921 -0.6570294 -0.6567668 -0.6565044 -0.6562420
#> [1549] -0.6559798 -0.6557176 -0.6554556 -0.6551937 -0.6549319 -0.6546702
#> [1555] -0.6544086 -0.6541471 -0.6538857 -0.6536245 -0.6533633 -0.6531023
#> [1561] -0.6528413 -0.6525805 -0.6523198 -0.6520592 -0.6517987 -0.6515383
#> [1567] -0.6512780 -0.6510179 -0.6507578 -0.6504979 -0.6502380 -0.6499783
#> [1573] -0.6497187 -0.6494592 -0.6491998 -0.6489405 -0.6486813 -0.6484222
#> [1579] -0.6481633 -0.6479044 -0.6476457 -0.6473870 -0.6471285 -0.6468701
#> [1585] -0.6466118 -0.6463536 -0.6460955 -0.6458376 -0.6455797 -0.6453219
#> [1591] -0.6450643 -0.6448067 -0.6445493 -0.6442920 -0.6440348 -0.6437777
#> [1597] -0.6435207 -0.6432638 -0.6430071 -0.6427504 -0.6424938 -0.6422374
#> [1603] -0.6419811 -0.6417248 -0.6414687 -0.6412127 -0.6409568 -0.6407010
#> [1609] -0.6404453 -0.6401898 -0.6399343 -0.6396790 -0.6394237 -0.6391686
#> [1615] -0.6389136 -0.6386586 -0.6384038 -0.6381491 -0.6378945 -0.6376401
#> [1621] -0.6373857 -0.6371314 -0.6368773 -0.6366232 -0.6363693 -0.6361155
#> [1627] -0.6358618 -0.6356081 -0.6353546 -0.6351013 -0.6348480 -0.6345948
#> [1633] -0.6343417 -0.6340888 -0.6338359 -0.6335832 -0.6333306 -0.6330780
#> [1639] -0.6328256 -0.6325733 -0.6323211 -0.6320690 -0.6318171 -0.6315652
#> [1645] -0.6313134 -0.6310618 -0.6308102 -0.6305588 -0.6303075 -0.6300562
#> [1651] -0.6298051 -0.6295541 -0.6293032 -0.6290524 -0.6288018 -0.6285512
#> [1657] -0.6283007 -0.6280504 -0.6278001 -0.6275500 -0.6273000 -0.6270500
#> [1663] -0.6268002 -0.6265505 -0.6263009 -0.6260514 -0.6258021 -0.6255528
#> [1669] -0.6253036 -0.6250546 -0.6248056 -0.6245568 -0.6243080 -0.6240594
#> [1675] -0.6238109 -0.6235625 -0.6233142 -0.6230660 -0.6228179 -0.6225699
#> [1681] -0.6223221 -0.6220743 -0.6218266 -0.6215791 -0.6213317 -0.6210843
#> [1687] -0.6208371 -0.6205900 -0.6203430 -0.6200961 -0.6198493 -0.6196026
#> [1693] -0.6193560 -0.6191095 -0.6188632 -0.6186169 -0.6183708 -0.6181247
#> [1699] -0.6178788 -0.6176329 -0.6173872 -0.6171416 -0.6168961 -0.6166507
#> [1705] -0.6164054 -0.6161602 -0.6159151 -0.6156702 -0.6154253 -0.6151805
#> [1711] -0.6149359 -0.6146913 -0.6144469 -0.6142026 -0.6139583 -0.6137142
#> [1717] -0.6134702 -0.6132263 -0.6129825 -0.6127388 -0.6124952 -0.6122517
#> [1723] -0.6120084 -0.6117651 -0.6115219 -0.6112789 -0.6110359 -0.6107931
#> [1729] -0.6105504 -0.6103077 -0.6100652 -0.6098228 -0.6095805 -0.6093383
#> [1735] -0.6090962 -0.6088542 -0.6086123 -0.6083706 -0.6081289 -0.6078873
#> [1741] -0.6076459 -0.6074045 -0.6071633 -0.6069221 -0.6066811 -0.6064401
#> [1747] -0.6061993 -0.6059586 -0.6057180 -0.6054775 -0.6052371 -0.6049968
#> [1753] -0.6047566 -0.6045165 -0.6042765 -0.6040367 -0.6037969 -0.6035572
#> [1759] -0.6033177 -0.6030782 -0.6028389 -0.6025996 -0.6023605 -0.6021215
#> [1765] -0.6018826 -0.6016437 -0.6014050 -0.6011664 -0.6009279 -0.6006895
#> [1771] -0.6004512 -0.6002130 -0.5999749 -0.5997370 -0.5994991 -0.5992613
#> [1777] -0.5990237 -0.5987861 -0.5985486 -0.5983113 -0.5980741 -0.5978369
#> [1783] -0.5975999 -0.5973629 -0.5971261 -0.5968894 -0.5966528 -0.5964163
#> [1789] -0.5961799 -0.5959436 -0.5957074 -0.5954713 -0.5952353 -0.5949994
#> [1795] -0.5947636 -0.5945279 -0.5942924 -0.5940569 -0.5938215 -0.5935863
#> [1801] -0.5933511 -0.5931161 -0.5928811 -0.5926463 -0.5924115 -0.5921769
#> [1807] -0.5919423 -0.5917079 -0.5914736 -0.5912394 -0.5910053 -0.5907712
#> [1813] -0.5905373 -0.5903035 -0.5900698 -0.5898362 -0.5896027 -0.5893693
#> [1819] -0.5891360 -0.5889029 -0.5886698 -0.5884368 -0.5882039 -0.5879711
#> [1825] -0.5877385 -0.5875059 -0.5872734 -0.5870411 -0.5868088 -0.5865767
#> [1831] -0.5863446 -0.5861127 -0.5858808 -0.5856491 -0.5854174 -0.5851859
#> [1837] -0.5849545 -0.5847231 -0.5844919 -0.5842608 -0.5840298 -0.5837989
#> [1843] -0.5835680 -0.5833373 -0.5831067 -0.5828762 -0.5826458 -0.5824155
#> [1849] -0.5821853 -0.5819552 -0.5817252 -0.5814953 -0.5812655 -0.5810358
#> [1855] -0.5808062 -0.5805767 -0.5803473 -0.5801181 -0.5798889 -0.5796598
#> [1861] -0.5794308 -0.5792019 -0.5789732 -0.5787445 -0.5785159 -0.5782875
#> [1867] -0.5780591 -0.5778308 -0.5776027 -0.5773746 -0.5771466 -0.5769188
#> [1873] -0.5766910 -0.5764634 -0.5762358 -0.5760084 -0.5757810 -0.5755538
#> [1879] -0.5753266 -0.5750996 -0.5748726 -0.5746458 -0.5744190 -0.5741924
#> [1885] -0.5739658 -0.5737394 -0.5735131 -0.5732868 -0.5730607 -0.5728346
#> [1891] -0.5726087 -0.5723829 -0.5721571 -0.5719315 -0.5717060 -0.5714805
#> [1897] -0.5712552 -0.5710300 -0.5708048 -0.5705798 -0.5703549 -0.5701300
#> [1903] -0.5699053 -0.5696807 -0.5694561 -0.5692317 -0.5690074 -0.5687831
#> [1909] -0.5685590 -0.5683350 -0.5681111 -0.5678872 -0.5676635 -0.5674399
#> [1915] -0.5672163 -0.5669929 -0.5667696 -0.5665463 -0.5663232 -0.5661002
#> [1921] -0.5658772 -0.5656544 -0.5654317 -0.5652090 -0.5649865 -0.5647641
#> [1927] -0.5645417 -0.5643195 -0.5640974 -0.5638753 -0.5636534 -0.5634316
#> [1933] -0.5632098 -0.5629882 -0.5627666 -0.5625452 -0.5623238 -0.5621026
#> [1939] -0.5618815 -0.5616604 -0.5614395 -0.5612186 -0.5609979 -0.5607772
#> [1945] -0.5605567 -0.5603362 -0.5601158 -0.5598956 -0.5596754 -0.5594554
#> [1951] -0.5592354 -0.5590155 -0.5587958 -0.5585761 -0.5583565 -0.5581371
#> [1957] -0.5579177 -0.5576984 -0.5574792 -0.5572602 -0.5570412 -0.5568223
#> [1963] -0.5566035 -0.5563848 -0.5561662 -0.5559478 -0.5557294 -0.5555111
#> [1969] -0.5552929 -0.5550748 -0.5548568 -0.5546389 -0.5544210 -0.5542033
#> [1975] -0.5539857 -0.5537682 -0.5535508 -0.5533335 -0.5531163 -0.5528991
#> [1981] -0.5526821 -0.5524652 -0.5522483 -0.5520316 -0.5518150 -0.5515984
#> [1987] -0.5513820 -0.5511656 -0.5509494 -0.5507332 -0.5505171 -0.5503012
#> [1993] -0.5500853 -0.5498695 -0.5496539 -0.5494383 -0.5492228 -0.5490074
#> [1999] -0.5487922 -0.5485770 -0.5483619
bsmdelta(c("call", "put"), c(50, 49, 48, 47), 45, 0.25, 0.13, 0.01, 0.2)
#> [1] 0.9174852 -0.1144770 0.8381276 -0.2157304
bsmdelta("call", 50, 45, 0.25, 0.13, 0.01, 1:1000 / 1000)
#> [1] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [8] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [15] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [22] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [29] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [36] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [43] 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031 0.9975031
#> [50] 0.9975031 0.9975031 0.9975030 0.9975030 0.9975029 0.9975027 0.9975025
#> [57] 0.9975022 0.9975017 0.9975010 0.9975001 0.9974989 0.9974973 0.9974951
#> [64] 0.9974923 0.9974887 0.9974841 0.9974784 0.9974713 0.9974626 0.9974521
#> [71] 0.9974394 0.9974243 0.9974064 0.9973854 0.9973609 0.9973325 0.9972998
#> [78] 0.9972625 0.9972200 0.9971719 0.9971179 0.9970573 0.9969899 0.9969150
#> [85] 0.9968323 0.9967413 0.9966416 0.9965326 0.9964141 0.9962855 0.9961464
#> [92] 0.9959965 0.9958354 0.9956627 0.9954781 0.9952812 0.9950718 0.9948495
#> [99] 0.9946141 0.9943654 0.9941032 0.9938271 0.9935371 0.9932331 0.9929148
#> [106] 0.9925822 0.9922351 0.9918736 0.9914975 0.9911068 0.9907015 0.9902816
#> [113] 0.9898472 0.9893983 0.9889349 0.9884571 0.9879650 0.9874587 0.9869383
#> [120] 0.9864040 0.9858559 0.9852941 0.9847188 0.9841303 0.9835285 0.9829139
#> [127] 0.9822864 0.9816465 0.9809942 0.9803298 0.9796536 0.9789657 0.9782663
#> [134] 0.9775558 0.9768344 0.9761022 0.9753597 0.9746069 0.9738442 0.9730717
#> [141] 0.9722899 0.9714988 0.9706988 0.9698901 0.9690730 0.9682477 0.9674145
#> [148] 0.9665736 0.9657252 0.9648697 0.9640072 0.9631380 0.9622623 0.9613804
#> [155] 0.9604925 0.9595988 0.9586995 0.9577950 0.9568854 0.9559709 0.9550517
#> [162] 0.9541281 0.9532003 0.9522684 0.9513327 0.9503933 0.9494506 0.9485046
#> [169] 0.9475555 0.9466036 0.9456489 0.9446918 0.9437323 0.9427707 0.9418071
#> [176] 0.9408416 0.9398744 0.9389058 0.9379357 0.9369645 0.9359922 0.9350189
#> [183] 0.9340449 0.9330702 0.9320950 0.9311194 0.9301435 0.9291675 0.9281915
#> [190] 0.9272155 0.9262398 0.9252644 0.9242894 0.9233150 0.9223412 0.9213682
#> [197] 0.9203959 0.9194246 0.9184544 0.9174852 0.9165172 0.9155505 0.9145852
#> [204] 0.9136213 0.9126589 0.9116982 0.9107390 0.9097817 0.9088261 0.9078724
#> [211] 0.9069206 0.9059708 0.9050231 0.9040774 0.9031340 0.9021927 0.9012538
#> [218] 0.9003171 0.8993829 0.8984510 0.8975216 0.8965947 0.8956704 0.8947487
#> [225] 0.8938295 0.8929131 0.8919993 0.8910883 0.8901801 0.8892746 0.8883720
#> [232] 0.8874723 0.8865754 0.8856815 0.8847905 0.8839024 0.8830174 0.8821354
#> [239] 0.8812564 0.8803804 0.8795076 0.8786378 0.8777711 0.8769076 0.8760472
#> [246] 0.8751899 0.8743359 0.8734850 0.8726373 0.8717928 0.8709515 0.8701134
#> [253] 0.8692786 0.8684470 0.8676187 0.8667936 0.8659718 0.8651533 0.8643380
#> [260] 0.8635260 0.8627173 0.8619119 0.8611098 0.8603109 0.8595154 0.8587231
#> [267] 0.8579342 0.8571485 0.8563661 0.8555871 0.8548113 0.8540388 0.8532696
#> [274] 0.8525037 0.8517410 0.8509817 0.8502256 0.8494728 0.8487233 0.8479770
#> [281] 0.8472340 0.8464943 0.8457578 0.8450246 0.8442945 0.8435678 0.8428442
#> [288] 0.8421239 0.8414068 0.8406929 0.8399821 0.8392746 0.8385703 0.8378691
#> [295] 0.8371711 0.8364763 0.8357846 0.8350960 0.8344106 0.8337283 0.8330492
#> [302] 0.8323731 0.8317001 0.8310302 0.8303634 0.8296997 0.8290390 0.8283813
#> [309] 0.8277267 0.8270752 0.8264266 0.8257810 0.8251385 0.8244989 0.8238623
#> [316] 0.8232286 0.8225979 0.8219702 0.8213454 0.8207235 0.8201045 0.8194884
#> [323] 0.8188752 0.8182648 0.8176573 0.8170527 0.8164509 0.8158520 0.8152558
#> [330] 0.8146625 0.8140719 0.8134842 0.8128992 0.8123170 0.8117375 0.8111607
#> [337] 0.8105867 0.8100154 0.8094468 0.8088808 0.8083176 0.8077570 0.8071991
#> [344] 0.8066438 0.8060912 0.8055411 0.8049937 0.8044489 0.8039066 0.8033669
#> [351] 0.8028298 0.8022952 0.8017632 0.8012337 0.8007067 0.8001822 0.7996602
#> [358] 0.7991407 0.7986237 0.7981091 0.7975969 0.7970872 0.7965799 0.7960750
#> [365] 0.7955725 0.7950724 0.7945747 0.7940794 0.7935864 0.7930957 0.7926074
#> [372] 0.7921214 0.7916377 0.7911563 0.7906772 0.7902003 0.7897258 0.7892535
#> [379] 0.7887834 0.7883156 0.7878499 0.7873865 0.7869253 0.7864663 0.7860095
#> [386] 0.7855548 0.7851023 0.7846520 0.7842037 0.7837577 0.7833137 0.7828718
#> [393] 0.7824320 0.7819943 0.7815587 0.7811252 0.7806937 0.7802642 0.7798368
#> [400] 0.7794114 0.7789880 0.7785667 0.7781473 0.7777299 0.7773145 0.7769010
#> [407] 0.7764895 0.7760799 0.7756723 0.7752666 0.7748629 0.7744610 0.7740610
#> [414] 0.7736629 0.7732667 0.7728724 0.7724799 0.7720893 0.7717006 0.7713136
#> [421] 0.7709285 0.7705452 0.7701637 0.7697840 0.7694061 0.7690300 0.7686556
#> [428] 0.7682830 0.7679121 0.7675430 0.7671757 0.7668100 0.7664461 0.7660839
#> [435] 0.7657234 0.7653646 0.7650075 0.7646520 0.7642982 0.7639461 0.7635956
#> [442] 0.7632468 0.7628996 0.7625540 0.7622101 0.7618678 0.7615270 0.7611879
#> [449] 0.7608503 0.7605144 0.7601800 0.7598471 0.7595159 0.7591861 0.7588580
#> [456] 0.7585313 0.7582062 0.7578826 0.7575605 0.7572399 0.7569208 0.7566032
#> [463] 0.7562871 0.7559724 0.7556593 0.7553475 0.7550373 0.7547285 0.7544211
#> [470] 0.7541151 0.7538106 0.7535075 0.7532058 0.7529055 0.7526066 0.7523091
#> [477] 0.7520130 0.7517183 0.7514249 0.7511329 0.7508423 0.7505530 0.7502650
#> [484] 0.7499784 0.7496931 0.7494092 0.7491265 0.7488452 0.7485652 0.7482865
#> [491] 0.7480091 0.7477329 0.7474581 0.7471845 0.7469122 0.7466411 0.7463713
#> [498] 0.7461028 0.7458355 0.7455695 0.7453046 0.7450410 0.7447787 0.7445175
#> [505] 0.7442576 0.7439988 0.7437413 0.7434849 0.7432297 0.7429758 0.7427229
#> [512] 0.7424713 0.7422208 0.7419715 0.7417234 0.7414763 0.7412305 0.7409857
#> [519] 0.7407421 0.7404997 0.7402583 0.7400181 0.7397790 0.7395410 0.7393040
#> [526] 0.7390682 0.7388335 0.7385999 0.7383673 0.7381358 0.7379054 0.7376760
#> [533] 0.7374478 0.7372205 0.7369943 0.7367692 0.7365451 0.7363221 0.7361000
#> [540] 0.7358790 0.7356591 0.7354401 0.7352222 0.7350052 0.7347893 0.7345743
#> [547] 0.7343604 0.7341475 0.7339355 0.7337245 0.7335145 0.7333055 0.7330974
#> [554] 0.7328903 0.7326842 0.7324790 0.7322747 0.7320714 0.7318691 0.7316677
#> [561] 0.7314672 0.7312677 0.7310690 0.7308713 0.7306745 0.7304787 0.7302837
#> [568] 0.7300896 0.7298965 0.7297042 0.7295128 0.7293224 0.7291328 0.7289440
#> [575] 0.7287562 0.7285692 0.7283831 0.7281979 0.7280135 0.7278300 0.7276473
#> [582] 0.7274655 0.7272846 0.7271044 0.7269252 0.7267467 0.7265691 0.7263923
#> [589] 0.7262163 0.7260412 0.7258669 0.7256933 0.7255206 0.7253487 0.7251776
#> [596] 0.7250073 0.7248378 0.7246691 0.7245012 0.7243341 0.7241677 0.7240022
#> [603] 0.7238374 0.7236733 0.7235101 0.7233476 0.7231859 0.7230249 0.7228647
#> [610] 0.7227052 0.7225465 0.7223885 0.7222313 0.7220748 0.7219191 0.7217641
#> [617] 0.7216098 0.7214562 0.7213034 0.7211513 0.7209999 0.7208492 0.7206993
#> [624] 0.7205500 0.7204015 0.7202536 0.7201065 0.7199600 0.7198143 0.7196692
#> [631] 0.7195249 0.7193812 0.7192382 0.7190958 0.7189542 0.7188132 0.7186729
#> [638] 0.7185333 0.7183943 0.7182560 0.7181184 0.7179814 0.7178450 0.7177094
#> [645] 0.7175743 0.7174400 0.7173062 0.7171731 0.7170407 0.7169088 0.7167777
#> [652] 0.7166471 0.7165172 0.7163879 0.7162592 0.7161311 0.7160037 0.7158769
#> [659] 0.7157507 0.7156251 0.7155001 0.7153757 0.7152519 0.7151287 0.7150061
#> [666] 0.7148842 0.7147628 0.7146420 0.7145218 0.7144021 0.7142831 0.7141646
#> [673] 0.7140468 0.7139295 0.7138127 0.7136966 0.7135810 0.7134660 0.7133515
#> [680] 0.7132376 0.7131243 0.7130116 0.7128994 0.7127877 0.7126766 0.7125661
#> [687] 0.7124561 0.7123466 0.7122377 0.7121293 0.7120215 0.7119142 0.7118074
#> [694] 0.7117012 0.7115955 0.7114904 0.7113857 0.7112816 0.7111780 0.7110750
#> [701] 0.7109724 0.7108704 0.7107689 0.7106679 0.7105674 0.7104674 0.7103679
#> [708] 0.7102690 0.7101705 0.7100725 0.7099751 0.7098781 0.7097816 0.7096857
#> [715] 0.7095902 0.7094952 0.7094007 0.7093066 0.7092131 0.7091200 0.7090275
#> [722] 0.7089354 0.7088438 0.7087526 0.7086619 0.7085717 0.7084820 0.7083927
#> [729] 0.7083039 0.7082156 0.7081277 0.7080403 0.7079534 0.7078669 0.7077809
#> [736] 0.7076953 0.7076101 0.7075255 0.7074412 0.7073575 0.7072741 0.7071912
#> [743] 0.7071088 0.7070268 0.7069452 0.7068641 0.7067834 0.7067031 0.7066233
#> [750] 0.7065439 0.7064649 0.7063863 0.7063082 0.7062305 0.7061533 0.7060764
#> [757] 0.7060000 0.7059240 0.7058484 0.7057732 0.7056984 0.7056241 0.7055502
#> [764] 0.7054766 0.7054035 0.7053308 0.7052585 0.7051866 0.7051151 0.7050440
#> [771] 0.7049732 0.7049029 0.7048330 0.7047635 0.7046944 0.7046256 0.7045573
#> [778] 0.7044894 0.7044218 0.7043546 0.7042878 0.7042214 0.7041554 0.7040897
#> [785] 0.7040245 0.7039596 0.7038951 0.7038309 0.7037672 0.7037038 0.7036407
#> [792] 0.7035781 0.7035158 0.7034539 0.7033923 0.7033312 0.7032703 0.7032099
#> [799] 0.7031498 0.7030901 0.7030307 0.7029717 0.7029130 0.7028547 0.7027967
#> [806] 0.7027391 0.7026819 0.7026250 0.7025684 0.7025122 0.7024563 0.7024008
#> [813] 0.7023457 0.7022908 0.7022363 0.7021822 0.7021284 0.7020749 0.7020218
#> [820] 0.7019690 0.7019165 0.7018644 0.7018126 0.7017611 0.7017100 0.7016592
#> [827] 0.7016087 0.7015585 0.7015087 0.7014592 0.7014100 0.7013611 0.7013126
#> [834] 0.7012644 0.7012165 0.7011689 0.7011216 0.7010747 0.7010280 0.7009817
#> [841] 0.7009357 0.7008900 0.7008446 0.7007995 0.7007548 0.7007103 0.7006661
#> [848] 0.7006223 0.7005787 0.7005355 0.7004925 0.7004499 0.7004075 0.7003655
#> [855] 0.7003237 0.7002823 0.7002411 0.7002002 0.7001597 0.7001194 0.7000794
#> [862] 0.7000397 0.7000003 0.6999612 0.6999224 0.6998838 0.6998456 0.6998076
#> [869] 0.6997699 0.6997325 0.6996954 0.6996586 0.6996220 0.6995857 0.6995497
#> [876] 0.6995140 0.6994786 0.6994434 0.6994085 0.6993739 0.6993396 0.6993055
#> [883] 0.6992717 0.6992382 0.6992049 0.6991719 0.6991392 0.6991067 0.6990745
#> [890] 0.6990426 0.6990110 0.6989796 0.6989484 0.6989176 0.6988869 0.6988566
#> [897] 0.6988265 0.6987967 0.6987671 0.6987378 0.6987087 0.6986799 0.6986514
#> [904] 0.6986231 0.6985950 0.6985672 0.6985397 0.6985124 0.6984854 0.6984586
#> [911] 0.6984320 0.6984057 0.6983797 0.6983539 0.6983283 0.6983030 0.6982779
#> [918] 0.6982531 0.6982285 0.6982041 0.6981800 0.6981562 0.6981325 0.6981091
#> [925] 0.6980860 0.6980631 0.6980404 0.6980179 0.6979957 0.6979738 0.6979520
#> [932] 0.6979305 0.6979092 0.6978882 0.6978673 0.6978467 0.6978264 0.6978062
#> [939] 0.6977863 0.6977667 0.6977472 0.6977280 0.6977090 0.6976902 0.6976716
#> [946] 0.6976533 0.6976352 0.6976173 0.6975996 0.6975821 0.6975649 0.6975479
#> [953] 0.6975311 0.6975145 0.6974981 0.6974820 0.6974660 0.6974503 0.6974348
#> [960] 0.6974195 0.6974044 0.6973895 0.6973749 0.6973604 0.6973462 0.6973321
#> [967] 0.6973183 0.6973047 0.6972913 0.6972780 0.6972650 0.6972523 0.6972397
#> [974] 0.6972273 0.6972151 0.6972031 0.6971913 0.6971798 0.6971684 0.6971572
#> [981] 0.6971462 0.6971354 0.6971249 0.6971145 0.6971043 0.6970943 0.6970845
#> [988] 0.6970749 0.6970655 0.6970563 0.6970473 0.6970385 0.6970299 0.6970214
#> [995] 0.6970132 0.6970051 0.6969973 0.6969896 0.6969821 0.6969748
bsmdelta("put", 20, 30, 0:2000 / 1000, 0.15, 0, 0.25)
#> [1] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [7] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [13] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [19] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [25] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [31] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [37] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [43] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [49] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [55] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [61] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [67] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [73] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [79] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
#> [85] -1.0000000 -1.0000000 -0.9999999 -0.9999999 -0.9999999 -0.9999999
#> [91] -0.9999999 -0.9999999 -0.9999999 -0.9999998 -0.9999998 -0.9999998
#> [97] -0.9999997 -0.9999997 -0.9999996 -0.9999996 -0.9999995 -0.9999995
#> [103] -0.9999994 -0.9999993 -0.9999992 -0.9999991 -0.9999990 -0.9999988
#> [109] -0.9999987 -0.9999985 -0.9999983 -0.9999981 -0.9999979 -0.9999977
#> [115] -0.9999974 -0.9999971 -0.9999968 -0.9999965 -0.9999961 -0.9999957
#> [121] -0.9999953 -0.9999948 -0.9999943 -0.9999938 -0.9999932 -0.9999926
#> [127] -0.9999919 -0.9999912 -0.9999904 -0.9999896 -0.9999887 -0.9999877
#> [133] -0.9999867 -0.9999856 -0.9999844 -0.9999832 -0.9999819 -0.9999805
#> [139] -0.9999790 -0.9999775 -0.9999758 -0.9999741 -0.9999722 -0.9999702
#> [145] -0.9999682 -0.9999660 -0.9999637 -0.9999613 -0.9999587 -0.9999561
#> [151] -0.9999532 -0.9999503 -0.9999472 -0.9999439 -0.9999405 -0.9999370
#> [157] -0.9999333 -0.9999294 -0.9999253 -0.9999210 -0.9999166 -0.9999120
#> [163] -0.9999072 -0.9999021 -0.9998969 -0.9998915 -0.9998858 -0.9998799
#> [169] -0.9998738 -0.9998674 -0.9998608 -0.9998540 -0.9998469 -0.9998395
#> [175] -0.9998319 -0.9998240 -0.9998158 -0.9998074 -0.9997986 -0.9997896
#> [181] -0.9997803 -0.9997706 -0.9997607 -0.9997504 -0.9997398 -0.9997288
#> [187] -0.9997175 -0.9997059 -0.9996939 -0.9996816 -0.9996689 -0.9996559
#> [193] -0.9996424 -0.9996286 -0.9996144 -0.9995998 -0.9995848 -0.9995694
#> [199] -0.9995535 -0.9995373 -0.9995206 -0.9995035 -0.9994860 -0.9994680
#> [205] -0.9994496 -0.9994307 -0.9994114 -0.9993915 -0.9993713 -0.9993505
#> [211] -0.9993293 -0.9993075 -0.9992853 -0.9992625 -0.9992393 -0.9992155
#> [217] -0.9991913 -0.9991665 -0.9991411 -0.9991153 -0.9990889 -0.9990619
#> [223] -0.9990344 -0.9990063 -0.9989777 -0.9989485 -0.9989187 -0.9988884
#> [229] -0.9988574 -0.9988259 -0.9987938 -0.9987611 -0.9987277 -0.9986938
#> [235] -0.9986593 -0.9986241 -0.9985883 -0.9985519 -0.9985149 -0.9984772
#> [241] -0.9984388 -0.9983999 -0.9983602 -0.9983200 -0.9982790 -0.9982374
#> [247] -0.9981952 -0.9981522 -0.9981086 -0.9980643 -0.9980193 -0.9979736
#> [253] -0.9979273 -0.9978802 -0.9978325 -0.9977840 -0.9977348 -0.9976849
#> [259] -0.9976343 -0.9975830 -0.9975310 -0.9974782 -0.9974248 -0.9973705
#> [265] -0.9973156 -0.9972599 -0.9972035 -0.9971463 -0.9970884 -0.9970297
#> [271] -0.9969703 -0.9969101 -0.9968492 -0.9967875 -0.9967251 -0.9966618
#> [277] -0.9965979 -0.9965331 -0.9964676 -0.9964013 -0.9963342 -0.9962663
#> [283] -0.9961977 -0.9961283 -0.9960581 -0.9959871 -0.9959153 -0.9958427
#> [289] -0.9957693 -0.9956951 -0.9956202 -0.9955444 -0.9954678 -0.9953905
#> [295] -0.9953123 -0.9952333 -0.9951535 -0.9950730 -0.9949916 -0.9949093
#> [301] -0.9948263 -0.9947425 -0.9946578 -0.9945724 -0.9944861 -0.9943990
#> [307] -0.9943111 -0.9942223 -0.9941328 -0.9940424 -0.9939512 -0.9938592
#> [313] -0.9937663 -0.9936727 -0.9935782 -0.9934829 -0.9933867 -0.9932897
#> [319] -0.9931919 -0.9930933 -0.9929939 -0.9928936 -0.9927925 -0.9926906
#> [325] -0.9925878 -0.9924842 -0.9923798 -0.9922746 -0.9921685 -0.9920616
#> [331] -0.9919539 -0.9918453 -0.9917359 -0.9916257 -0.9915147 -0.9914028
#> [337] -0.9912901 -0.9911766 -0.9910622 -0.9909470 -0.9908310 -0.9907142
#> [343] -0.9905966 -0.9904781 -0.9903588 -0.9902387 -0.9901177 -0.9899960
#> [349] -0.9898734 -0.9897499 -0.9896257 -0.9895007 -0.9893748 -0.9892481
#> [355] -0.9891206 -0.9889923 -0.9888631 -0.9887332 -0.9886024 -0.9884709
#> [361] -0.9883385 -0.9882053 -0.9880713 -0.9879364 -0.9878008 -0.9876644
#> [367] -0.9875272 -0.9873891 -0.9872503 -0.9871106 -0.9869702 -0.9868289
#> [373] -0.9866869 -0.9865441 -0.9864004 -0.9862560 -0.9861108 -0.9859648
#> [379] -0.9858180 -0.9856704 -0.9855220 -0.9853728 -0.9852229 -0.9850722
#> [385] -0.9849207 -0.9847684 -0.9846153 -0.9844615 -0.9843068 -0.9841514
#> [391] -0.9839953 -0.9838384 -0.9836806 -0.9835222 -0.9833629 -0.9832030
#> [397] -0.9830422 -0.9828807 -0.9827184 -0.9825554 -0.9823916 -0.9822270
#> [403] -0.9820617 -0.9818957 -0.9817289 -0.9815614 -0.9813931 -0.9812241
#> [409] -0.9810543 -0.9808838 -0.9807126 -0.9805406 -0.9803679 -0.9801945
#> [415] -0.9800203 -0.9798454 -0.9796698 -0.9794935 -0.9793164 -0.9791387
#> [421] -0.9789602 -0.9787810 -0.9786010 -0.9784204 -0.9782391 -0.9780570
#> [427] -0.9778743 -0.9776908 -0.9775066 -0.9773218 -0.9771362 -0.9769500
#> [433] -0.9767630 -0.9765754 -0.9763871 -0.9761981 -0.9760084 -0.9758180
#> [439] -0.9756270 -0.9754352 -0.9752428 -0.9750498 -0.9748560 -0.9746616
#> [445] -0.9744665 -0.9742707 -0.9740743 -0.9738773 -0.9736795 -0.9734811
#> [451] -0.9732821 -0.9730824 -0.9728820 -0.9726810 -0.9724794 -0.9722771
#> [457] -0.9720742 -0.9718706 -0.9716664 -0.9714616 -0.9712561 -0.9710500
#> [463] -0.9708433 -0.9706359 -0.9704280 -0.9702194 -0.9700102 -0.9698003
#> [469] -0.9695899 -0.9693788 -0.9691671 -0.9689549 -0.9687420 -0.9685285
#> [475] -0.9683144 -0.9680997 -0.9678844 -0.9676685 -0.9674521 -0.9672350
#> [481] -0.9670173 -0.9667991 -0.9665803 -0.9663609 -0.9661409 -0.9659203
#> [487] -0.9656992 -0.9654775 -0.9652552 -0.9650323 -0.9648089 -0.9645850
#> [493] -0.9643604 -0.9641353 -0.9639097 -0.9636835 -0.9634567 -0.9632294
#> [499] -0.9630015 -0.9627731 -0.9625442 -0.9623147 -0.9620846 -0.9618541
#> [505] -0.9616229 -0.9613913 -0.9611591 -0.9609264 -0.9606932 -0.9604595
#> [511] -0.9602252 -0.9599904 -0.9597551 -0.9595193 -0.9592829 -0.9590461
#> [517] -0.9588087 -0.9585709 -0.9583325 -0.9580936 -0.9578542 -0.9576144
#> [523] -0.9573740 -0.9571331 -0.9568918 -0.9566500 -0.9564076 -0.9561648
#> [529] -0.9559215 -0.9556777 -0.9554335 -0.9551887 -0.9549435 -0.9546978
#> [535] -0.9544517 -0.9542051 -0.9539580 -0.9537104 -0.9534624 -0.9532139
#> [541] -0.9529650 -0.9527156 -0.9524658 -0.9522155 -0.9519647 -0.9517135
#> [547] -0.9514619 -0.9512098 -0.9509573 -0.9507043 -0.9504509 -0.9501971
#> [553] -0.9499428 -0.9496881 -0.9494330 -0.9491775 -0.9489215 -0.9486651
#> [559] -0.9484082 -0.9481510 -0.9478933 -0.9476353 -0.9473768 -0.9471179
#> [565] -0.9468586 -0.9465988 -0.9463387 -0.9460782 -0.9458173 -0.9455559
#> [571] -0.9452942 -0.9450321 -0.9447696 -0.9445067 -0.9442434 -0.9439797
#> [577] -0.9437156 -0.9434512 -0.9431864 -0.9429211 -0.9426555 -0.9423896
#> [583] -0.9421232 -0.9418565 -0.9415894 -0.9413220 -0.9410542 -0.9407860
#> [589] -0.9405174 -0.9402485 -0.9399792 -0.9397096 -0.9394396 -0.9391693
#> [595] -0.9388986 -0.9386276 -0.9383562 -0.9380844 -0.9378124 -0.9375399
#> [601] -0.9372672 -0.9369941 -0.9367206 -0.9364469 -0.9361728 -0.9358983
#> [607] -0.9356235 -0.9353484 -0.9350730 -0.9347973 -0.9345212 -0.9342448
#> [613] -0.9339681 -0.9336910 -0.9334137 -0.9331360 -0.9328581 -0.9325798
#> [619] -0.9323012 -0.9320223 -0.9317430 -0.9314635 -0.9311837 -0.9309036
#> [625] -0.9306232 -0.9303425 -0.9300614 -0.9297801 -0.9294985 -0.9292166
#> [631] -0.9289345 -0.9286520 -0.9283692 -0.9280862 -0.9278029 -0.9275193
#> [637] -0.9272354 -0.9269512 -0.9266668 -0.9263821 -0.9260971 -0.9258119
#> [643] -0.9255263 -0.9252405 -0.9249545 -0.9246682 -0.9243816 -0.9240947
#> [649] -0.9238076 -0.9235202 -0.9232326 -0.9229447 -0.9226566 -0.9223682
#> [655] -0.9220796 -0.9217907 -0.9215015 -0.9212122 -0.9209225 -0.9206327
#> [661] -0.9203425 -0.9200522 -0.9197616 -0.9194708 -0.9191797 -0.9188884
#> [667] -0.9185969 -0.9183051 -0.9180131 -0.9177209 -0.9174284 -0.9171357
#> [673] -0.9168428 -0.9165497 -0.9162563 -0.9159628 -0.9156690 -0.9153750
#> [679] -0.9150808 -0.9147863 -0.9144917 -0.9141968 -0.9139017 -0.9136065
#> [685] -0.9133110 -0.9130153 -0.9127194 -0.9124233 -0.9121270 -0.9118305
#> [691] -0.9115337 -0.9112368 -0.9109397 -0.9106424 -0.9103450 -0.9100473
#> [697] -0.9097494 -0.9094513 -0.9091531 -0.9088546 -0.9085560 -0.9082572
#> [703] -0.9079582 -0.9076590 -0.9073597 -0.9070601 -0.9067604 -0.9064605
#> [709] -0.9061605 -0.9058602 -0.9055598 -0.9052592 -0.9049584 -0.9046575
#> [715] -0.9043564 -0.9040551 -0.9037537 -0.9034521 -0.9031504 -0.9028484
#> [721] -0.9025464 -0.9022441 -0.9019417 -0.9016391 -0.9013364 -0.9010336
#> [727] -0.9007305 -0.9004274 -0.9001240 -0.8998205 -0.8995169 -0.8992131
#> [733] -0.8989092 -0.8986051 -0.8983009 -0.8979966 -0.8976921 -0.8973874
#> [739] -0.8970827 -0.8967777 -0.8964727 -0.8961675 -0.8958622 -0.8955567
#> [745] -0.8952511 -0.8949454 -0.8946395 -0.8943335 -0.8940274 -0.8937211
#> [751] -0.8934148 -0.8931083 -0.8928016 -0.8924949 -0.8921880 -0.8918810
#> [757] -0.8915739 -0.8912667 -0.8909593 -0.8906519 -0.8903443 -0.8900366
#> [763] -0.8897288 -0.8894209 -0.8891128 -0.8888047 -0.8884964 -0.8881880
#> [769] -0.8878796 -0.8875710 -0.8872623 -0.8869535 -0.8866446 -0.8863356
#> [775] -0.8860265 -0.8857173 -0.8854080 -0.8850986 -0.8847891 -0.8844795
#> [781] -0.8841698 -0.8838600 -0.8835501 -0.8832401 -0.8829301 -0.8826199
#> [787] -0.8823097 -0.8819993 -0.8816889 -0.8813784 -0.8810678 -0.8807571
#> [793] -0.8804463 -0.8801355 -0.8798245 -0.8795135 -0.8792024 -0.8788912
#> [799] -0.8785799 -0.8782686 -0.8779572 -0.8776457 -0.8773341 -0.8770225
#> [805] -0.8767107 -0.8763989 -0.8760871 -0.8757751 -0.8754631 -0.8751511
#> [811] -0.8748389 -0.8745267 -0.8742144 -0.8739021 -0.8735896 -0.8732772
#> [817] -0.8729646 -0.8726520 -0.8723393 -0.8720266 -0.8717138 -0.8714010
#> [823] -0.8710880 -0.8707751 -0.8704621 -0.8701490 -0.8698358 -0.8695226
#> [829] -0.8692094 -0.8688961 -0.8685827 -0.8682693 -0.8679559 -0.8676424
#> [835] -0.8673288 -0.8670152 -0.8667016 -0.8663879 -0.8660741 -0.8657603
#> [841] -0.8654465 -0.8651326 -0.8648187 -0.8645047 -0.8641907 -0.8638767
#> [847] -0.8635626 -0.8632484 -0.8629343 -0.8626201 -0.8623058 -0.8619916
#> [853] -0.8616772 -0.8613629 -0.8610485 -0.8607341 -0.8604196 -0.8601051
#> [859] -0.8597906 -0.8594761 -0.8591615 -0.8588469 -0.8585323 -0.8582176
#> [865] -0.8579029 -0.8575882 -0.8572734 -0.8569587 -0.8566439 -0.8563290
#> [871] -0.8560142 -0.8556993 -0.8553844 -0.8550695 -0.8547546 -0.8544397
#> [877] -0.8541247 -0.8538097 -0.8534947 -0.8531797 -0.8528646 -0.8525496
#> [883] -0.8522345 -0.8519194 -0.8516043 -0.8512892 -0.8509740 -0.8506589
#> [889] -0.8503437 -0.8500286 -0.8497134 -0.8493982 -0.8490830 -0.8487678
#> [895] -0.8484526 -0.8481374 -0.8478222 -0.8475069 -0.8471917 -0.8468764
#> [901] -0.8465612 -0.8462459 -0.8459307 -0.8456154 -0.8453001 -0.8449849
#> [907] -0.8446696 -0.8443543 -0.8440391 -0.8437238 -0.8434085 -0.8430933
#> [913] -0.8427780 -0.8424628 -0.8421475 -0.8418322 -0.8415170 -0.8412018
#> [919] -0.8408865 -0.8405713 -0.8402561 -0.8399408 -0.8396256 -0.8393104
#> [925] -0.8389952 -0.8386801 -0.8383649 -0.8380497 -0.8377346 -0.8374194
#> [931] -0.8371043 -0.8367892 -0.8364741 -0.8361590 -0.8358439 -0.8355288
#> [937] -0.8352138 -0.8348988 -0.8345837 -0.8342687 -0.8339538 -0.8336388
#> [943] -0.8333238 -0.8330089 -0.8326940 -0.8323791 -0.8320642 -0.8317494
#> [949] -0.8314346 -0.8311198 -0.8308050 -0.8304902 -0.8301755 -0.8298607
#> [955] -0.8295460 -0.8292314 -0.8289167 -0.8286021 -0.8282875 -0.8279729
#> [961] -0.8276584 -0.8273439 -0.8270294 -0.8267149 -0.8264005 -0.8260861
#> [967] -0.8257717 -0.8254574 -0.8251431 -0.8248288 -0.8245145 -0.8242003
#> [973] -0.8238861 -0.8235719 -0.8232578 -0.8229437 -0.8226297 -0.8223156
#> [979] -0.8220016 -0.8216877 -0.8213738 -0.8210599 -0.8207460 -0.8204322
#> [985] -0.8201184 -0.8198047 -0.8194910 -0.8191773 -0.8188637 -0.8185501
#> [991] -0.8182366 -0.8179230 -0.8176096 -0.8172961 -0.8169828 -0.8166694
#> [997] -0.8163561 -0.8160428 -0.8157296 -0.8154164 -0.8151033 -0.8147902
#> [1003] -0.8144772 -0.8141642 -0.8138512 -0.8135383 -0.8132254 -0.8129126
#> [1009] -0.8125998 -0.8122871 -0.8119744 -0.8116618 -0.8113492 -0.8110366
#> [1015] -0.8107241 -0.8104117 -0.8100993 -0.8097869 -0.8094746 -0.8091624
#> [1021] -0.8088502 -0.8085380 -0.8082259 -0.8079139 -0.8076019 -0.8072900
#> [1027] -0.8069781 -0.8066662 -0.8063545 -0.8060427 -0.8057311 -0.8054194
#> [1033] -0.8051079 -0.8047963 -0.8044849 -0.8041735 -0.8038621 -0.8035508
#> [1039] -0.8032396 -0.8029284 -0.8026173 -0.8023063 -0.8019952 -0.8016843
#> [1045] -0.8013734 -0.8010626 -0.8007518 -0.8004411 -0.8001304 -0.7998198
#> [1051] -0.7995093 -0.7991988 -0.7988884 -0.7985781 -0.7982678 -0.7979575
#> [1057] -0.7976474 -0.7973373 -0.7970272 -0.7967172 -0.7964073 -0.7960975
#> [1063] -0.7957877 -0.7954779 -0.7951683 -0.7948587 -0.7945491 -0.7942397
#> [1069] -0.7939303 -0.7936209 -0.7933117 -0.7930024 -0.7926933 -0.7923842
#> [1075] -0.7920752 -0.7917663 -0.7914574 -0.7911486 -0.7908399 -0.7905312
#> [1081] -0.7902226 -0.7899141 -0.7896056 -0.7892972 -0.7889889 -0.7886806
#> [1087] -0.7883724 -0.7880643 -0.7877563 -0.7874483 -0.7871404 -0.7868326
#> [1093] -0.7865248 -0.7862171 -0.7859095 -0.7856020 -0.7852945 -0.7849871
#> [1099] -0.7846798 -0.7843725 -0.7840653 -0.7837582 -0.7834512 -0.7831442
#> [1105] -0.7828374 -0.7825305 -0.7822238 -0.7819171 -0.7816106 -0.7813041
#> [1111] -0.7809976 -0.7806913 -0.7803850 -0.7800788 -0.7797727 -0.7794666
#> [1117] -0.7791606 -0.7788547 -0.7785489 -0.7782432 -0.7779375 -0.7776319
#> [1123] -0.7773264 -0.7770210 -0.7767156 -0.7764104 -0.7761052 -0.7758001
#> [1129] -0.7754950 -0.7751901 -0.7748852 -0.7745804 -0.7742757 -0.7739711
#> [1135] -0.7736665 -0.7733621 -0.7730577 -0.7727534 -0.7724492 -0.7721450
#> [1141] -0.7718410 -0.7715370 -0.7712331 -0.7709293 -0.7706255 -0.7703219
#> [1147] -0.7700183 -0.7697148 -0.7694114 -0.7691081 -0.7688049 -0.7685018
#> [1153] -0.7681987 -0.7678957 -0.7675928 -0.7672900 -0.7669873 -0.7666847
#> [1159] -0.7663821 -0.7660797 -0.7657773 -0.7654750 -0.7651728 -0.7648706
#> [1165] -0.7645686 -0.7642667 -0.7639648 -0.7636630 -0.7633613 -0.7630597
#> [1171] -0.7627582 -0.7624568 -0.7621555 -0.7618542 -0.7615530 -0.7612520
#> [1177] -0.7609510 -0.7606501 -0.7603493 -0.7600486 -0.7597479 -0.7594474
#> [1183] -0.7591469 -0.7588466 -0.7585463 -0.7582461 -0.7579460 -0.7576460
#> [1189] -0.7573461 -0.7570463 -0.7567466 -0.7564469 -0.7561474 -0.7558479
#> [1195] -0.7555486 -0.7552493 -0.7549501 -0.7546510 -0.7543520 -0.7540531
#> [1201] -0.7537543 -0.7534555 -0.7531569 -0.7528584 -0.7525599 -0.7522616
#> [1207] -0.7519633 -0.7516651 -0.7513671 -0.7510691 -0.7507712 -0.7504734
#> [1213] -0.7501757 -0.7498781 -0.7495806 -0.7492832 -0.7489858 -0.7486886
#> [1219] -0.7483915 -0.7480944 -0.7477975 -0.7475006 -0.7472039 -0.7469072
#> [1225] -0.7466106 -0.7463142 -0.7460178 -0.7457215 -0.7454253 -0.7451292
#> [1231] -0.7448332 -0.7445373 -0.7442415 -0.7439458 -0.7436502 -0.7433547
#> [1237] -0.7430593 -0.7427640 -0.7424687 -0.7421736 -0.7418786 -0.7415837
#> [1243] -0.7412888 -0.7409941 -0.7406994 -0.7404049 -0.7401105 -0.7398161
#> [1249] -0.7395219 -0.7392277 -0.7389337 -0.7386397 -0.7383459 -0.7380521
#> [1255] -0.7377584 -0.7374649 -0.7371714 -0.7368781 -0.7365848 -0.7362916
#> [1261] -0.7359986 -0.7357056 -0.7354127 -0.7351200 -0.7348273 -0.7345348
#> [1267] -0.7342423 -0.7339499 -0.7336577 -0.7333655 -0.7330734 -0.7327815
#> [1273] -0.7324896 -0.7321978 -0.7319062 -0.7316146 -0.7313231 -0.7310318
#> [1279] -0.7307405 -0.7304493 -0.7301583 -0.7298673 -0.7295765 -0.7292857
#> [1285] -0.7289951 -0.7287045 -0.7284141 -0.7281237 -0.7278335 -0.7275433
#> [1291] -0.7272533 -0.7269633 -0.7266735 -0.7263837 -0.7260941 -0.7258046
#> [1297] -0.7255151 -0.7252258 -0.7249366 -0.7246475 -0.7243584 -0.7240695
#> [1303] -0.7237807 -0.7234920 -0.7232034 -0.7229149 -0.7226265 -0.7223382
#> [1309] -0.7220500 -0.7217619 -0.7214739 -0.7211860 -0.7208982 -0.7206106
#> [1315] -0.7203230 -0.7200355 -0.7197481 -0.7194609 -0.7191737 -0.7188867
#> [1321] -0.7185997 -0.7183129 -0.7180261 -0.7177395 -0.7174530 -0.7171665
#> [1327] -0.7168802 -0.7165940 -0.7163079 -0.7160219 -0.7157359 -0.7154501
#> [1333] -0.7151644 -0.7148789 -0.7145934 -0.7143080 -0.7140227 -0.7137375
#> [1339] -0.7134525 -0.7131675 -0.7128827 -0.7125979 -0.7123133 -0.7120287
#> [1345] -0.7117443 -0.7114600 -0.7111757 -0.7108916 -0.7106076 -0.7103237
#> [1351] -0.7100399 -0.7097562 -0.7094726 -0.7091892 -0.7089058 -0.7086225
#> [1357] -0.7083394 -0.7080563 -0.7077733 -0.7074905 -0.7072078 -0.7069251
#> [1363] -0.7066426 -0.7063602 -0.7060779 -0.7057957 -0.7055136 -0.7052316
#> [1369] -0.7049497 -0.7046679 -0.7043863 -0.7041047 -0.7038233 -0.7035419
#> [1375] -0.7032607 -0.7029795 -0.7026985 -0.7024176 -0.7021368 -0.7018561
#> [1381] -0.7015755 -0.7012950 -0.7010146 -0.7007343 -0.7004541 -0.7001741
#> [1387] -0.6998941 -0.6996143 -0.6993346 -0.6990549 -0.6987754 -0.6984960
#> [1393] -0.6982167 -0.6979375 -0.6976584 -0.6973794 -0.6971005 -0.6968218
#> [1399] -0.6965431 -0.6962645 -0.6959861 -0.6957078 -0.6954295 -0.6951514
#> [1405] -0.6948734 -0.6945955 -0.6943177 -0.6940400 -0.6937624 -0.6934850
#> [1411] -0.6932076 -0.6929304 -0.6926532 -0.6923762 -0.6920993 -0.6918224
#> [1417] -0.6915457 -0.6912691 -0.6909926 -0.6907162 -0.6904400 -0.6901638
#> [1423] -0.6898877 -0.6896118 -0.6893360 -0.6890602 -0.6887846 -0.6885091
#> [1429] -0.6882337 -0.6879584 -0.6876832 -0.6874081 -0.6871331 -0.6868583
#> [1435] -0.6865835 -0.6863089 -0.6860343 -0.6857599 -0.6854856 -0.6852114
#> [1441] -0.6849373 -0.6846633 -0.6843894 -0.6841157 -0.6838420 -0.6835684
#> [1447] -0.6832950 -0.6830217 -0.6827484 -0.6824753 -0.6822023 -0.6819294
#> [1453] -0.6816566 -0.6813840 -0.6811114 -0.6808389 -0.6805666 -0.6802944
#> [1459] -0.6800222 -0.6797502 -0.6794783 -0.6792065 -0.6789348 -0.6786632
#> [1465] -0.6783917 -0.6781204 -0.6778491 -0.6775780 -0.6773069 -0.6770360
#> [1471] -0.6767652 -0.6764945 -0.6762239 -0.6759534 -0.6756830 -0.6754128
#> [1477] -0.6751426 -0.6748725 -0.6746026 -0.6743328 -0.6740631 -0.6737935
#> [1483] -0.6735240 -0.6732546 -0.6729853 -0.6727161 -0.6724470 -0.6721781
#> [1489] -0.6719093 -0.6716405 -0.6713719 -0.6711034 -0.6708350 -0.6705667
#> [1495] -0.6702985 -0.6700304 -0.6697625 -0.6694946 -0.6692269 -0.6689592
#> [1501] -0.6686917 -0.6684243 -0.6681570 -0.6678898 -0.6676227 -0.6673557
#> [1507] -0.6670889 -0.6668221 -0.6665555 -0.6662889 -0.6660225 -0.6657562
#> [1513] -0.6654900 -0.6652239 -0.6649579 -0.6646920 -0.6644263 -0.6641606
#> [1519] -0.6638951 -0.6636296 -0.6633643 -0.6630991 -0.6628340 -0.6625690
#> [1525] -0.6623041 -0.6620393 -0.6617747 -0.6615101 -0.6612456 -0.6609813
#> [1531] -0.6607171 -0.6604530 -0.6601890 -0.6599251 -0.6596613 -0.6593976
#> [1537] -0.6591340 -0.6588706 -0.6586072 -0.6583440 -0.6580808 -0.6578178
#> [1543] -0.6575549 -0.6572921 -0.6570294 -0.6567668 -0.6565044 -0.6562420
#> [1549] -0.6559798 -0.6557176 -0.6554556 -0.6551937 -0.6549319 -0.6546702
#> [1555] -0.6544086 -0.6541471 -0.6538857 -0.6536245 -0.6533633 -0.6531023
#> [1561] -0.6528413 -0.6525805 -0.6523198 -0.6520592 -0.6517987 -0.6515383
#> [1567] -0.6512780 -0.6510179 -0.6507578 -0.6504979 -0.6502380 -0.6499783
#> [1573] -0.6497187 -0.6494592 -0.6491998 -0.6489405 -0.6486813 -0.6484222
#> [1579] -0.6481633 -0.6479044 -0.6476457 -0.6473870 -0.6471285 -0.6468701
#> [1585] -0.6466118 -0.6463536 -0.6460955 -0.6458376 -0.6455797 -0.6453219
#> [1591] -0.6450643 -0.6448067 -0.6445493 -0.6442920 -0.6440348 -0.6437777
#> [1597] -0.6435207 -0.6432638 -0.6430071 -0.6427504 -0.6424938 -0.6422374
#> [1603] -0.6419811 -0.6417248 -0.6414687 -0.6412127 -0.6409568 -0.6407010
#> [1609] -0.6404453 -0.6401898 -0.6399343 -0.6396790 -0.6394237 -0.6391686
#> [1615] -0.6389136 -0.6386586 -0.6384038 -0.6381491 -0.6378945 -0.6376401
#> [1621] -0.6373857 -0.6371314 -0.6368773 -0.6366232 -0.6363693 -0.6361155
#> [1627] -0.6358618 -0.6356081 -0.6353546 -0.6351013 -0.6348480 -0.6345948
#> [1633] -0.6343417 -0.6340888 -0.6338359 -0.6335832 -0.6333306 -0.6330780
#> [1639] -0.6328256 -0.6325733 -0.6323211 -0.6320690 -0.6318171 -0.6315652
#> [1645] -0.6313134 -0.6310618 -0.6308102 -0.6305588 -0.6303075 -0.6300562
#> [1651] -0.6298051 -0.6295541 -0.6293032 -0.6290524 -0.6288018 -0.6285512
#> [1657] -0.6283007 -0.6280504 -0.6278001 -0.6275500 -0.6273000 -0.6270500
#> [1663] -0.6268002 -0.6265505 -0.6263009 -0.6260514 -0.6258021 -0.6255528
#> [1669] -0.6253036 -0.6250546 -0.6248056 -0.6245568 -0.6243080 -0.6240594
#> [1675] -0.6238109 -0.6235625 -0.6233142 -0.6230660 -0.6228179 -0.6225699
#> [1681] -0.6223221 -0.6220743 -0.6218266 -0.6215791 -0.6213317 -0.6210843
#> [1687] -0.6208371 -0.6205900 -0.6203430 -0.6200961 -0.6198493 -0.6196026
#> [1693] -0.6193560 -0.6191095 -0.6188632 -0.6186169 -0.6183708 -0.6181247
#> [1699] -0.6178788 -0.6176329 -0.6173872 -0.6171416 -0.6168961 -0.6166507
#> [1705] -0.6164054 -0.6161602 -0.6159151 -0.6156702 -0.6154253 -0.6151805
#> [1711] -0.6149359 -0.6146913 -0.6144469 -0.6142026 -0.6139583 -0.6137142
#> [1717] -0.6134702 -0.6132263 -0.6129825 -0.6127388 -0.6124952 -0.6122517
#> [1723] -0.6120084 -0.6117651 -0.6115219 -0.6112789 -0.6110359 -0.6107931
#> [1729] -0.6105504 -0.6103077 -0.6100652 -0.6098228 -0.6095805 -0.6093383
#> [1735] -0.6090962 -0.6088542 -0.6086123 -0.6083706 -0.6081289 -0.6078873
#> [1741] -0.6076459 -0.6074045 -0.6071633 -0.6069221 -0.6066811 -0.6064401
#> [1747] -0.6061993 -0.6059586 -0.6057180 -0.6054775 -0.6052371 -0.6049968
#> [1753] -0.6047566 -0.6045165 -0.6042765 -0.6040367 -0.6037969 -0.6035572
#> [1759] -0.6033177 -0.6030782 -0.6028389 -0.6025996 -0.6023605 -0.6021215
#> [1765] -0.6018826 -0.6016437 -0.6014050 -0.6011664 -0.6009279 -0.6006895
#> [1771] -0.6004512 -0.6002130 -0.5999749 -0.5997370 -0.5994991 -0.5992613
#> [1777] -0.5990237 -0.5987861 -0.5985486 -0.5983113 -0.5980741 -0.5978369
#> [1783] -0.5975999 -0.5973629 -0.5971261 -0.5968894 -0.5966528 -0.5964163
#> [1789] -0.5961799 -0.5959436 -0.5957074 -0.5954713 -0.5952353 -0.5949994
#> [1795] -0.5947636 -0.5945279 -0.5942924 -0.5940569 -0.5938215 -0.5935863
#> [1801] -0.5933511 -0.5931161 -0.5928811 -0.5926463 -0.5924115 -0.5921769
#> [1807] -0.5919423 -0.5917079 -0.5914736 -0.5912394 -0.5910053 -0.5907712
#> [1813] -0.5905373 -0.5903035 -0.5900698 -0.5898362 -0.5896027 -0.5893693
#> [1819] -0.5891360 -0.5889029 -0.5886698 -0.5884368 -0.5882039 -0.5879711
#> [1825] -0.5877385 -0.5875059 -0.5872734 -0.5870411 -0.5868088 -0.5865767
#> [1831] -0.5863446 -0.5861127 -0.5858808 -0.5856491 -0.5854174 -0.5851859
#> [1837] -0.5849545 -0.5847231 -0.5844919 -0.5842608 -0.5840298 -0.5837989
#> [1843] -0.5835680 -0.5833373 -0.5831067 -0.5828762 -0.5826458 -0.5824155
#> [1849] -0.5821853 -0.5819552 -0.5817252 -0.5814953 -0.5812655 -0.5810358
#> [1855] -0.5808062 -0.5805767 -0.5803473 -0.5801181 -0.5798889 -0.5796598
#> [1861] -0.5794308 -0.5792019 -0.5789732 -0.5787445 -0.5785159 -0.5782875
#> [1867] -0.5780591 -0.5778308 -0.5776027 -0.5773746 -0.5771466 -0.5769188
#> [1873] -0.5766910 -0.5764634 -0.5762358 -0.5760084 -0.5757810 -0.5755538
#> [1879] -0.5753266 -0.5750996 -0.5748726 -0.5746458 -0.5744190 -0.5741924
#> [1885] -0.5739658 -0.5737394 -0.5735131 -0.5732868 -0.5730607 -0.5728346
#> [1891] -0.5726087 -0.5723829 -0.5721571 -0.5719315 -0.5717060 -0.5714805
#> [1897] -0.5712552 -0.5710300 -0.5708048 -0.5705798 -0.5703549 -0.5701300
#> [1903] -0.5699053 -0.5696807 -0.5694561 -0.5692317 -0.5690074 -0.5687831
#> [1909] -0.5685590 -0.5683350 -0.5681111 -0.5678872 -0.5676635 -0.5674399
#> [1915] -0.5672163 -0.5669929 -0.5667696 -0.5665463 -0.5663232 -0.5661002
#> [1921] -0.5658772 -0.5656544 -0.5654317 -0.5652090 -0.5649865 -0.5647641
#> [1927] -0.5645417 -0.5643195 -0.5640974 -0.5638753 -0.5636534 -0.5634316
#> [1933] -0.5632098 -0.5629882 -0.5627666 -0.5625452 -0.5623238 -0.5621026
#> [1939] -0.5618815 -0.5616604 -0.5614395 -0.5612186 -0.5609979 -0.5607772
#> [1945] -0.5605567 -0.5603362 -0.5601158 -0.5598956 -0.5596754 -0.5594554
#> [1951] -0.5592354 -0.5590155 -0.5587958 -0.5585761 -0.5583565 -0.5581371
#> [1957] -0.5579177 -0.5576984 -0.5574792 -0.5572602 -0.5570412 -0.5568223
#> [1963] -0.5566035 -0.5563848 -0.5561662 -0.5559478 -0.5557294 -0.5555111
#> [1969] -0.5552929 -0.5550748 -0.5548568 -0.5546389 -0.5544210 -0.5542033
#> [1975] -0.5539857 -0.5537682 -0.5535508 -0.5533335 -0.5531163 -0.5528991
#> [1981] -0.5526821 -0.5524652 -0.5522483 -0.5520316 -0.5518150 -0.5515984
#> [1987] -0.5513820 -0.5511656 -0.5509494 -0.5507332 -0.5505171 -0.5503012
#> [1993] -0.5500853 -0.5498695 -0.5496539 -0.5494383 -0.5492228 -0.5490074
#> [1999] -0.5487922 -0.5485770 -0.5483619
bsmvega(c("call", "put"), c(50, 49, 48, 47), 45, 0.25, 0.13, 0.01, 0.2)
#> [1] 3.715018 4.736695 5.819530 6.872763
bsmvega("call", 50, 45, 0.25, 0.13, 0.01, 1:1000 / 1000)
#> [1] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [6] 0.000000e+00 0.000000e+00 2.001097e-248 3.094994e-196 6.628640e-159
#> [11] 2.766740e-131 2.816159e-110 6.288958e-94 5.901296e-81 1.723425e-70
#> [16] 6.332747e-62 7.947308e-55 7.062187e-49 7.644338e-44 1.519251e-39
#> [21] 7.596656e-36 1.221137e-32 7.653768e-30 2.181149e-27 3.197801e-25
#> [26] 2.666333e-23 1.372475e-21 4.666650e-20 1.108722e-18 1.929146e-17
#> [31] 2.557419e-16 2.670935e-15 2.261059e-14 1.589713e-13 9.479102e-13
#> [36] 4.880864e-12 2.204458e-11 8.853092e-11 3.199194e-10 1.051152e-09
#> [41] 3.169212e-09 8.839171e-09 2.296973e-08 5.596865e-08 1.285983e-07
#> [46] 2.800401e-07 5.805799e-07 1.150589e-06 2.187649e-06 4.003681e-06
#> [51] 7.073801e-06 1.209825e-05 2.007819e-05 3.240540e-05 5.096524e-05
#> [56] 7.825098e-05 1.174873e-04 1.727592e-04 2.491435e-04 3.528368e-04
#> [61] 4.912773e-04 6.732556e-04 9.090089e-04 1.210297e-03 1.590458e-03
#> [66] 2.064434e-03 2.648776e-03 3.361625e-03 4.222655e-03 5.253005e-03
#> [71] 6.475177e-03 7.912917e-03 9.591072e-03 1.153544e-02 1.377260e-02
#> [76] 1.632972e-02 1.923439e-02 2.251444e-02 2.619771e-02 3.031191e-02
#> [81] 3.488441e-02 3.994208e-02 4.551110e-02 5.161685e-02 5.828372e-02
#> [86] 6.553499e-02 7.339276e-02 8.187778e-02 9.100940e-02 1.008055e-01
#> [91] 1.112824e-01 1.224548e-01 1.343359e-01 1.469371e-01 1.602683e-01
#> [96] 1.743377e-01 1.891517e-01 2.047154e-01 2.210321e-01 2.381036e-01
#> [101] 2.559302e-01 2.745107e-01 2.938425e-01 3.139218e-01 3.347433e-01
#> [106] 3.563006e-01 3.785862e-01 4.015913e-01 4.253064e-01 4.497208e-01
#> [111] 4.748229e-01 5.006004e-01 5.270403e-01 5.541288e-01 5.818515e-01
#> [116] 6.101934e-01 6.391391e-01 6.686727e-01 6.987780e-01 7.294384e-01
#> [121] 7.606370e-01 7.923566e-01 8.245801e-01 8.572900e-01 8.904687e-01
#> [126] 9.240988e-01 9.581627e-01 9.926427e-01 1.027521e+00 1.062781e+00
#> [131] 1.098405e+00 1.134376e+00 1.170676e+00 1.207289e+00 1.244198e+00
#> [136] 1.281387e+00 1.318840e+00 1.356540e+00 1.394471e+00 1.432620e+00
#> [141] 1.470970e+00 1.509506e+00 1.548214e+00 1.587080e+00 1.626089e+00
#> [146] 1.665229e+00 1.704486e+00 1.743846e+00 1.783298e+00 1.822830e+00
#> [151] 1.862428e+00 1.902081e+00 1.941779e+00 1.981510e+00 2.021263e+00
#> [156] 2.061029e+00 2.100796e+00 2.140556e+00 2.180299e+00 2.220015e+00
#> [161] 2.259697e+00 2.299335e+00 2.338922e+00 2.378449e+00 2.417909e+00
#> [166] 2.457294e+00 2.496597e+00 2.535813e+00 2.574933e+00 2.613951e+00
#> [171] 2.652862e+00 2.691661e+00 2.730340e+00 2.768895e+00 2.807321e+00
#> [176] 2.845613e+00 2.883766e+00 2.921775e+00 2.959637e+00 2.997348e+00
#> [181] 3.034903e+00 3.072299e+00 3.109533e+00 3.146600e+00 3.183499e+00
#> [186] 3.220225e+00 3.256776e+00 3.293150e+00 3.329344e+00 3.365356e+00
#> [191] 3.401183e+00 3.436823e+00 3.472275e+00 3.507536e+00 3.542605e+00
#> [196] 3.577480e+00 3.612161e+00 3.646645e+00 3.680931e+00 3.715018e+00
#> [201] 3.748906e+00 3.782593e+00 3.816078e+00 3.849361e+00 3.882442e+00
#> [206] 3.915319e+00 3.947991e+00 3.980460e+00 4.012724e+00 4.044783e+00
#> [211] 4.076637e+00 4.108286e+00 4.139730e+00 4.170968e+00 4.202002e+00
#> [216] 4.232830e+00 4.263454e+00 4.293873e+00 4.324088e+00 4.354099e+00
#> [221] 4.383907e+00 4.413511e+00 4.442913e+00 4.472113e+00 4.501112e+00
#> [226] 4.529909e+00 4.558506e+00 4.586904e+00 4.615103e+00 4.643103e+00
#> [231] 4.670906e+00 4.698513e+00 4.725924e+00 4.753139e+00 4.780161e+00
#> [236] 4.806989e+00 4.833625e+00 4.860070e+00 4.886324e+00 4.912388e+00
#> [241] 4.938264e+00 4.963952e+00 4.989454e+00 5.014770e+00 5.039902e+00
#> [246] 5.064850e+00 5.089616e+00 5.114201e+00 5.138605e+00 5.162830e+00
#> [251] 5.186877e+00 5.210747e+00 5.234441e+00 5.257961e+00 5.281306e+00
#> [256] 5.304479e+00 5.327481e+00 5.350313e+00 5.372975e+00 5.395470e+00
#> [261] 5.417797e+00 5.439959e+00 5.461956e+00 5.483790e+00 5.505462e+00
#> [266] 5.526972e+00 5.548323e+00 5.569515e+00 5.590548e+00 5.611426e+00
#> [271] 5.632148e+00 5.652716e+00 5.673130e+00 5.693393e+00 5.713505e+00
#> [276] 5.733466e+00 5.753280e+00 5.772946e+00 5.792465e+00 5.811839e+00
#> [281] 5.831069e+00 5.850156e+00 5.869101e+00 5.887906e+00 5.906570e+00
#> [286] 5.925096e+00 5.943484e+00 5.961736e+00 5.979852e+00 5.997834e+00
#> [291] 6.015682e+00 6.033399e+00 6.050984e+00 6.068439e+00 6.085764e+00
#> [296] 6.102962e+00 6.120032e+00 6.136977e+00 6.153796e+00 6.170492e+00
#> [301] 6.187064e+00 6.203515e+00 6.219844e+00 6.236053e+00 6.252143e+00
#> [306] 6.268115e+00 6.283970e+00 6.299708e+00 6.315332e+00 6.330841e+00
#> [311] 6.346236e+00 6.361519e+00 6.376691e+00 6.391751e+00 6.406702e+00
#> [316] 6.421545e+00 6.436279e+00 6.450906e+00 6.465427e+00 6.479843e+00
#> [321] 6.494155e+00 6.508362e+00 6.522467e+00 6.536470e+00 6.550373e+00
#> [326] 6.564174e+00 6.577877e+00 6.591481e+00 6.604987e+00 6.618396e+00
#> [331] 6.631709e+00 6.644927e+00 6.658050e+00 6.671080e+00 6.684016e+00
#> [336] 6.696860e+00 6.709613e+00 6.722275e+00 6.734847e+00 6.747329e+00
#> [341] 6.759724e+00 6.772030e+00 6.784249e+00 6.796382e+00 6.808430e+00
#> [346] 6.820392e+00 6.832270e+00 6.844065e+00 6.855777e+00 6.867407e+00
#> [351] 6.878955e+00 6.890422e+00 6.901809e+00 6.913117e+00 6.924346e+00
#> [356] 6.935497e+00 6.946570e+00 6.957566e+00 6.968486e+00 6.979330e+00
#> [361] 6.990099e+00 7.000793e+00 7.011414e+00 7.021962e+00 7.032436e+00
#> [366] 7.042839e+00 7.053171e+00 7.063431e+00 7.073621e+00 7.083741e+00
#> [371] 7.093793e+00 7.103775e+00 7.113690e+00 7.123537e+00 7.133317e+00
#> [376] 7.143030e+00 7.152678e+00 7.162260e+00 7.171777e+00 7.181230e+00
#> [381] 7.190620e+00 7.199946e+00 7.209209e+00 7.218410e+00 7.227549e+00
#> [386] 7.236626e+00 7.245643e+00 7.254600e+00 7.263497e+00 7.272334e+00
#> [391] 7.281113e+00 7.289833e+00 7.298495e+00 7.307099e+00 7.315647e+00
#> [396] 7.324138e+00 7.332572e+00 7.340951e+00 7.349275e+00 7.357544e+00
#> [401] 7.365758e+00 7.373919e+00 7.382026e+00 7.390079e+00 7.398080e+00
#> [406] 7.406029e+00 7.413926e+00 7.421771e+00 7.429565e+00 7.437309e+00
#> [411] 7.445002e+00 7.452645e+00 7.460238e+00 7.467783e+00 7.475278e+00
#> [416] 7.482726e+00 7.490125e+00 7.497476e+00 7.504781e+00 7.512038e+00
#> [421] 7.519249e+00 7.526413e+00 7.533532e+00 7.540605e+00 7.547633e+00
#> [426] 7.554616e+00 7.561554e+00 7.568449e+00 7.575299e+00 7.582106e+00
#> [431] 7.588870e+00 7.595591e+00 7.602270e+00 7.608906e+00 7.615501e+00
#> [436] 7.622054e+00 7.628565e+00 7.635036e+00 7.641466e+00 7.647856e+00
#> [441] 7.654206e+00 7.660516e+00 7.666786e+00 7.673017e+00 7.679210e+00
#> [446] 7.685364e+00 7.691480e+00 7.697557e+00 7.703597e+00 7.709600e+00
#> [451] 7.715565e+00 7.721493e+00 7.727385e+00 7.733240e+00 7.739060e+00
#> [456] 7.744843e+00 7.750591e+00 7.756304e+00 7.761981e+00 7.767624e+00
#> [461] 7.773232e+00 7.778806e+00 7.784346e+00 7.789851e+00 7.795324e+00
#> [466] 7.800763e+00 7.806169e+00 7.811542e+00 7.816882e+00 7.822191e+00
#> [471] 7.827467e+00 7.832711e+00 7.837923e+00 7.843104e+00 7.848253e+00
#> [476] 7.853372e+00 7.858460e+00 7.863517e+00 7.868544e+00 7.873540e+00
#> [481] 7.878507e+00 7.883444e+00 7.888351e+00 7.893230e+00 7.898078e+00
#> [486] 7.902899e+00 7.907690e+00 7.912453e+00 7.917187e+00 7.921894e+00
#> [491] 7.926572e+00 7.931223e+00 7.935846e+00 7.940442e+00 7.945010e+00
#> [496] 7.949552e+00 7.954067e+00 7.958555e+00 7.963017e+00 7.967452e+00
#> [501] 7.971862e+00 7.976245e+00 7.980603e+00 7.984936e+00 7.989242e+00
#> [506] 7.993524e+00 7.997781e+00 8.002013e+00 8.006220e+00 8.010403e+00
#> [511] 8.014561e+00 8.018695e+00 8.022805e+00 8.026891e+00 8.030954e+00
#> [516] 8.034992e+00 8.039008e+00 8.043000e+00 8.046969e+00 8.050916e+00
#> [521] 8.054839e+00 8.058740e+00 8.062618e+00 8.066474e+00 8.070308e+00
#> [526] 8.074119e+00 8.077909e+00 8.081677e+00 8.085423e+00 8.089148e+00
#> [531] 8.092852e+00 8.096534e+00 8.100196e+00 8.103836e+00 8.107455e+00
#> [536] 8.111054e+00 8.114633e+00 8.118191e+00 8.121729e+00 8.125246e+00
#> [541] 8.128744e+00 8.132221e+00 8.135679e+00 8.139118e+00 8.142537e+00
#> [546] 8.145936e+00 8.149316e+00 8.152677e+00 8.156020e+00 8.159343e+00
#> [551] 8.162647e+00 8.165933e+00 8.169200e+00 8.172449e+00 8.175680e+00
#> [556] 8.178892e+00 8.182086e+00 8.185262e+00 8.188421e+00 8.191562e+00
#> [561] 8.194685e+00 8.197790e+00 8.200878e+00 8.203949e+00 8.207003e+00
#> [566] 8.210039e+00 8.213059e+00 8.216062e+00 8.219048e+00 8.222017e+00
#> [571] 8.224970e+00 8.227906e+00 8.230826e+00 8.233729e+00 8.236617e+00
#> [576] 8.239488e+00 8.242343e+00 8.245183e+00 8.248006e+00 8.250814e+00
#> [581] 8.253607e+00 8.256384e+00 8.259145e+00 8.261891e+00 8.264622e+00
#> [586] 8.267338e+00 8.270039e+00 8.272724e+00 8.275395e+00 8.278051e+00
#> [591] 8.280693e+00 8.283320e+00 8.285932e+00 8.288530e+00 8.291114e+00
#> [596] 8.293683e+00 8.296238e+00 8.298779e+00 8.301306e+00 8.303819e+00
#> [601] 8.306318e+00 8.308804e+00 8.311276e+00 8.313734e+00 8.316178e+00
#> [606] 8.318609e+00 8.321027e+00 8.323432e+00 8.325823e+00 8.328201e+00
#> [611] 8.330566e+00 8.332918e+00 8.335257e+00 8.337584e+00 8.339897e+00
#> [616] 8.342198e+00 8.344486e+00 8.346762e+00 8.349025e+00 8.351276e+00
#> [621] 8.353514e+00 8.355740e+00 8.357954e+00 8.360156e+00 8.362346e+00
#> [626] 8.364523e+00 8.366689e+00 8.368843e+00 8.370985e+00 8.373115e+00
#> [631] 8.375234e+00 8.377341e+00 8.379437e+00 8.381521e+00 8.383593e+00
#> [636] 8.385655e+00 8.387705e+00 8.389743e+00 8.391771e+00 8.393788e+00
#> [641] 8.395793e+00 8.397787e+00 8.399771e+00 8.401744e+00 8.403706e+00
#> [646] 8.405657e+00 8.407597e+00 8.409527e+00 8.411446e+00 8.413355e+00
#> [651] 8.415253e+00 8.417141e+00 8.419019e+00 8.420886e+00 8.422743e+00
#> [656] 8.424590e+00 8.426426e+00 8.428253e+00 8.430070e+00 8.431876e+00
#> [661] 8.433673e+00 8.435460e+00 8.437237e+00 8.439004e+00 8.440762e+00
#> [666] 8.442510e+00 8.444248e+00 8.445977e+00 8.447696e+00 8.449406e+00
#> [671] 8.451107e+00 8.452798e+00 8.454479e+00 8.456152e+00 8.457815e+00
#> [676] 8.459469e+00 8.461115e+00 8.462750e+00 8.464377e+00 8.465995e+00
#> [681] 8.467604e+00 8.469205e+00 8.470796e+00 8.472378e+00 8.473952e+00
#> [686] 8.475517e+00 8.477074e+00 8.478622e+00 8.480161e+00 8.481692e+00
#> [691] 8.483214e+00 8.484728e+00 8.486233e+00 8.487730e+00 8.489219e+00
#> [696] 8.490699e+00 8.492172e+00 8.493636e+00 8.495092e+00 8.496539e+00
#> [701] 8.497979e+00 8.499411e+00 8.500835e+00 8.502250e+00 8.503658e+00
#> [706] 8.505058e+00 8.506450e+00 8.507835e+00 8.509211e+00 8.510580e+00
#> [711] 8.511941e+00 8.513295e+00 8.514641e+00 8.515979e+00 8.517310e+00
#> [716] 8.518634e+00 8.519950e+00 8.521258e+00 8.522559e+00 8.523853e+00
#> [721] 8.525140e+00 8.526419e+00 8.527691e+00 8.528956e+00 8.530213e+00
#> [726] 8.531464e+00 8.532707e+00 8.533943e+00 8.535173e+00 8.536395e+00
#> [731] 8.537610e+00 8.538819e+00 8.540020e+00 8.541215e+00 8.542402e+00
#> [736] 8.543583e+00 8.544757e+00 8.545925e+00 8.547086e+00 8.548240e+00
#> [741] 8.549387e+00 8.550528e+00 8.551662e+00 8.552790e+00 8.553911e+00
#> [746] 8.555025e+00 8.556133e+00 8.557235e+00 8.558330e+00 8.559419e+00
#> [751] 8.560502e+00 8.561578e+00 8.562648e+00 8.563712e+00 8.564769e+00
#> [756] 8.565821e+00 8.566866e+00 8.567905e+00 8.568938e+00 8.569964e+00
#> [761] 8.570985e+00 8.572000e+00 8.573008e+00 8.574011e+00 8.575008e+00
#> [766] 8.575999e+00 8.576984e+00 8.577963e+00 8.578936e+00 8.579903e+00
#> [771] 8.580865e+00 8.581821e+00 8.582771e+00 8.583715e+00 8.584654e+00
#> [776] 8.585587e+00 8.586514e+00 8.587436e+00 8.588352e+00 8.589263e+00
#> [781] 8.590168e+00 8.591067e+00 8.591961e+00 8.592850e+00 8.593733e+00
#> [786] 8.594610e+00 8.595483e+00 8.596350e+00 8.597211e+00 8.598067e+00
#> [791] 8.598918e+00 8.599764e+00 8.600604e+00 8.601439e+00 8.602269e+00
#> [796] 8.603094e+00 8.603914e+00 8.604728e+00 8.605537e+00 8.606342e+00
#> [801] 8.607141e+00 8.607935e+00 8.608724e+00 8.609508e+00 8.610287e+00
#> [806] 8.611061e+00 8.611830e+00 8.612594e+00 8.613353e+00 8.614107e+00
#> [811] 8.614857e+00 8.615601e+00 8.616341e+00 8.617076e+00 8.617806e+00
#> [816] 8.618531e+00 8.619252e+00 8.619968e+00 8.620679e+00 8.621386e+00
#> [821] 8.622087e+00 8.622785e+00 8.623477e+00 8.624165e+00 8.624848e+00
#> [826] 8.625527e+00 8.626201e+00 8.626871e+00 8.627536e+00 8.628196e+00
#> [831] 8.628853e+00 8.629504e+00 8.630151e+00 8.630794e+00 8.631433e+00
#> [836] 8.632066e+00 8.632696e+00 8.633321e+00 8.633942e+00 8.634559e+00
#> [841] 8.635171e+00 8.635779e+00 8.636382e+00 8.636982e+00 8.637577e+00
#> [846] 8.638168e+00 8.638755e+00 8.639337e+00 8.639916e+00 8.640490e+00
#> [851] 8.641060e+00 8.641626e+00 8.642188e+00 8.642745e+00 8.643299e+00
#> [856] 8.643849e+00 8.644394e+00 8.644936e+00 8.645473e+00 8.646007e+00
#> [861] 8.646536e+00 8.647062e+00 8.647583e+00 8.648101e+00 8.648615e+00
#> [866] 8.649125e+00 8.649631e+00 8.650133e+00 8.650631e+00 8.651125e+00
#> [871] 8.651616e+00 8.652103e+00 8.652585e+00 8.653065e+00 8.653540e+00
#> [876] 8.654011e+00 8.654479e+00 8.654943e+00 8.655404e+00 8.655861e+00
#> [881] 8.656314e+00 8.656763e+00 8.657208e+00 8.657650e+00 8.658089e+00
#> [886] 8.658524e+00 8.658955e+00 8.659382e+00 8.659806e+00 8.660227e+00
#> [891] 8.660643e+00 8.661057e+00 8.661466e+00 8.661873e+00 8.662275e+00
#> [896] 8.662675e+00 8.663070e+00 8.663463e+00 8.663852e+00 8.664237e+00
#> [901] 8.664619e+00 8.664998e+00 8.665373e+00 8.665745e+00 8.666113e+00
#> [906] 8.666478e+00 8.666840e+00 8.667198e+00 8.667553e+00 8.667905e+00
#> [911] 8.668253e+00 8.668598e+00 8.668940e+00 8.669278e+00 8.669614e+00
#> [916] 8.669946e+00 8.670274e+00 8.670600e+00 8.670922e+00 8.671241e+00
#> [921] 8.671557e+00 8.671870e+00 8.672180e+00 8.672486e+00 8.672790e+00
#> [926] 8.673090e+00 8.673387e+00 8.673681e+00 8.673971e+00 8.674259e+00
#> [931] 8.674544e+00 8.674825e+00 8.675104e+00 8.675379e+00 8.675652e+00
#> [936] 8.675921e+00 8.676187e+00 8.676451e+00 8.676711e+00 8.676969e+00
#> [941] 8.677223e+00 8.677474e+00 8.677723e+00 8.677968e+00 8.678211e+00
#> [946] 8.678451e+00 8.678687e+00 8.678921e+00 8.679152e+00 8.679380e+00
#> [951] 8.679605e+00 8.679827e+00 8.680047e+00 8.680263e+00 8.680477e+00
#> [956] 8.680688e+00 8.680896e+00 8.681101e+00 8.681304e+00 8.681504e+00
#> [961] 8.681700e+00 8.681895e+00 8.682086e+00 8.682274e+00 8.682460e+00
#> [966] 8.682643e+00 8.682824e+00 8.683001e+00 8.683176e+00 8.683348e+00
#> [971] 8.683518e+00 8.683685e+00 8.683849e+00 8.684010e+00 8.684169e+00
#> [976] 8.684325e+00 8.684479e+00 8.684630e+00 8.684778e+00 8.684924e+00
#> [981] 8.685067e+00 8.685207e+00 8.685345e+00 8.685480e+00 8.685613e+00
#> [986] 8.685743e+00 8.685871e+00 8.685996e+00 8.686118e+00 8.686238e+00
#> [991] 8.686355e+00 8.686470e+00 8.686583e+00 8.686692e+00 8.686800e+00
#> [996] 8.686905e+00 8.687007e+00 8.687107e+00 8.687204e+00 8.687299e+00
bsmvega("put", 20, 30, 0:2000 / 1000, 0.15, 0, 0.25)
#> [1] 0.000000e+00 0.000000e+00 2.933904e-286 5.673607e-191 2.602887e-143
#> [6] 1.055215e-114 1.266233e-95 5.440716e-82 9.212451e-72 8.376144e-64
#> [11] 1.960533e-57 3.203324e-52 7.105338e-48 3.391031e-44 4.838619e-41
#> [16] 2.627517e-38 6.507404e-36 8.441598e-34 6.387916e-32 3.069972e-30
#> [21] 1.002980e-28 2.353701e-27 4.150331e-26 5.707644e-25 6.314669e-24
#> [26] 5.768802e-23 4.448805e-22 2.951119e-21 1.711249e-20 8.795410e-20
#> [31] 4.055504e-19 1.695254e-18 6.483536e-18 2.287074e-17 7.494305e-17
#> [36] 2.295642e-16 6.610485e-16 1.798419e-15 4.643228e-15 1.142261e-14
#> [41] 2.687181e-14 6.065014e-14 1.317202e-13 2.760082e-13 5.593683e-13
#> [46] 1.098864e-12 2.096718e-12 3.893063e-12 7.045900e-12 1.244953e-11
#> [51] 2.150626e-11 3.637034e-11 6.028802e-11 9.806335e-11 1.566856e-10
#> [56] 2.461612e-10 3.806008e-10 5.796201e-10 8.701215e-10 1.288531e-09
#> [61] 1.883579e-09 2.719707e-09 3.881215e-09 5.477246e-09 7.647724e-09
#> [66] 1.057037e-08 1.446892e-08 1.962265e-08 2.637738e-08 3.515806e-08
#> [71] 4.648301e-08 6.098008e-08 7.940470e-08 1.026600e-07 1.318192e-07
#> [76] 1.681498e-07 2.131412e-07 2.685332e-07 3.363482e-07 4.189256e-07
#> [81] 5.189584e-07 6.395325e-07 7.841691e-07 9.568687e-07 1.162158e-06
#> [86] 1.405140e-06 1.691545e-06 2.027784e-06 2.421009e-06 2.879163e-06
#> [91] 3.411050e-06 4.026390e-06 4.735887e-06 5.551289e-06 6.485461e-06
#> [96] 7.552447e-06 8.767544e-06 1.014737e-05 1.170992e-05 1.347466e-05
#> [101] 1.546258e-05 1.769628e-05 2.020003e-05 2.299982e-05 2.612347e-05
#> [106] 2.960068e-05 3.346306e-05 3.774429e-05 4.248006e-05 4.770825e-05
#> [111] 5.346892e-05 5.980438e-05 6.675927e-05 7.438060e-05 8.271780e-05
#> [116] 9.182278e-05 1.017500e-04 1.125564e-04 1.243016e-04 1.370479e-04
#> [121] 1.508602e-04 1.658062e-04 1.819564e-04 1.993838e-04 2.181646e-04
#> [126] 2.383775e-04 2.601043e-04 2.834294e-04 3.084404e-04 3.352273e-04
#> [131] 3.638835e-04 3.945050e-04 4.271907e-04 4.620424e-04 4.991649e-04
#> [136] 5.386657e-04 5.806553e-04 6.252468e-04 6.725565e-04 7.227031e-04
#> [141] 7.758084e-04 8.319967e-04 8.913951e-04 9.541334e-04 1.020344e-03
#> [146] 1.090162e-03 1.163726e-03 1.241174e-03 1.322651e-03 1.408301e-03
#> [151] 1.498271e-03 1.592712e-03 1.691775e-03 1.795616e-03 1.904391e-03
#> [156] 2.018258e-03 2.137378e-03 2.261915e-03 2.392033e-03 2.527899e-03
#> [161] 2.669682e-03 2.817552e-03 2.971681e-03 3.132243e-03 3.299413e-03
#> [166] 3.473369e-03 3.654289e-03 3.842352e-03 4.037740e-03 4.240636e-03
#> [171] 4.451222e-03 4.669685e-03 4.896209e-03 5.130981e-03 5.374190e-03
#> [176] 5.626025e-03 5.886674e-03 6.156328e-03 6.435178e-03 6.723416e-03
#> [181] 7.021233e-03 7.328823e-03 7.646379e-03 7.974093e-03 8.312160e-03
#> [186] 8.660774e-03 9.020129e-03 9.390419e-03 9.771838e-03 1.016458e-02
#> [191] 1.056884e-02 1.098482e-02 1.141270e-02 1.185268e-02 1.230495e-02
#> [196] 1.276971e-02 1.324715e-02 1.373746e-02 1.424084e-02 1.475747e-02
#> [201] 1.528754e-02 1.583125e-02 1.638879e-02 1.696034e-02 1.754609e-02
#> [206] 1.814623e-02 1.876094e-02 1.939041e-02 2.003483e-02 2.069437e-02
#> [211] 2.136922e-02 2.205957e-02 2.276558e-02 2.348744e-02 2.422533e-02
#> [216] 2.497943e-02 2.574990e-02 2.653692e-02 2.734067e-02 2.816132e-02
#> [221] 2.899903e-02 2.985398e-02 3.072632e-02 3.161624e-02 3.252389e-02
#> [226] 3.344943e-02 3.439303e-02 3.535484e-02 3.633502e-02 3.733374e-02
#> [231] 3.835114e-02 3.938737e-02 4.044259e-02 4.151695e-02 4.261060e-02
#> [236] 4.372368e-02 4.485633e-02 4.600871e-02 4.718094e-02 4.837318e-02
#> [241] 4.958555e-02 5.081820e-02 5.207126e-02 5.334485e-02 5.463912e-02
#> [246] 5.595418e-02 5.729017e-02 5.864721e-02 6.002543e-02 6.142493e-02
#> [251] 6.284586e-02 6.428831e-02 6.575241e-02 6.723827e-02 6.874601e-02
#> [256] 7.027572e-02 7.182753e-02 7.340154e-02 7.499784e-02 7.661655e-02
#> [261] 7.825777e-02 7.992159e-02 8.160810e-02 8.331742e-02 8.504962e-02
#> [266] 8.680480e-02 8.858305e-02 9.038446e-02 9.220911e-02 9.405708e-02
#> [271] 9.592847e-02 9.782334e-02 9.974178e-02 1.016839e-01 1.036497e-01
#> [276] 1.056393e-01 1.076527e-01 1.096901e-01 1.117515e-01 1.138369e-01
#> [281] 1.159465e-01 1.180803e-01 1.202383e-01 1.224206e-01 1.246273e-01
#> [286] 1.268584e-01 1.291140e-01 1.313941e-01 1.336988e-01 1.360281e-01
#> [291] 1.383821e-01 1.407608e-01 1.431643e-01 1.455925e-01 1.480456e-01
#> [296] 1.505236e-01 1.530265e-01 1.555544e-01 1.581072e-01 1.606851e-01
#> [301] 1.632880e-01 1.659160e-01 1.685691e-01 1.712473e-01 1.739507e-01
#> [306] 1.766792e-01 1.794330e-01 1.822120e-01 1.850162e-01 1.878456e-01
#> [311] 1.907004e-01 1.935804e-01 1.964857e-01 1.994163e-01 2.023722e-01
#> [316] 2.053535e-01 2.083601e-01 2.113920e-01 2.144493e-01 2.175319e-01
#> [321] 2.206399e-01 2.237732e-01 2.269318e-01 2.301159e-01 2.333252e-01
#> [326] 2.365599e-01 2.398199e-01 2.431052e-01 2.464159e-01 2.497519e-01
#> [331] 2.531131e-01 2.564997e-01 2.599115e-01 2.633485e-01 2.668108e-01
#> [336] 2.702984e-01 2.738111e-01 2.773491e-01 2.809122e-01 2.845004e-01
#> [341] 2.881138e-01 2.917523e-01 2.954158e-01 2.991044e-01 3.028181e-01
#> [346] 3.065567e-01 3.103204e-01 3.141089e-01 3.179224e-01 3.217608e-01
#> [351] 3.256240e-01 3.295121e-01 3.334249e-01 3.373625e-01 3.413248e-01
#> [356] 3.453118e-01 3.493235e-01 3.533597e-01 3.574206e-01 3.615059e-01
#> [361] 3.656158e-01 3.697501e-01 3.739088e-01 3.780918e-01 3.822992e-01
#> [366] 3.865309e-01 3.907868e-01 3.950669e-01 3.993711e-01 4.036995e-01
#> [371] 4.080518e-01 4.124282e-01 4.168285e-01 4.212528e-01 4.257009e-01
#> [376] 4.301727e-01 4.346684e-01 4.391877e-01 4.437307e-01 4.482972e-01
#> [381] 4.528873e-01 4.575009e-01 4.621379e-01 4.667982e-01 4.714819e-01
#> [386] 4.761889e-01 4.809190e-01 4.856723e-01 4.904487e-01 4.952481e-01
#> [391] 5.000704e-01 5.049157e-01 5.097838e-01 5.146747e-01 5.195883e-01
#> [396] 5.245246e-01 5.294835e-01 5.344649e-01 5.394688e-01 5.444951e-01
#> [401] 5.495438e-01 5.546147e-01 5.597078e-01 5.648232e-01 5.699605e-01
#> [406] 5.751200e-01 5.803013e-01 5.855046e-01 5.907297e-01 5.959765e-01
#> [411] 6.012451e-01 6.065352e-01 6.118469e-01 6.171801e-01 6.225348e-01
#> [416] 6.279107e-01 6.333079e-01 6.387264e-01 6.441660e-01 6.496266e-01
#> [421] 6.551083e-01 6.606108e-01 6.661343e-01 6.716785e-01 6.772434e-01
#> [426] 6.828290e-01 6.884351e-01 6.940618e-01 6.997089e-01 7.053763e-01
#> [431] 7.110640e-01 7.167719e-01 7.225000e-01 7.282481e-01 7.340162e-01
#> [436] 7.398042e-01 7.456121e-01 7.514397e-01 7.572870e-01 7.631540e-01
#> [441] 7.690405e-01 7.749465e-01 7.808718e-01 7.868165e-01 7.927805e-01
#> [446] 7.987636e-01 8.047658e-01 8.107871e-01 8.168273e-01 8.228863e-01
#> [451] 8.289642e-01 8.350608e-01 8.411760e-01 8.473098e-01 8.534621e-01
#> [456] 8.596329e-01 8.658220e-01 8.720293e-01 8.782548e-01 8.844985e-01
#> [461] 8.907602e-01 8.970399e-01 9.033375e-01 9.096528e-01 9.159859e-01
#> [466] 9.223367e-01 9.287051e-01 9.350910e-01 9.414943e-01 9.479150e-01
#> [471] 9.543529e-01 9.608081e-01 9.672804e-01 9.737697e-01 9.802760e-01
#> [476] 9.867993e-01 9.933393e-01 9.998961e-01 1.006470e+00 1.013060e+00
#> [481] 1.019666e+00 1.026289e+00 1.032929e+00 1.039584e+00 1.046256e+00
#> [486] 1.052944e+00 1.059649e+00 1.066369e+00 1.073105e+00 1.079857e+00
#> [491] 1.086624e+00 1.093408e+00 1.100207e+00 1.107021e+00 1.113851e+00
#> [496] 1.120696e+00 1.127557e+00 1.134433e+00 1.141324e+00 1.148230e+00
#> [501] 1.155151e+00 1.162088e+00 1.169039e+00 1.176004e+00 1.182985e+00
#> [506] 1.189980e+00 1.196990e+00 1.204014e+00 1.211052e+00 1.218105e+00
#> [511] 1.225173e+00 1.232254e+00 1.239350e+00 1.246459e+00 1.253583e+00
#> [516] 1.260720e+00 1.267872e+00 1.275037e+00 1.282215e+00 1.289408e+00
#> [521] 1.296614e+00 1.303833e+00 1.311066e+00 1.318312e+00 1.325571e+00
#> [526] 1.332844e+00 1.340129e+00 1.347428e+00 1.354740e+00 1.362064e+00
#> [531] 1.369402e+00 1.376752e+00 1.384114e+00 1.391490e+00 1.398878e+00
#> [536] 1.406278e+00 1.413691e+00 1.421116e+00 1.428553e+00 1.436003e+00
#> [541] 1.443465e+00 1.450938e+00 1.458424e+00 1.465922e+00 1.473431e+00
#> [546] 1.480952e+00 1.488485e+00 1.496030e+00 1.503586e+00 1.511153e+00
#> [551] 1.518732e+00 1.526323e+00 1.533924e+00 1.541537e+00 1.549161e+00
#> [556] 1.556796e+00 1.564443e+00 1.572100e+00 1.579768e+00 1.587446e+00
#> [561] 1.595136e+00 1.602836e+00 1.610547e+00 1.618268e+00 1.626000e+00
#> [566] 1.633743e+00 1.641495e+00 1.649258e+00 1.657031e+00 1.664815e+00
#> [571] 1.672608e+00 1.680412e+00 1.688225e+00 1.696048e+00 1.703881e+00
#> [576] 1.711724e+00 1.719577e+00 1.727439e+00 1.735311e+00 1.743192e+00
#> [581] 1.751083e+00 1.758983e+00 1.766893e+00 1.774812e+00 1.782740e+00
#> [586] 1.790677e+00 1.798623e+00 1.806578e+00 1.814542e+00 1.822516e+00
#> [591] 1.830497e+00 1.838488e+00 1.846488e+00 1.854496e+00 1.862512e+00
#> [596] 1.870537e+00 1.878571e+00 1.886613e+00 1.894663e+00 1.902722e+00
#> [601] 1.910789e+00 1.918864e+00 1.926947e+00 1.935038e+00 1.943138e+00
#> [606] 1.951245e+00 1.959360e+00 1.967482e+00 1.975613e+00 1.983751e+00
#> [611] 1.991897e+00 2.000051e+00 2.008212e+00 2.016380e+00 2.024556e+00
#> [616] 2.032739e+00 2.040930e+00 2.049128e+00 2.057333e+00 2.065545e+00
#> [621] 2.073764e+00 2.081990e+00 2.090224e+00 2.098464e+00 2.106711e+00
#> [626] 2.114964e+00 2.123225e+00 2.131492e+00 2.139766e+00 2.148046e+00
#> [631] 2.156333e+00 2.164626e+00 2.172926e+00 2.181232e+00 2.189545e+00
#> [636] 2.197864e+00 2.206188e+00 2.214520e+00 2.222857e+00 2.231200e+00
#> [641] 2.239549e+00 2.247904e+00 2.256265e+00 2.264632e+00 2.273005e+00
#> [646] 2.281383e+00 2.289767e+00 2.298157e+00 2.306553e+00 2.314953e+00
#> [651] 2.323360e+00 2.331772e+00 2.340189e+00 2.348611e+00 2.357039e+00
#> [656] 2.365472e+00 2.373910e+00 2.382353e+00 2.390802e+00 2.399255e+00
#> [661] 2.407714e+00 2.416177e+00 2.424645e+00 2.433118e+00 2.441596e+00
#> [666] 2.450079e+00 2.458566e+00 2.467058e+00 2.475555e+00 2.484056e+00
#> [671] 2.492562e+00 2.501072e+00 2.509586e+00 2.518105e+00 2.526629e+00
#> [676] 2.535156e+00 2.543688e+00 2.552224e+00 2.560764e+00 2.569308e+00
#> [681] 2.577856e+00 2.586409e+00 2.594965e+00 2.603525e+00 2.612089e+00
#> [686] 2.620657e+00 2.629228e+00 2.637804e+00 2.646383e+00 2.654965e+00
#> [691] 2.663552e+00 2.672142e+00 2.680735e+00 2.689332e+00 2.697932e+00
#> [696] 2.706536e+00 2.715143e+00 2.723753e+00 2.732367e+00 2.740984e+00
#> [701] 2.749604e+00 2.758227e+00 2.766853e+00 2.775483e+00 2.784115e+00
#> [706] 2.792750e+00 2.801389e+00 2.810030e+00 2.818674e+00 2.827321e+00
#> [711] 2.835970e+00 2.844623e+00 2.853278e+00 2.861935e+00 2.870596e+00
#> [716] 2.879259e+00 2.887924e+00 2.896592e+00 2.905262e+00 2.913935e+00
#> [721] 2.922610e+00 2.931288e+00 2.939968e+00 2.948650e+00 2.957334e+00
#> [726] 2.966020e+00 2.974709e+00 2.983400e+00 2.992093e+00 3.000788e+00
#> [731] 3.009485e+00 3.018183e+00 3.026884e+00 3.035587e+00 3.044291e+00
#> [736] 3.052998e+00 3.061706e+00 3.070416e+00 3.079127e+00 3.087841e+00
#> [741] 3.096555e+00 3.105272e+00 3.113990e+00 3.122710e+00 3.131431e+00
#> [746] 3.140153e+00 3.148877e+00 3.157603e+00 3.166329e+00 3.175057e+00
#> [751] 3.183787e+00 3.192517e+00 3.201249e+00 3.209982e+00 3.218716e+00
#> [756] 3.227452e+00 3.236188e+00 3.244926e+00 3.253664e+00 3.262404e+00
#> [761] 3.271144e+00 3.279885e+00 3.288627e+00 3.297371e+00 3.306114e+00
#> [766] 3.314859e+00 3.323605e+00 3.332351e+00 3.341098e+00 3.349845e+00
#> [771] 3.358594e+00 3.367342e+00 3.376092e+00 3.384842e+00 3.393592e+00
#> [776] 3.402343e+00 3.411094e+00 3.419846e+00 3.428598e+00 3.437351e+00
#> [781] 3.446104e+00 3.454857e+00 3.463610e+00 3.472364e+00 3.481118e+00
#> [786] 3.489872e+00 3.498626e+00 3.507380e+00 3.516135e+00 3.524889e+00
#> [791] 3.533644e+00 3.542398e+00 3.551153e+00 3.559907e+00 3.568662e+00
#> [796] 3.577416e+00 3.586170e+00 3.594924e+00 3.603678e+00 3.612431e+00
#> [801] 3.621185e+00 3.629938e+00 3.638690e+00 3.647443e+00 3.656195e+00
#> [806] 3.664947e+00 3.673698e+00 3.682449e+00 3.691199e+00 3.699949e+00
#> [811] 3.708698e+00 3.717447e+00 3.726195e+00 3.734943e+00 3.743690e+00
#> [816] 3.752436e+00 3.761182e+00 3.769927e+00 3.778671e+00 3.787415e+00
#> [821] 3.796157e+00 3.804899e+00 3.813640e+00 3.822381e+00 3.831120e+00
#> [826] 3.839859e+00 3.848596e+00 3.857333e+00 3.866068e+00 3.874803e+00
#> [831] 3.883537e+00 3.892269e+00 3.901001e+00 3.909731e+00 3.918460e+00
#> [836] 3.927189e+00 3.935916e+00 3.944641e+00 3.953366e+00 3.962089e+00
#> [841] 3.970811e+00 3.979532e+00 3.988252e+00 3.996970e+00 4.005687e+00
#> [846] 4.014402e+00 4.023116e+00 4.031829e+00 4.040540e+00 4.049250e+00
#> [851] 4.057958e+00 4.066665e+00 4.075370e+00 4.084074e+00 4.092776e+00
#> [856] 4.101477e+00 4.110176e+00 4.118873e+00 4.127568e+00 4.136262e+00
#> [861] 4.144955e+00 4.153645e+00 4.162334e+00 4.171021e+00 4.179706e+00
#> [866] 4.188390e+00 4.197071e+00 4.205751e+00 4.214429e+00 4.223105e+00
#> [871] 4.231779e+00 4.240452e+00 4.249122e+00 4.257790e+00 4.266456e+00
#> [876] 4.275121e+00 4.283783e+00 4.292443e+00 4.301101e+00 4.309758e+00
#> [881] 4.318412e+00 4.327064e+00 4.335713e+00 4.344361e+00 4.353006e+00
#> [886] 4.361650e+00 4.370291e+00 4.378929e+00 4.387566e+00 4.396200e+00
#> [891] 4.404832e+00 4.413462e+00 4.422089e+00 4.430714e+00 4.439337e+00
#> [896] 4.447957e+00 4.456575e+00 4.465190e+00 4.473804e+00 4.482414e+00
#> [901] 4.491022e+00 4.499628e+00 4.508231e+00 4.516832e+00 4.525430e+00
#> [906] 4.534025e+00 4.542618e+00 4.551209e+00 4.559796e+00 4.568382e+00
#> [911] 4.576964e+00 4.585544e+00 4.594121e+00 4.602696e+00 4.611268e+00
#> [916] 4.619837e+00 4.628403e+00 4.636967e+00 4.645528e+00 4.654086e+00
#> [921] 4.662641e+00 4.671194e+00 4.679743e+00 4.688290e+00 4.696834e+00
#> [926] 4.705375e+00 4.713913e+00 4.722449e+00 4.730981e+00 4.739510e+00
#> [931] 4.748037e+00 4.756560e+00 4.765081e+00 4.773598e+00 4.782113e+00
#> [936] 4.790624e+00 4.799133e+00 4.807638e+00 4.816141e+00 4.824640e+00
#> [941] 4.833136e+00 4.841629e+00 4.850119e+00 4.858606e+00 4.867089e+00
#> [946] 4.875570e+00 4.884047e+00 4.892521e+00 4.900992e+00 4.909460e+00
#> [951] 4.917924e+00 4.926385e+00 4.934843e+00 4.943298e+00 4.951749e+00
#> [956] 4.960197e+00 4.968642e+00 4.977083e+00 4.985521e+00 4.993956e+00
#> [961] 5.002387e+00 5.010815e+00 5.019240e+00 5.027661e+00 5.036079e+00
#> [966] 5.044493e+00 5.052904e+00 5.061311e+00 5.069715e+00 5.078116e+00
#> [971] 5.086512e+00 5.094906e+00 5.103296e+00 5.111682e+00 5.120065e+00
#> [976] 5.128444e+00 5.136820e+00 5.145192e+00 5.153561e+00 5.161926e+00
#> [981] 5.170287e+00 5.178645e+00 5.186999e+00 5.195349e+00 5.203696e+00
#> [986] 5.212039e+00 5.220378e+00 5.228714e+00 5.237046e+00 5.245374e+00
#> [991] 5.253699e+00 5.262020e+00 5.270337e+00 5.278650e+00 5.286960e+00
#> [996] 5.295265e+00 5.303567e+00 5.311865e+00 5.320160e+00 5.328450e+00
#> [1001] 5.336737e+00 5.345020e+00 5.353299e+00 5.361574e+00 5.369845e+00
#> [1006] 5.378113e+00 5.386376e+00 5.394636e+00 5.402891e+00 5.411143e+00
#> [1011] 5.419391e+00 5.427635e+00 5.435874e+00 5.444110e+00 5.452342e+00
#> [1016] 5.460570e+00 5.468794e+00 5.477014e+00 5.485230e+00 5.493442e+00
#> [1021] 5.501650e+00 5.509854e+00 5.518054e+00 5.526249e+00 5.534441e+00
#> [1026] 5.542628e+00 5.550812e+00 5.558991e+00 5.567167e+00 5.575338e+00
#> [1031] 5.583505e+00 5.591668e+00 5.599827e+00 5.607981e+00 5.616132e+00
#> [1036] 5.624278e+00 5.632420e+00 5.640558e+00 5.648692e+00 5.656821e+00
#> [1041] 5.664947e+00 5.673068e+00 5.681185e+00 5.689297e+00 5.697406e+00
#> [1046] 5.705510e+00 5.713610e+00 5.721706e+00 5.729797e+00 5.737884e+00
#> [1051] 5.745967e+00 5.754045e+00 5.762120e+00 5.770189e+00 5.778255e+00
#> [1056] 5.786316e+00 5.794373e+00 5.802426e+00 5.810474e+00 5.818518e+00
#> [1061] 5.826557e+00 5.834592e+00 5.842623e+00 5.850649e+00 5.858671e+00
#> [1066] 5.866689e+00 5.874702e+00 5.882711e+00 5.890715e+00 5.898715e+00
#> [1071] 5.906710e+00 5.914701e+00 5.922688e+00 5.930670e+00 5.938647e+00
#> [1076] 5.946620e+00 5.954589e+00 5.962553e+00 5.970513e+00 5.978468e+00
#> [1081] 5.986419e+00 5.994365e+00 6.002306e+00 6.010243e+00 6.018176e+00
#> [1086] 6.026104e+00 6.034027e+00 6.041946e+00 6.049861e+00 6.057770e+00
#> [1091] 6.065676e+00 6.073576e+00 6.081472e+00 6.089364e+00 6.097251e+00
#> [1096] 6.105133e+00 6.113011e+00 6.120884e+00 6.128752e+00 6.136616e+00
#> [1101] 6.144475e+00 6.152330e+00 6.160180e+00 6.168025e+00 6.175865e+00
#> [1106] 6.183701e+00 6.191533e+00 6.199359e+00 6.207181e+00 6.214998e+00
#> [1111] 6.222811e+00 6.230619e+00 6.238422e+00 6.246221e+00 6.254014e+00
#> [1116] 6.261803e+00 6.269588e+00 6.277367e+00 6.285142e+00 6.292912e+00
#> [1121] 6.300678e+00 6.308439e+00 6.316194e+00 6.323946e+00 6.331692e+00
#> [1126] 6.339434e+00 6.347171e+00 6.354903e+00 6.362630e+00 6.370353e+00
#> [1131] 6.378070e+00 6.385783e+00 6.393492e+00 6.401195e+00 6.408894e+00
#> [1136] 6.416587e+00 6.424276e+00 6.431960e+00 6.439640e+00 6.447314e+00
#> [1141] 6.454984e+00 6.462649e+00 6.470309e+00 6.477964e+00 6.485614e+00
#> [1146] 6.493259e+00 6.500900e+00 6.508536e+00 6.516166e+00 6.523792e+00
#> [1151] 6.531414e+00 6.539030e+00 6.546641e+00 6.554247e+00 6.561849e+00
#> [1156] 6.569446e+00 6.577037e+00 6.584624e+00 6.592206e+00 6.599783e+00
#> [1161] 6.607355e+00 6.614923e+00 6.622485e+00 6.630042e+00 6.637595e+00
#> [1166] 6.645142e+00 6.652685e+00 6.660222e+00 6.667755e+00 6.675283e+00
#> [1171] 6.682805e+00 6.690323e+00 6.697836e+00 6.705344e+00 6.712847e+00
#> [1176] 6.720345e+00 6.727838e+00 6.735326e+00 6.742809e+00 6.750287e+00
#> [1181] 6.757760e+00 6.765228e+00 6.772691e+00 6.780150e+00 6.787603e+00
#> [1186] 6.795051e+00 6.802494e+00 6.809932e+00 6.817365e+00 6.824793e+00
#> [1191] 6.832216e+00 6.839634e+00 6.847047e+00 6.854455e+00 6.861858e+00
#> [1196] 6.869256e+00 6.876649e+00 6.884037e+00 6.891420e+00 6.898798e+00
#> [1201] 6.906171e+00 6.913538e+00 6.920901e+00 6.928259e+00 6.935611e+00
#> [1206] 6.942959e+00 6.950301e+00 6.957639e+00 6.964971e+00 6.972298e+00
#> [1211] 6.979620e+00 6.986938e+00 6.994250e+00 7.001557e+00 7.008859e+00
#> [1216] 7.016155e+00 7.023447e+00 7.030734e+00 7.038015e+00 7.045292e+00
#> [1221] 7.052563e+00 7.059830e+00 7.067091e+00 7.074347e+00 7.081598e+00
#> [1226] 7.088844e+00 7.096085e+00 7.103320e+00 7.110551e+00 7.117776e+00
#> [1231] 7.124997e+00 7.132212e+00 7.139422e+00 7.146627e+00 7.153827e+00
#> [1236] 7.161022e+00 7.168211e+00 7.175396e+00 7.182575e+00 7.189750e+00
#> [1241] 7.196919e+00 7.204083e+00 7.211242e+00 7.218395e+00 7.225544e+00
#> [1246] 7.232687e+00 7.239826e+00 7.246959e+00 7.254087e+00 7.261210e+00
#> [1251] 7.268327e+00 7.275440e+00 7.282547e+00 7.289650e+00 7.296747e+00
#> [1256] 7.303839e+00 7.310926e+00 7.318007e+00 7.325084e+00 7.332155e+00
#> [1261] 7.339221e+00 7.346282e+00 7.353338e+00 7.360389e+00 7.367434e+00
#> [1266] 7.374475e+00 7.381510e+00 7.388540e+00 7.395565e+00 7.402584e+00
#> [1271] 7.409599e+00 7.416608e+00 7.423612e+00 7.430611e+00 7.437605e+00
#> [1276] 7.444593e+00 7.451577e+00 7.458555e+00 7.465528e+00 7.472496e+00
#> [1281] 7.479458e+00 7.486416e+00 7.493368e+00 7.500315e+00 7.507257e+00
#> [1286] 7.514194e+00 7.521125e+00 7.528052e+00 7.534973e+00 7.541889e+00
#> [1291] 7.548799e+00 7.555705e+00 7.562605e+00 7.569500e+00 7.576390e+00
#> [1296] 7.583275e+00 7.590155e+00 7.597029e+00 7.603898e+00 7.610762e+00
#> [1301] 7.617621e+00 7.624474e+00 7.631323e+00 7.638166e+00 7.645004e+00
#> [1306] 7.651837e+00 7.658664e+00 7.665486e+00 7.672303e+00 7.679115e+00
#> [1311] 7.685922e+00 7.692724e+00 7.699520e+00 7.706311e+00 7.713097e+00
#> [1316] 7.719877e+00 7.726653e+00 7.733423e+00 7.740188e+00 7.746948e+00
#> [1321] 7.753702e+00 7.760452e+00 7.767196e+00 7.773935e+00 7.780668e+00
#> [1326] 7.787397e+00 7.794120e+00 7.800838e+00 7.807551e+00 7.814259e+00
#> [1331] 7.820961e+00 7.827658e+00 7.834350e+00 7.841037e+00 7.847719e+00
#> [1336] 7.854395e+00 7.861066e+00 7.867732e+00 7.874393e+00 7.881048e+00
#> [1341] 7.887699e+00 7.894344e+00 7.900983e+00 7.907618e+00 7.914247e+00
#> [1346] 7.920872e+00 7.927491e+00 7.934104e+00 7.940713e+00 7.947316e+00
#> [1351] 7.953914e+00 7.960507e+00 7.967095e+00 7.973677e+00 7.980255e+00
#> [1356] 7.986827e+00 7.993393e+00 7.999955e+00 8.006511e+00 8.013062e+00
#> [1361] 8.019608e+00 8.026149e+00 8.032685e+00 8.039215e+00 8.045740e+00
#> [1366] 8.052260e+00 8.058774e+00 8.065284e+00 8.071788e+00 8.078287e+00
#> [1371] 8.084781e+00 8.091269e+00 8.097753e+00 8.104231e+00 8.110704e+00
#> [1376] 8.117172e+00 8.123634e+00 8.130091e+00 8.136544e+00 8.142990e+00
#> [1381] 8.149432e+00 8.155869e+00 8.162300e+00 8.168726e+00 8.175147e+00
#> [1386] 8.181562e+00 8.187973e+00 8.194378e+00 8.200778e+00 8.207173e+00
#> [1391] 8.213563e+00 8.219947e+00 8.226326e+00 8.232700e+00 8.239069e+00
#> [1396] 8.245433e+00 8.251791e+00 8.258144e+00 8.264492e+00 8.270835e+00
#> [1401] 8.277173e+00 8.283505e+00 8.289832e+00 8.296154e+00 8.302471e+00
#> [1406] 8.308783e+00 8.315089e+00 8.321390e+00 8.327686e+00 8.333977e+00
#> [1411] 8.340263e+00 8.346543e+00 8.352819e+00 8.359089e+00 8.365354e+00
#> [1416] 8.371613e+00 8.377868e+00 8.384117e+00 8.390361e+00 8.396600e+00
#> [1421] 8.402834e+00 8.409063e+00 8.415286e+00 8.421504e+00 8.427718e+00
#> [1426] 8.433925e+00 8.440128e+00 8.446326e+00 8.452518e+00 8.458705e+00
#> [1431] 8.464887e+00 8.471064e+00 8.477236e+00 8.483402e+00 8.489564e+00
#> [1436] 8.495720e+00 8.501871e+00 8.508016e+00 8.514157e+00 8.520293e+00
#> [1441] 8.526423e+00 8.532548e+00 8.538668e+00 8.544783e+00 8.550893e+00
#> [1446] 8.556997e+00 8.563096e+00 8.569191e+00 8.575280e+00 8.581364e+00
#> [1451] 8.587442e+00 8.593516e+00 8.599584e+00 8.605648e+00 8.611706e+00
#> [1456] 8.617759e+00 8.623807e+00 8.629849e+00 8.635887e+00 8.641919e+00
#> [1461] 8.647947e+00 8.653969e+00 8.659986e+00 8.665997e+00 8.672004e+00
#> [1466] 8.678006e+00 8.684002e+00 8.689994e+00 8.695980e+00 8.701961e+00
#> [1471] 8.707937e+00 8.713907e+00 8.719873e+00 8.725834e+00 8.731789e+00
#> [1476] 8.737739e+00 8.743684e+00 8.749625e+00 8.755559e+00 8.761489e+00
#> [1481] 8.767414e+00 8.773334e+00 8.779248e+00 8.785157e+00 8.791062e+00
#> [1486] 8.796961e+00 8.802855e+00 8.808744e+00 8.814627e+00 8.820506e+00
#> [1491] 8.826380e+00 8.832248e+00 8.838112e+00 8.843970e+00 8.849823e+00
#> [1496] 8.855671e+00 8.861514e+00 8.867352e+00 8.873185e+00 8.879013e+00
#> [1501] 8.884835e+00 8.890653e+00 8.896465e+00 8.902273e+00 8.908075e+00
#> [1506] 8.913872e+00 8.919665e+00 8.925452e+00 8.931234e+00 8.937011e+00
#> [1511] 8.942782e+00 8.948549e+00 8.954311e+00 8.960068e+00 8.965819e+00
#> [1516] 8.971566e+00 8.977307e+00 8.983044e+00 8.988775e+00 8.994501e+00
#> [1521] 9.000222e+00 9.005938e+00 9.011650e+00 9.017356e+00 9.023057e+00
#> [1526] 9.028753e+00 9.034443e+00 9.040129e+00 9.045810e+00 9.051486e+00
#> [1531] 9.057157e+00 9.062822e+00 9.068483e+00 9.074139e+00 9.079789e+00
#> [1536] 9.085435e+00 9.091075e+00 9.096711e+00 9.102341e+00 9.107967e+00
#> [1541] 9.113587e+00 9.119202e+00 9.124813e+00 9.130418e+00 9.136019e+00
#> [1546] 9.141614e+00 9.147204e+00 9.152789e+00 9.158370e+00 9.163945e+00
#> [1551] 9.169515e+00 9.175081e+00 9.180641e+00 9.186196e+00 9.191746e+00
#> [1556] 9.197292e+00 9.202832e+00 9.208367e+00 9.213897e+00 9.219423e+00
#> [1561] 9.224943e+00 9.230458e+00 9.235969e+00 9.241474e+00 9.246974e+00
#> [1566] 9.252470e+00 9.257960e+00 9.263446e+00 9.268926e+00 9.274402e+00
#> [1571] 9.279872e+00 9.285338e+00 9.290798e+00 9.296254e+00 9.301705e+00
#> [1576] 9.307150e+00 9.312591e+00 9.318027e+00 9.323458e+00 9.328884e+00
#> [1581] 9.334305e+00 9.339720e+00 9.345132e+00 9.350538e+00 9.355939e+00
#> [1586] 9.361335e+00 9.366726e+00 9.372113e+00 9.377494e+00 9.382870e+00
#> [1591] 9.388242e+00 9.393608e+00 9.398970e+00 9.404327e+00 9.409679e+00
#> [1596] 9.415026e+00 9.420368e+00 9.425705e+00 9.431037e+00 9.436364e+00
#> [1601] 9.441686e+00 9.447004e+00 9.452316e+00 9.457624e+00 9.462926e+00
#> [1606] 9.468224e+00 9.473517e+00 9.478805e+00 9.484088e+00 9.489366e+00
#> [1611] 9.494640e+00 9.499908e+00 9.505172e+00 9.510430e+00 9.515684e+00
#> [1616] 9.520933e+00 9.526177e+00 9.531416e+00 9.536650e+00 9.541880e+00
#> [1621] 9.547104e+00 9.552324e+00 9.557539e+00 9.562748e+00 9.567953e+00
#> [1626] 9.573154e+00 9.578349e+00 9.583539e+00 9.588725e+00 9.593906e+00
#> [1631] 9.599082e+00 9.604253e+00 9.609419e+00 9.614580e+00 9.619737e+00
#> [1636] 9.624888e+00 9.630035e+00 9.635177e+00 9.640314e+00 9.645447e+00
#> [1641] 9.650574e+00 9.655697e+00 9.660815e+00 9.665928e+00 9.671036e+00
#> [1646] 9.676139e+00 9.681238e+00 9.686332e+00 9.691421e+00 9.696505e+00
#> [1651] 9.701584e+00 9.706659e+00 9.711728e+00 9.716793e+00 9.721853e+00
#> [1656] 9.726909e+00 9.731959e+00 9.737005e+00 9.742046e+00 9.747082e+00
#> [1661] 9.752114e+00 9.757140e+00 9.762162e+00 9.767179e+00 9.772191e+00
#> [1666] 9.777199e+00 9.782201e+00 9.787199e+00 9.792192e+00 9.797181e+00
#> [1671] 9.802164e+00 9.807143e+00 9.812117e+00 9.817087e+00 9.822051e+00
#> [1676] 9.827011e+00 9.831966e+00 9.836917e+00 9.841862e+00 9.846803e+00
#> [1681] 9.851739e+00 9.856671e+00 9.861597e+00 9.866519e+00 9.871436e+00
#> [1686] 9.876349e+00 9.881256e+00 9.886159e+00 9.891058e+00 9.895951e+00
#> [1691] 9.900840e+00 9.905724e+00 9.910603e+00 9.915478e+00 9.920348e+00
#> [1696] 9.925213e+00 9.930074e+00 9.934930e+00 9.939781e+00 9.944627e+00
#> [1701] 9.949469e+00 9.954306e+00 9.959138e+00 9.963966e+00 9.968789e+00
#> [1706] 9.973607e+00 9.978421e+00 9.983230e+00 9.988034e+00 9.992834e+00
#> [1711] 9.997629e+00 1.000242e+01 1.000720e+01 1.001199e+01 1.001676e+01
#> [1716] 1.002153e+01 1.002630e+01 1.003106e+01 1.003582e+01 1.004057e+01
#> [1721] 1.004532e+01 1.005006e+01 1.005480e+01 1.005954e+01 1.006427e+01
#> [1726] 1.006899e+01 1.007371e+01 1.007843e+01 1.008314e+01 1.008785e+01
#> [1731] 1.009255e+01 1.009725e+01 1.010194e+01 1.010663e+01 1.011131e+01
#> [1736] 1.011599e+01 1.012066e+01 1.012533e+01 1.013000e+01 1.013466e+01
#> [1741] 1.013931e+01 1.014396e+01 1.014861e+01 1.015325e+01 1.015789e+01
#> [1746] 1.016252e+01 1.016715e+01 1.017178e+01 1.017639e+01 1.018101e+01
#> [1751] 1.018562e+01 1.019022e+01 1.019482e+01 1.019942e+01 1.020401e+01
#> [1756] 1.020860e+01 1.021318e+01 1.021776e+01 1.022233e+01 1.022690e+01
#> [1761] 1.023147e+01 1.023603e+01 1.024058e+01 1.024513e+01 1.024968e+01
#> [1766] 1.025422e+01 1.025876e+01 1.026329e+01 1.026782e+01 1.027234e+01
#> [1771] 1.027686e+01 1.028137e+01 1.028588e+01 1.029039e+01 1.029489e+01
#> [1776] 1.029938e+01 1.030387e+01 1.030836e+01 1.031284e+01 1.031732e+01
#> [1781] 1.032180e+01 1.032627e+01 1.033073e+01 1.033519e+01 1.033965e+01
#> [1786] 1.034410e+01 1.034854e+01 1.035299e+01 1.035742e+01 1.036186e+01
#> [1791] 1.036628e+01 1.037071e+01 1.037513e+01 1.037954e+01 1.038395e+01
#> [1796] 1.038836e+01 1.039276e+01 1.039716e+01 1.040155e+01 1.040594e+01
#> [1801] 1.041032e+01 1.041470e+01 1.041908e+01 1.042345e+01 1.042782e+01
#> [1806] 1.043218e+01 1.043653e+01 1.044089e+01 1.044524e+01 1.044958e+01
#> [1811] 1.045392e+01 1.045825e+01 1.046258e+01 1.046691e+01 1.047123e+01
#> [1816] 1.047555e+01 1.047986e+01 1.048417e+01 1.048847e+01 1.049277e+01
#> [1821] 1.049707e+01 1.050136e+01 1.050565e+01 1.050993e+01 1.051421e+01
#> [1826] 1.051848e+01 1.052275e+01 1.052701e+01 1.053127e+01 1.053553e+01
#> [1831] 1.053978e+01 1.054403e+01 1.054827e+01 1.055251e+01 1.055674e+01
#> [1836] 1.056097e+01 1.056519e+01 1.056942e+01 1.057363e+01 1.057784e+01
#> [1841] 1.058205e+01 1.058625e+01 1.059045e+01 1.059465e+01 1.059884e+01
#> [1846] 1.060302e+01 1.060720e+01 1.061138e+01 1.061555e+01 1.061972e+01
#> [1851] 1.062389e+01 1.062805e+01 1.063220e+01 1.063635e+01 1.064050e+01
#> [1856] 1.064464e+01 1.064878e+01 1.065291e+01 1.065704e+01 1.066117e+01
#> [1861] 1.066529e+01 1.066940e+01 1.067352e+01 1.067762e+01 1.068173e+01
#> [1866] 1.068583e+01 1.068992e+01 1.069401e+01 1.069810e+01 1.070218e+01
#> [1871] 1.070626e+01 1.071033e+01 1.071440e+01 1.071847e+01 1.072253e+01
#> [1876] 1.072658e+01 1.073064e+01 1.073468e+01 1.073873e+01 1.074277e+01
#> [1881] 1.074680e+01 1.075083e+01 1.075486e+01 1.075888e+01 1.076290e+01
#> [1886] 1.076691e+01 1.077092e+01 1.077493e+01 1.077893e+01 1.078292e+01
#> [1891] 1.078692e+01 1.079091e+01 1.079489e+01 1.079887e+01 1.080285e+01
#> [1896] 1.080682e+01 1.081078e+01 1.081475e+01 1.081871e+01 1.082266e+01
#> [1901] 1.082661e+01 1.083056e+01 1.083450e+01 1.083844e+01 1.084237e+01
#> [1906] 1.084630e+01 1.085022e+01 1.085414e+01 1.085806e+01 1.086197e+01
#> [1911] 1.086588e+01 1.086979e+01 1.087369e+01 1.087758e+01 1.088147e+01
#> [1916] 1.088536e+01 1.088924e+01 1.089312e+01 1.089700e+01 1.090087e+01
#> [1921] 1.090473e+01 1.090860e+01 1.091245e+01 1.091631e+01 1.092016e+01
#> [1926] 1.092400e+01 1.092785e+01 1.093168e+01 1.093552e+01 1.093935e+01
#> [1931] 1.094317e+01 1.094699e+01 1.095081e+01 1.095462e+01 1.095843e+01
#> [1936] 1.096223e+01 1.096603e+01 1.096983e+01 1.097362e+01 1.097741e+01
#> [1941] 1.098119e+01 1.098497e+01 1.098875e+01 1.099252e+01 1.099629e+01
#> [1946] 1.100005e+01 1.100381e+01 1.100756e+01 1.101131e+01 1.101506e+01
#> [1951] 1.101880e+01 1.102254e+01 1.102628e+01 1.103001e+01 1.103373e+01
#> [1956] 1.103746e+01 1.104117e+01 1.104489e+01 1.104860e+01 1.105231e+01
#> [1961] 1.105601e+01 1.105970e+01 1.106340e+01 1.106709e+01 1.107077e+01
#> [1966] 1.107446e+01 1.107813e+01 1.108181e+01 1.108548e+01 1.108914e+01
#> [1971] 1.109280e+01 1.109646e+01 1.110011e+01 1.110376e+01 1.110741e+01
#> [1976] 1.111105e+01 1.111469e+01 1.111832e+01 1.112195e+01 1.112557e+01
#> [1981] 1.112920e+01 1.113281e+01 1.113643e+01 1.114004e+01 1.114364e+01
#> [1986] 1.114724e+01 1.115084e+01 1.115443e+01 1.115802e+01 1.116161e+01
#> [1991] 1.116519e+01 1.116876e+01 1.117234e+01 1.117591e+01 1.117947e+01
#> [1996] 1.118303e+01 1.118659e+01 1.119014e+01 1.119369e+01 1.119724e+01
#> [2001] 1.120078e+01
bsmgamma(c("call", "put"), c(50, 49, 48, 47), 45, 0.25, 0.13, 0.01, 0.2)
#> [1] 0.02972015 0.03945602 0.05051675 0.06222511
bsmgamma("call", 50, 45, 0.25, 0.13, 0.01, 1:1000 / 1000)
#> [1] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [6] 0.000000e+00 0.000000e+00 4.002194e-249 5.502211e-197 1.060582e-159
#> [11] 4.024350e-132 3.754879e-111 7.740257e-95 6.744339e-82 1.838320e-71
#> [16] 6.332747e-63 7.479820e-56 6.277499e-50 6.437337e-45 1.215400e-40
#> [21] 5.787929e-37 8.880995e-34 5.324360e-31 1.454099e-28 2.046593e-26
#> [26] 1.640821e-24 8.133188e-23 2.666657e-21 6.117090e-20 1.028878e-18
#> [31] 1.319958e-17 1.335468e-16 1.096271e-15 7.481002e-15 4.333304e-14
#> [36] 2.169273e-13 9.532791e-13 3.727618e-12 1.312490e-11 4.204607e-11
#> [41] 1.236766e-10 3.367303e-10 8.546878e-10 2.035224e-09 4.572385e-09
#> [46] 9.740526e-09 1.976442e-08 3.835298e-08 7.143344e-08 1.281178e-07
#> [51] 2.219232e-07 3.722539e-07 6.061339e-07 9.601601e-07 1.482625e-06
#> [56] 2.235742e-06 3.297888e-06 4.765772e-06 6.756435e-06 9.408980e-06
#> [61] 1.288596e-05 1.737434e-05 2.308594e-05 3.025744e-05 3.914974e-05
#> [66] 5.004687e-05 6.325436e-05 7.909705e-05 9.791664e-05 1.200687e-04
#> [71] 1.459195e-04 1.758426e-04 2.102153e-04 2.494149e-04 2.938154e-04
#> [76] 3.437835e-04 3.996757e-04 4.618346e-04 5.305865e-04 6.062382e-04
#> [81] 6.890748e-04 7.793576e-04 8.773224e-04 9.831781e-04 1.097105e-03
#> [86] 1.219256e-03 1.349752e-03 1.488687e-03 1.636124e-03 1.792097e-03
#> [91] 1.956613e-03 2.129648e-03 2.311155e-03 2.501057e-03 2.699256e-03
#> [96] 2.905628e-03 3.120029e-03 3.342293e-03 3.572237e-03 3.809658e-03
#> [101] 4.054340e-03 4.306050e-03 4.564544e-03 4.829565e-03 5.100850e-03
#> [106] 5.378122e-03 5.661102e-03 5.949501e-03 6.243030e-03 6.541393e-03
#> [111] 6.844294e-03 7.151435e-03 7.462518e-03 7.777246e-03 8.095325e-03
#> [116] 8.416461e-03 8.740364e-03 9.066749e-03 9.395335e-03 9.725845e-03
#> [121] 1.005801e-02 1.039156e-02 1.072624e-02 1.106181e-02 1.139800e-02
#> [126] 1.173459e-02 1.207134e-02 1.240803e-02 1.274445e-02 1.308039e-02
#> [131] 1.341564e-02 1.375001e-02 1.408332e-02 1.441539e-02 1.474605e-02
#> [136] 1.507514e-02 1.540251e-02 1.572800e-02 1.605147e-02 1.637280e-02
#> [141] 1.669185e-02 1.700851e-02 1.732267e-02 1.763422e-02 1.794305e-02
#> [146] 1.824908e-02 1.855223e-02 1.885239e-02 1.914951e-02 1.944351e-02
#> [151] 1.973433e-02 2.002191e-02 2.030619e-02 2.058712e-02 2.086465e-02
#> [156] 2.113875e-02 2.140939e-02 2.167652e-02 2.194011e-02 2.220015e-02
#> [161] 2.245662e-02 2.270948e-02 2.295874e-02 2.320438e-02 2.344639e-02
#> [166] 2.368476e-02 2.391950e-02 2.415060e-02 2.437806e-02 2.460189e-02
#> [171] 2.482211e-02 2.503870e-02 2.525170e-02 2.546110e-02 2.566693e-02
#> [176] 2.586921e-02 2.606794e-02 2.626315e-02 2.645486e-02 2.664309e-02
#> [181] 2.682787e-02 2.700922e-02 2.718717e-02 2.736174e-02 2.753296e-02
#> [186] 2.770086e-02 2.786547e-02 2.802681e-02 2.818492e-02 2.833984e-02
#> [191] 2.849158e-02 2.864019e-02 2.878570e-02 2.892813e-02 2.906753e-02
#> [196] 2.920392e-02 2.933735e-02 2.946783e-02 2.959542e-02 2.972015e-02
#> [201] 2.984204e-02 2.996113e-02 3.007746e-02 3.019107e-02 3.030198e-02
#> [206] 3.041024e-02 3.051588e-02 3.061892e-02 3.071942e-02 3.081739e-02
#> [211] 3.091289e-02 3.100593e-02 3.109656e-02 3.118481e-02 3.127071e-02
#> [216] 3.135430e-02 3.143560e-02 3.151466e-02 3.159151e-02 3.166617e-02
#> [221] 3.173869e-02 3.180909e-02 3.187740e-02 3.194366e-02 3.200790e-02
#> [226] 3.207015e-02 3.213044e-02 3.218880e-02 3.224526e-02 3.229985e-02
#> [231] 3.235260e-02 3.240354e-02 3.245269e-02 3.250010e-02 3.254578e-02
#> [236] 3.258976e-02 3.263207e-02 3.267274e-02 3.271179e-02 3.274925e-02
#> [241] 3.278515e-02 3.281952e-02 3.285237e-02 3.288374e-02 3.291365e-02
#> [246] 3.294212e-02 3.296917e-02 3.299484e-02 3.301915e-02 3.304211e-02
#> [251] 3.306376e-02 3.308411e-02 3.310319e-02 3.312101e-02 3.313761e-02
#> [256] 3.315300e-02 3.316720e-02 3.318023e-02 3.319212e-02 3.320289e-02
#> [261] 3.321255e-02 3.322112e-02 3.322863e-02 3.323509e-02 3.324052e-02
#> [266] 3.324495e-02 3.324838e-02 3.325083e-02 3.325233e-02 3.325289e-02
#> [271] 3.325253e-02 3.325127e-02 3.324911e-02 3.324609e-02 3.324221e-02
#> [276] 3.323749e-02 3.323194e-02 3.322559e-02 3.321844e-02 3.321051e-02
#> [281] 3.320182e-02 3.319238e-02 3.318220e-02 3.317130e-02 3.315969e-02
#> [286] 3.314739e-02 3.313441e-02 3.312075e-02 3.310645e-02 3.309150e-02
#> [291] 3.307592e-02 3.305972e-02 3.304291e-02 3.302552e-02 3.300753e-02
#> [296] 3.298898e-02 3.296987e-02 3.295021e-02 3.293001e-02 3.290929e-02
#> [301] 3.288805e-02 3.286630e-02 3.284406e-02 3.282133e-02 3.279813e-02
#> [306] 3.277446e-02 3.275033e-02 3.272576e-02 3.270075e-02 3.267531e-02
#> [311] 3.264945e-02 3.262317e-02 3.259650e-02 3.256943e-02 3.254198e-02
#> [316] 3.251415e-02 3.248595e-02 3.245739e-02 3.242848e-02 3.239922e-02
#> [321] 3.236962e-02 3.233969e-02 3.230944e-02 3.227887e-02 3.224799e-02
#> [326] 3.221681e-02 3.218533e-02 3.215357e-02 3.212152e-02 3.208919e-02
#> [331] 3.205660e-02 3.202375e-02 3.199063e-02 3.195727e-02 3.192366e-02
#> [336] 3.188981e-02 3.185573e-02 3.182142e-02 3.178689e-02 3.175214e-02
#> [341] 3.171718e-02 3.168201e-02 3.164664e-02 3.161108e-02 3.157533e-02
#> [346] 3.153939e-02 3.150326e-02 3.146697e-02 3.143050e-02 3.139386e-02
#> [351] 3.135706e-02 3.132010e-02 3.128299e-02 3.124573e-02 3.120832e-02
#> [356] 3.117077e-02 3.113309e-02 3.109527e-02 3.105732e-02 3.101924e-02
#> [361] 3.098105e-02 3.094273e-02 3.090430e-02 3.086577e-02 3.082712e-02
#> [366] 3.078837e-02 3.074952e-02 3.071057e-02 3.067153e-02 3.063240e-02
#> [371] 3.059318e-02 3.055387e-02 3.051449e-02 3.047502e-02 3.043548e-02
#> [376] 3.039587e-02 3.035619e-02 3.031644e-02 3.027663e-02 3.023676e-02
#> [381] 3.019683e-02 3.015684e-02 3.011680e-02 3.007671e-02 3.003657e-02
#> [386] 2.999638e-02 2.995615e-02 2.991588e-02 2.987556e-02 2.983522e-02
#> [391] 2.979483e-02 2.975442e-02 2.971397e-02 2.967350e-02 2.963300e-02
#> [396] 2.959248e-02 2.955193e-02 2.951136e-02 2.947078e-02 2.943018e-02
#> [401] 2.938956e-02 2.934893e-02 2.930829e-02 2.926764e-02 2.922698e-02
#> [406] 2.918632e-02 2.914565e-02 2.910498e-02 2.906431e-02 2.902364e-02
#> [411] 2.898297e-02 2.894231e-02 2.890165e-02 2.886100e-02 2.882035e-02
#> [416] 2.877971e-02 2.873909e-02 2.869847e-02 2.865787e-02 2.861729e-02
#> [421] 2.857672e-02 2.853616e-02 2.849563e-02 2.845511e-02 2.841462e-02
#> [426] 2.837414e-02 2.833369e-02 2.829327e-02 2.825286e-02 2.821249e-02
#> [431] 2.817214e-02 2.813182e-02 2.809153e-02 2.805127e-02 2.801104e-02
#> [436] 2.797084e-02 2.793067e-02 2.789054e-02 2.785045e-02 2.781038e-02
#> [441] 2.777036e-02 2.773037e-02 2.769042e-02 2.765051e-02 2.761064e-02
#> [446] 2.757081e-02 2.753102e-02 2.749128e-02 2.745157e-02 2.741191e-02
#> [451] 2.737229e-02 2.733272e-02 2.729319e-02 2.725371e-02 2.721428e-02
#> [456] 2.717489e-02 2.713555e-02 2.709626e-02 2.705701e-02 2.701782e-02
#> [461] 2.697868e-02 2.693959e-02 2.690055e-02 2.686156e-02 2.682262e-02
#> [466] 2.678374e-02 2.674490e-02 2.670613e-02 2.666740e-02 2.662873e-02
#> [471] 2.659012e-02 2.655156e-02 2.651306e-02 2.647461e-02 2.643622e-02
#> [476] 2.639789e-02 2.635961e-02 2.632140e-02 2.628324e-02 2.624513e-02
#> [481] 2.620709e-02 2.616911e-02 2.613118e-02 2.609332e-02 2.605552e-02
#> [486] 2.601777e-02 2.598009e-02 2.594247e-02 2.590491e-02 2.586741e-02
#> [491] 2.582997e-02 2.579259e-02 2.575528e-02 2.571803e-02 2.568084e-02
#> [496] 2.564372e-02 2.560665e-02 2.556965e-02 2.553272e-02 2.549585e-02
#> [501] 2.545904e-02 2.542230e-02 2.538562e-02 2.534900e-02 2.531245e-02
#> [506] 2.527597e-02 2.523955e-02 2.520319e-02 2.516690e-02 2.513067e-02
#> [511] 2.509452e-02 2.505842e-02 2.502239e-02 2.498643e-02 2.495054e-02
#> [516] 2.491471e-02 2.487894e-02 2.484324e-02 2.480761e-02 2.477205e-02
#> [521] 2.473655e-02 2.470112e-02 2.466575e-02 2.463045e-02 2.459522e-02
#> [526] 2.456006e-02 2.452496e-02 2.448993e-02 2.445497e-02 2.442007e-02
#> [531] 2.438524e-02 2.435048e-02 2.431578e-02 2.428116e-02 2.424660e-02
#> [536] 2.421210e-02 2.417768e-02 2.414332e-02 2.410903e-02 2.407480e-02
#> [541] 2.404065e-02 2.400656e-02 2.397254e-02 2.393858e-02 2.390469e-02
#> [546] 2.387088e-02 2.383712e-02 2.380344e-02 2.376982e-02 2.373627e-02
#> [551] 2.370279e-02 2.366937e-02 2.363602e-02 2.360274e-02 2.356953e-02
#> [556] 2.353638e-02 2.350330e-02 2.347029e-02 2.343734e-02 2.340446e-02
#> [561] 2.337165e-02 2.333890e-02 2.330623e-02 2.327361e-02 2.324107e-02
#> [566] 2.320859e-02 2.317618e-02 2.314384e-02 2.311156e-02 2.307935e-02
#> [571] 2.304720e-02 2.301512e-02 2.298311e-02 2.295116e-02 2.291928e-02
#> [576] 2.288747e-02 2.285572e-02 2.282404e-02 2.279242e-02 2.276087e-02
#> [581] 2.272938e-02 2.269796e-02 2.266661e-02 2.263532e-02 2.260409e-02
#> [586] 2.257294e-02 2.254184e-02 2.251081e-02 2.247985e-02 2.244895e-02
#> [591] 2.241812e-02 2.238735e-02 2.235665e-02 2.232601e-02 2.229543e-02
#> [596] 2.226492e-02 2.223447e-02 2.220409e-02 2.217377e-02 2.214352e-02
#> [601] 2.211333e-02 2.208320e-02 2.205314e-02 2.202314e-02 2.199320e-02
#> [606] 2.196333e-02 2.193351e-02 2.190377e-02 2.187408e-02 2.184446e-02
#> [611] 2.181490e-02 2.178541e-02 2.175597e-02 2.172660e-02 2.169729e-02
#> [616] 2.166805e-02 2.163886e-02 2.160974e-02 2.158068e-02 2.155168e-02
#> [621] 2.152274e-02 2.149387e-02 2.146505e-02 2.143630e-02 2.140760e-02
#> [626] 2.137897e-02 2.135040e-02 2.132189e-02 2.129344e-02 2.126505e-02
#> [631] 2.123673e-02 2.120846e-02 2.118025e-02 2.115210e-02 2.112401e-02
#> [636] 2.109599e-02 2.106802e-02 2.104011e-02 2.101226e-02 2.098447e-02
#> [641] 2.095674e-02 2.092907e-02 2.090145e-02 2.087390e-02 2.084640e-02
#> [646] 2.081896e-02 2.079159e-02 2.076426e-02 2.073700e-02 2.070980e-02
#> [651] 2.068265e-02 2.065556e-02 2.062853e-02 2.060156e-02 2.057464e-02
#> [656] 2.054778e-02 2.052098e-02 2.049423e-02 2.046754e-02 2.044091e-02
#> [661] 2.041434e-02 2.038782e-02 2.036136e-02 2.033495e-02 2.030860e-02
#> [666] 2.028231e-02 2.025607e-02 2.022989e-02 2.020376e-02 2.017769e-02
#> [671] 2.015167e-02 2.012571e-02 2.009980e-02 2.007395e-02 2.004815e-02
#> [676] 2.002241e-02 1.999673e-02 1.997109e-02 1.994551e-02 1.991999e-02
#> [681] 1.989452e-02 1.986910e-02 1.984374e-02 1.981843e-02 1.979317e-02
#> [686] 1.976797e-02 1.974282e-02 1.971772e-02 1.969268e-02 1.966769e-02
#> [691] 1.964275e-02 1.961787e-02 1.959303e-02 1.956825e-02 1.954353e-02
#> [696] 1.951885e-02 1.949422e-02 1.946965e-02 1.944513e-02 1.942066e-02
#> [701] 1.939624e-02 1.937188e-02 1.934756e-02 1.932330e-02 1.929908e-02
#> [706] 1.927492e-02 1.925081e-02 1.922675e-02 1.920273e-02 1.917877e-02
#> [711] 1.915486e-02 1.913100e-02 1.910719e-02 1.908343e-02 1.905972e-02
#> [716] 1.903605e-02 1.901244e-02 1.898888e-02 1.896536e-02 1.894190e-02
#> [721] 1.891848e-02 1.889511e-02 1.887179e-02 1.884852e-02 1.882530e-02
#> [726] 1.880212e-02 1.877900e-02 1.875592e-02 1.873289e-02 1.870991e-02
#> [731] 1.868697e-02 1.866408e-02 1.864124e-02 1.861845e-02 1.859571e-02
#> [736] 1.857301e-02 1.855036e-02 1.852775e-02 1.850519e-02 1.848268e-02
#> [741] 1.846021e-02 1.843780e-02 1.841542e-02 1.839310e-02 1.837081e-02
#> [746] 1.834858e-02 1.832639e-02 1.830425e-02 1.828215e-02 1.826009e-02
#> [751] 1.823809e-02 1.821612e-02 1.819421e-02 1.817233e-02 1.815050e-02
#> [756] 1.812872e-02 1.810698e-02 1.808529e-02 1.806364e-02 1.804203e-02
#> [761] 1.802047e-02 1.799895e-02 1.797748e-02 1.795604e-02 1.793466e-02
#> [766] 1.791331e-02 1.789201e-02 1.787076e-02 1.784954e-02 1.782837e-02
#> [771] 1.780724e-02 1.778616e-02 1.776511e-02 1.774411e-02 1.772316e-02
#> [776] 1.770224e-02 1.768137e-02 1.766054e-02 1.763975e-02 1.761900e-02
#> [781] 1.759829e-02 1.757763e-02 1.755701e-02 1.753643e-02 1.751589e-02
#> [786] 1.749539e-02 1.747493e-02 1.745452e-02 1.743414e-02 1.741381e-02
#> [791] 1.739351e-02 1.737326e-02 1.735305e-02 1.733288e-02 1.731274e-02
#> [796] 1.729265e-02 1.727260e-02 1.725259e-02 1.723262e-02 1.721268e-02
#> [801] 1.719279e-02 1.717294e-02 1.715312e-02 1.713335e-02 1.711361e-02
#> [806] 1.709392e-02 1.707426e-02 1.705464e-02 1.703506e-02 1.701552e-02
#> [811] 1.699602e-02 1.697655e-02 1.695713e-02 1.693774e-02 1.691839e-02
#> [816] 1.689908e-02 1.687981e-02 1.686057e-02 1.684138e-02 1.682222e-02
#> [821] 1.680309e-02 1.678401e-02 1.676496e-02 1.674595e-02 1.672698e-02
#> [826] 1.670804e-02 1.668914e-02 1.667028e-02 1.665146e-02 1.663267e-02
#> [831] 1.661392e-02 1.659520e-02 1.657652e-02 1.655788e-02 1.653927e-02
#> [836] 1.652070e-02 1.650217e-02 1.648367e-02 1.646521e-02 1.644678e-02
#> [841] 1.642839e-02 1.641003e-02 1.639171e-02 1.637343e-02 1.635518e-02
#> [846] 1.633696e-02 1.631878e-02 1.630064e-02 1.628253e-02 1.626445e-02
#> [851] 1.624641e-02 1.622841e-02 1.621043e-02 1.619250e-02 1.617459e-02
#> [856] 1.615673e-02 1.613889e-02 1.612109e-02 1.610333e-02 1.608559e-02
#> [861] 1.606790e-02 1.605023e-02 1.603260e-02 1.601500e-02 1.599744e-02
#> [866] 1.597991e-02 1.596241e-02 1.594495e-02 1.592751e-02 1.591012e-02
#> [871] 1.589275e-02 1.587542e-02 1.585812e-02 1.584085e-02 1.582362e-02
#> [876] 1.580641e-02 1.578924e-02 1.577211e-02 1.575500e-02 1.573793e-02
#> [881] 1.572089e-02 1.570388e-02 1.568690e-02 1.566996e-02 1.565304e-02
#> [886] 1.563616e-02 1.561931e-02 1.560249e-02 1.558570e-02 1.556895e-02
#> [891] 1.555222e-02 1.553553e-02 1.551886e-02 1.550223e-02 1.548563e-02
#> [896] 1.546906e-02 1.545252e-02 1.543601e-02 1.541954e-02 1.540309e-02
#> [901] 1.538667e-02 1.537028e-02 1.535393e-02 1.533760e-02 1.532130e-02
#> [906] 1.530504e-02 1.528880e-02 1.527260e-02 1.525642e-02 1.524027e-02
#> [911] 1.522415e-02 1.520807e-02 1.519201e-02 1.517598e-02 1.515998e-02
#> [916] 1.514401e-02 1.512807e-02 1.511216e-02 1.509627e-02 1.508042e-02
#> [921] 1.506459e-02 1.504880e-02 1.503303e-02 1.501729e-02 1.500158e-02
#> [926] 1.498590e-02 1.497025e-02 1.495462e-02 1.493903e-02 1.492346e-02
#> [931] 1.490792e-02 1.489240e-02 1.487692e-02 1.486146e-02 1.484603e-02
#> [936] 1.483063e-02 1.481526e-02 1.479992e-02 1.478460e-02 1.476931e-02
#> [941] 1.475405e-02 1.473881e-02 1.472360e-02 1.470842e-02 1.469327e-02
#> [946] 1.467814e-02 1.466304e-02 1.464797e-02 1.463292e-02 1.461790e-02
#> [951] 1.460291e-02 1.458795e-02 1.457301e-02 1.455809e-02 1.454321e-02
#> [956] 1.452835e-02 1.451351e-02 1.449871e-02 1.448393e-02 1.446917e-02
#> [961] 1.445444e-02 1.443974e-02 1.442506e-02 1.441041e-02 1.439579e-02
#> [966] 1.438119e-02 1.436662e-02 1.435207e-02 1.433755e-02 1.432305e-02
#> [971] 1.430858e-02 1.429413e-02 1.427971e-02 1.426531e-02 1.425094e-02
#> [976] 1.423660e-02 1.422228e-02 1.420798e-02 1.419371e-02 1.417947e-02
#> [981] 1.416525e-02 1.415105e-02 1.413688e-02 1.412273e-02 1.410861e-02
#> [986] 1.409451e-02 1.408044e-02 1.406639e-02 1.405236e-02 1.403836e-02
#> [991] 1.402439e-02 1.401044e-02 1.399651e-02 1.398260e-02 1.396872e-02
#> [996] 1.395487e-02 1.394103e-02 1.392723e-02 1.391344e-02 1.389968e-02
bsmgamma("put", 20, 30, 0:2000 / 1000, 0.15, 0, 0.25)
#> [1] NaN 0.000000e+00 1.466952e-285 1.891202e-190 6.507218e-143
#> [6] 2.110429e-114 2.110388e-95 7.772451e-82 1.151556e-71 9.306827e-64
#> [11] 1.960533e-57 2.912113e-52 5.921115e-48 2.608485e-44 3.456156e-41
#> [16] 1.751678e-38 4.067128e-36 4.965646e-34 3.548842e-32 1.615775e-30
#> [21] 5.014901e-29 1.120810e-27 1.886514e-26 2.481584e-25 2.631112e-24
#> [26] 2.307521e-23 1.711079e-22 1.093007e-21 6.111603e-21 3.032900e-20
#> [31] 1.351835e-19 5.468560e-19 2.026105e-18 6.930528e-18 2.204207e-17
#> [36] 6.558977e-17 1.836246e-16 4.860591e-16 1.221902e-15 2.928874e-15
#> [41] 6.717952e-15 1.479272e-14 3.136196e-14 6.418794e-14 1.271291e-13
#> [46] 2.441919e-13 4.558082e-13 8.283114e-13 1.467896e-12 2.540721e-12
#> [51] 4.301253e-12 7.131439e-12 1.159385e-11 1.850252e-11 2.901585e-11
#> [56] 4.475658e-11 6.796442e-11 1.016877e-10 1.500209e-10 2.183952e-10
#> [61] 3.139299e-10 4.458536e-10 6.260024e-10 8.694041e-10 1.194957e-09
#> [66] 1.626211e-09 2.192261e-09 2.928754e-09 3.879027e-09 5.095371e-09
#> [71] 6.640429e-09 8.588743e-09 1.102843e-08 1.406302e-08 1.781340e-08
#> [76] 2.241998e-08 2.804489e-08 3.487444e-08 4.312156e-08 5.302856e-08
#> [81] 6.486980e-08 7.895463e-08 9.563038e-08 1.152854e-07 1.383522e-07
#> [86] 1.653106e-07 1.966913e-07 2.330787e-07 2.751146e-07 3.235015e-07
#> [91] 3.790056e-07 4.424605e-07 5.147703e-07 5.969128e-07 6.899426e-07
#> [96] 7.949945e-07 9.132859e-07 1.046120e-06 1.194889e-06 1.361076e-06
#> [101] 1.546258e-06 1.752107e-06 1.980395e-06 2.232992e-06 2.511872e-06
#> [106] 2.819112e-06 3.156893e-06 3.527503e-06 3.933339e-06 4.376904e-06
#> [111] 4.860811e-06 5.387782e-06 5.960649e-06 6.582354e-06 7.255948e-06
#> [116] 7.984590e-06 8.771549e-06 9.620202e-06 1.053403e-05 1.151663e-05
#> [121] 1.257168e-05 1.370299e-05 1.491446e-05 1.621007e-05 1.759392e-05
#> [126] 1.907020e-05 2.064320e-05 2.231728e-05 2.409690e-05 2.598661e-05
#> [131] 2.799104e-05 3.011488e-05 3.236293e-05 3.474003e-05 3.725111e-05
#> [136] 3.990116e-05 4.269524e-05 4.563846e-05 4.873598e-05 5.199303e-05
#> [141] 5.541488e-05 5.900686e-05 6.277430e-05 6.672262e-05 7.085723e-05
#> [146] 7.518361e-05 7.970724e-05 8.443363e-05 8.936830e-05 9.451682e-05
#> [151] 9.988473e-05 1.054776e-04 1.113010e-04 1.173605e-04 1.236617e-04
#> [156] 1.302102e-04 1.370114e-04 1.440710e-04 1.513945e-04 1.589874e-04
#> [161] 1.668551e-04 1.750032e-04 1.834371e-04 1.921621e-04 2.011837e-04
#> [166] 2.105072e-04 2.201379e-04 2.300810e-04 2.403417e-04 2.509252e-04
#> [171] 2.618366e-04 2.730810e-04 2.846633e-04 2.965885e-04 3.088615e-04
#> [176] 3.214871e-04 3.344701e-04 3.478151e-04 3.615268e-04 3.756098e-04
#> [181] 3.900685e-04 4.049074e-04 4.201307e-04 4.357428e-04 4.517478e-04
#> [186] 4.681500e-04 4.849532e-04 5.021614e-04 5.197786e-04 5.378085e-04
#> [191] 5.562549e-04 5.751213e-04 5.944113e-04 6.141283e-04 6.342758e-04
#> [196] 6.548569e-04 6.758750e-04 6.973331e-04 7.192342e-04 7.415812e-04
#> [201] 7.643771e-04 7.876245e-04 8.113261e-04 8.354846e-04 8.601023e-04
#> [206] 8.851818e-04 9.107252e-04 9.367349e-04 9.632129e-04 9.901613e-04
#> [211] 1.017582e-03 1.045477e-03 1.073848e-03 1.102697e-03 1.132025e-03
#> [216] 1.161834e-03 1.192125e-03 1.222900e-03 1.254159e-03 1.285905e-03
#> [221] 1.318138e-03 1.350859e-03 1.384069e-03 1.417769e-03 1.451959e-03
#> [226] 1.486641e-03 1.521815e-03 1.557482e-03 1.593641e-03 1.630294e-03
#> [231] 1.667441e-03 1.705081e-03 1.743215e-03 1.781843e-03 1.820966e-03
#> [236] 1.860582e-03 1.900692e-03 1.941296e-03 1.982393e-03 2.023982e-03
#> [241] 2.066065e-03 2.108639e-03 2.151705e-03 2.195261e-03 2.239308e-03
#> [246] 2.283844e-03 2.328869e-03 2.374381e-03 2.420380e-03 2.466865e-03
#> [251] 2.513834e-03 2.561287e-03 2.609223e-03 2.657639e-03 2.706536e-03
#> [256] 2.755911e-03 2.805763e-03 2.856091e-03 2.906893e-03 2.958168e-03
#> [261] 3.009914e-03 3.062130e-03 3.114813e-03 3.167963e-03 3.221577e-03
#> [266] 3.275653e-03 3.330190e-03 3.385186e-03 3.440638e-03 3.496546e-03
#> [271] 3.552906e-03 3.609717e-03 3.666977e-03 3.724684e-03 3.782834e-03
#> [276] 3.841427e-03 3.900460e-03 3.959931e-03 4.019837e-03 4.080176e-03
#> [281] 4.140946e-03 4.202144e-03 4.263769e-03 4.325816e-03 4.388285e-03
#> [286] 4.451172e-03 4.514475e-03 4.578192e-03 4.642319e-03 4.706855e-03
#> [291] 4.771797e-03 4.837141e-03 4.902886e-03 4.969029e-03 5.035566e-03
#> [296] 5.102496e-03 5.169816e-03 5.237522e-03 5.305612e-03 5.374084e-03
#> [301] 5.442934e-03 5.512159e-03 5.581758e-03 5.651726e-03 5.722062e-03
#> [306] 5.792762e-03 5.863823e-03 5.935243e-03 6.007018e-03 6.079147e-03
#> [311] 6.151625e-03 6.224449e-03 6.297618e-03 6.371128e-03 6.444976e-03
#> [316] 6.519159e-03 6.593674e-03 6.668518e-03 6.743688e-03 6.819182e-03
#> [321] 6.894996e-03 6.971127e-03 7.047573e-03 7.124330e-03 7.201395e-03
#> [326] 7.278766e-03 7.356439e-03 7.434411e-03 7.512680e-03 7.591242e-03
#> [331] 7.670094e-03 7.749234e-03 7.828659e-03 7.908364e-03 7.988349e-03
#> [336] 8.068608e-03 8.149141e-03 8.229942e-03 8.311011e-03 8.392342e-03
#> [341] 8.473935e-03 8.555785e-03 8.637890e-03 8.720246e-03 8.802852e-03
#> [346] 8.885703e-03 8.968797e-03 9.052131e-03 9.135702e-03 9.219507e-03
#> [351] 9.303544e-03 9.387809e-03 9.472299e-03 9.557012e-03 9.641945e-03
#> [356] 9.727094e-03 9.812457e-03 9.898032e-03 9.983815e-03 1.006980e-02
#> [361] 1.015599e-02 1.024238e-02 1.032897e-02 1.041575e-02 1.050273e-02
#> [366] 1.058989e-02 1.067724e-02 1.076477e-02 1.085248e-02 1.094036e-02
#> [371] 1.102843e-02 1.111666e-02 1.120507e-02 1.129364e-02 1.138238e-02
#> [376] 1.147127e-02 1.156033e-02 1.164954e-02 1.173891e-02 1.182842e-02
#> [381] 1.191809e-02 1.200790e-02 1.209785e-02 1.218794e-02 1.227818e-02
#> [386] 1.236854e-02 1.245904e-02 1.254967e-02 1.264043e-02 1.273131e-02
#> [391] 1.282232e-02 1.291344e-02 1.300469e-02 1.309605e-02 1.318752e-02
#> [396] 1.327910e-02 1.337079e-02 1.346259e-02 1.355449e-02 1.364649e-02
#> [401] 1.373859e-02 1.383079e-02 1.392308e-02 1.401546e-02 1.410793e-02
#> [406] 1.420049e-02 1.429314e-02 1.438586e-02 1.447867e-02 1.457155e-02
#> [411] 1.466451e-02 1.475755e-02 1.485065e-02 1.494383e-02 1.503707e-02
#> [416] 1.513038e-02 1.522375e-02 1.531718e-02 1.541067e-02 1.550422e-02
#> [421] 1.559782e-02 1.569147e-02 1.578517e-02 1.587892e-02 1.597272e-02
#> [426] 1.606656e-02 1.616045e-02 1.625437e-02 1.634834e-02 1.644234e-02
#> [431] 1.653637e-02 1.663044e-02 1.672454e-02 1.681866e-02 1.691282e-02
#> [436] 1.700699e-02 1.710119e-02 1.719542e-02 1.728966e-02 1.738392e-02
#> [441] 1.747819e-02 1.757248e-02 1.766678e-02 1.776110e-02 1.785542e-02
#> [446] 1.794974e-02 1.804408e-02 1.813841e-02 1.823275e-02 1.832709e-02
#> [451] 1.842143e-02 1.851576e-02 1.861009e-02 1.870441e-02 1.879873e-02
#> [456] 1.889303e-02 1.898732e-02 1.908160e-02 1.917587e-02 1.927012e-02
#> [461] 1.936435e-02 1.945857e-02 1.955276e-02 1.964693e-02 1.974108e-02
#> [466] 1.983520e-02 1.992929e-02 2.002336e-02 2.011740e-02 2.021141e-02
#> [471] 2.030538e-02 2.039932e-02 2.049323e-02 2.058710e-02 2.068093e-02
#> [476] 2.077472e-02 2.086847e-02 2.096218e-02 2.105585e-02 2.114947e-02
#> [481] 2.124305e-02 2.133658e-02 2.143006e-02 2.152349e-02 2.161687e-02
#> [486] 2.171020e-02 2.180347e-02 2.189669e-02 2.198985e-02 2.208296e-02
#> [491] 2.217601e-02 2.226900e-02 2.236192e-02 2.245479e-02 2.254759e-02
#> [496] 2.264033e-02 2.273301e-02 2.282561e-02 2.291815e-02 2.301063e-02
#> [501] 2.310303e-02 2.319536e-02 2.328762e-02 2.337981e-02 2.347192e-02
#> [506] 2.356396e-02 2.365592e-02 2.374781e-02 2.383961e-02 2.393134e-02
#> [511] 2.402299e-02 2.411456e-02 2.420605e-02 2.429745e-02 2.438877e-02
#> [516] 2.448000e-02 2.457115e-02 2.466222e-02 2.475319e-02 2.484408e-02
#> [521] 2.493488e-02 2.502559e-02 2.511620e-02 2.520673e-02 2.529716e-02
#> [526] 2.538750e-02 2.547775e-02 2.556790e-02 2.565795e-02 2.574791e-02
#> [531] 2.583777e-02 2.592753e-02 2.601719e-02 2.610675e-02 2.619621e-02
#> [536] 2.628557e-02 2.637483e-02 2.646399e-02 2.655304e-02 2.664198e-02
#> [541] 2.673083e-02 2.681956e-02 2.690819e-02 2.699672e-02 2.708513e-02
#> [546] 2.717344e-02 2.726163e-02 2.734972e-02 2.743770e-02 2.752556e-02
#> [551] 2.761332e-02 2.770096e-02 2.778849e-02 2.787590e-02 2.796320e-02
#> [556] 2.805039e-02 2.813746e-02 2.822441e-02 2.831125e-02 2.839797e-02
#> [561] 2.848457e-02 2.857105e-02 2.865742e-02 2.874367e-02 2.882979e-02
#> [566] 2.891580e-02 2.900168e-02 2.908745e-02 2.917309e-02 2.925861e-02
#> [571] 2.934400e-02 2.942927e-02 2.951442e-02 2.959945e-02 2.968434e-02
#> [576] 2.976912e-02 2.985377e-02 2.993829e-02 3.002268e-02 3.010695e-02
#> [581] 3.019109e-02 3.027510e-02 3.035898e-02 3.044274e-02 3.052636e-02
#> [586] 3.060986e-02 3.069323e-02 3.077646e-02 3.085957e-02 3.094254e-02
#> [591] 3.102538e-02 3.110809e-02 3.119067e-02 3.127311e-02 3.135542e-02
#> [596] 3.143760e-02 3.151965e-02 3.160156e-02 3.168333e-02 3.176498e-02
#> [601] 3.184648e-02 3.192785e-02 3.200909e-02 3.209019e-02 3.217115e-02
#> [606] 3.225198e-02 3.233267e-02 3.241322e-02 3.249364e-02 3.257391e-02
#> [611] 3.265405e-02 3.273405e-02 3.281392e-02 3.289364e-02 3.297323e-02
#> [616] 3.305267e-02 3.313198e-02 3.321115e-02 3.329017e-02 3.336906e-02
#> [621] 3.344781e-02 3.352641e-02 3.360488e-02 3.368320e-02 3.376139e-02
#> [626] 3.383943e-02 3.391733e-02 3.399509e-02 3.407270e-02 3.415018e-02
#> [631] 3.422751e-02 3.430470e-02 3.438174e-02 3.445865e-02 3.453541e-02
#> [636] 3.461202e-02 3.468850e-02 3.476483e-02 3.484101e-02 3.491706e-02
#> [641] 3.499296e-02 3.506871e-02 3.514432e-02 3.521979e-02 3.529511e-02
#> [646] 3.537029e-02 3.544532e-02 3.552020e-02 3.559495e-02 3.566954e-02
#> [651] 3.574400e-02 3.581830e-02 3.589246e-02 3.596648e-02 3.604035e-02
#> [656] 3.611408e-02 3.618765e-02 3.626109e-02 3.633437e-02 3.640752e-02
#> [661] 3.648051e-02 3.655336e-02 3.662606e-02 3.669862e-02 3.677103e-02
#> [666] 3.684329e-02 3.691541e-02 3.698738e-02 3.705921e-02 3.713088e-02
#> [671] 3.720241e-02 3.727380e-02 3.734504e-02 3.741613e-02 3.748707e-02
#> [676] 3.755787e-02 3.762852e-02 3.769902e-02 3.776938e-02 3.783959e-02
#> [681] 3.790965e-02 3.797957e-02 3.804934e-02 3.811896e-02 3.818843e-02
#> [686] 3.825776e-02 3.832694e-02 3.839598e-02 3.846487e-02 3.853361e-02
#> [691] 3.860220e-02 3.867065e-02 3.873895e-02 3.880710e-02 3.887510e-02
#> [696] 3.894296e-02 3.901067e-02 3.907824e-02 3.914566e-02 3.921293e-02
#> [701] 3.928006e-02 3.934703e-02 3.941387e-02 3.948055e-02 3.954709e-02
#> [706] 3.961348e-02 3.967973e-02 3.974583e-02 3.981178e-02 3.987758e-02
#> [711] 3.994324e-02 4.000876e-02 4.007413e-02 4.013935e-02 4.020442e-02
#> [716] 4.026935e-02 4.033413e-02 4.039877e-02 4.046326e-02 4.052761e-02
#> [721] 4.059181e-02 4.065586e-02 4.071977e-02 4.078354e-02 4.084715e-02
#> [726] 4.091063e-02 4.097396e-02 4.103714e-02 4.110018e-02 4.116307e-02
#> [731] 4.122582e-02 4.128842e-02 4.135088e-02 4.141319e-02 4.147536e-02
#> [736] 4.153738e-02 4.159926e-02 4.166100e-02 4.172259e-02 4.178404e-02
#> [741] 4.184534e-02 4.190650e-02 4.196752e-02 4.202839e-02 4.208912e-02
#> [746] 4.214971e-02 4.221015e-02 4.227045e-02 4.233061e-02 4.239062e-02
#> [751] 4.245049e-02 4.251022e-02 4.256980e-02 4.262925e-02 4.268855e-02
#> [756] 4.274771e-02 4.280672e-02 4.286560e-02 4.292433e-02 4.298292e-02
#> [761] 4.304137e-02 4.309967e-02 4.315784e-02 4.321587e-02 4.327375e-02
#> [766] 4.333149e-02 4.338909e-02 4.344656e-02 4.350388e-02 4.356106e-02
#> [771] 4.361810e-02 4.367500e-02 4.373176e-02 4.378838e-02 4.384486e-02
#> [776] 4.390120e-02 4.395740e-02 4.401346e-02 4.406939e-02 4.412517e-02
#> [781] 4.418082e-02 4.423632e-02 4.429169e-02 4.434692e-02 4.440201e-02
#> [786] 4.445697e-02 4.451178e-02 4.456646e-02 4.462100e-02 4.467540e-02
#> [791] 4.472967e-02 4.478380e-02 4.483779e-02 4.489164e-02 4.494536e-02
#> [796] 4.499894e-02 4.505239e-02 4.510570e-02 4.515887e-02 4.521191e-02
#> [801] 4.526481e-02 4.531757e-02 4.537021e-02 4.542270e-02 4.547506e-02
#> [806] 4.552729e-02 4.557938e-02 4.563133e-02 4.568316e-02 4.573484e-02
#> [811] 4.578640e-02 4.583782e-02 4.588910e-02 4.594026e-02 4.599128e-02
#> [816] 4.604216e-02 4.609291e-02 4.614354e-02 4.619402e-02 4.624438e-02
#> [821] 4.629460e-02 4.634469e-02 4.639465e-02 4.644448e-02 4.649418e-02
#> [826] 4.654374e-02 4.659317e-02 4.664248e-02 4.669165e-02 4.674069e-02
#> [831] 4.678960e-02 4.683838e-02 4.688703e-02 4.693555e-02 4.698394e-02
#> [836] 4.703220e-02 4.708033e-02 4.712833e-02 4.717621e-02 4.722395e-02
#> [841] 4.727156e-02 4.731905e-02 4.736641e-02 4.741364e-02 4.746074e-02
#> [846] 4.750772e-02 4.755457e-02 4.760129e-02 4.764788e-02 4.769435e-02
#> [851] 4.774069e-02 4.778690e-02 4.783298e-02 4.787894e-02 4.792478e-02
#> [856] 4.797049e-02 4.801607e-02 4.806153e-02 4.810686e-02 4.815207e-02
#> [861] 4.819715e-02 4.824210e-02 4.828694e-02 4.833165e-02 4.837623e-02
#> [866] 4.842069e-02 4.846503e-02 4.850924e-02 4.855333e-02 4.859730e-02
#> [871] 4.864114e-02 4.868486e-02 4.872846e-02 4.877194e-02 4.881529e-02
#> [876] 4.885852e-02 4.890163e-02 4.894462e-02 4.898749e-02 4.903023e-02
#> [881] 4.907286e-02 4.911536e-02 4.915775e-02 4.920001e-02 4.924215e-02
#> [886] 4.928418e-02 4.932608e-02 4.936786e-02 4.940953e-02 4.945107e-02
#> [891] 4.949250e-02 4.953380e-02 4.957499e-02 4.961606e-02 4.965701e-02
#> [896] 4.969784e-02 4.973856e-02 4.977916e-02 4.981964e-02 4.986000e-02
#> [901] 4.990025e-02 4.994038e-02 4.998039e-02 5.002028e-02 5.006006e-02
#> [906] 5.009973e-02 5.013927e-02 5.017871e-02 5.021802e-02 5.025722e-02
#> [911] 5.029631e-02 5.033528e-02 5.037414e-02 5.041288e-02 5.045151e-02
#> [916] 5.049002e-02 5.052842e-02 5.056670e-02 5.060488e-02 5.064294e-02
#> [921] 5.068088e-02 5.071871e-02 5.075643e-02 5.079404e-02 5.083154e-02
#> [926] 5.086892e-02 5.090619e-02 5.094335e-02 5.098040e-02 5.101733e-02
#> [931] 5.105416e-02 5.109087e-02 5.112748e-02 5.116397e-02 5.120035e-02
#> [936] 5.123662e-02 5.127279e-02 5.130884e-02 5.134478e-02 5.138062e-02
#> [941] 5.141634e-02 5.145196e-02 5.148746e-02 5.152286e-02 5.155815e-02
#> [946] 5.159333e-02 5.162841e-02 5.166337e-02 5.169823e-02 5.173298e-02
#> [951] 5.176762e-02 5.180216e-02 5.183659e-02 5.187091e-02 5.190513e-02
#> [956] 5.193924e-02 5.197324e-02 5.200714e-02 5.204093e-02 5.207462e-02
#> [961] 5.210820e-02 5.214168e-02 5.217505e-02 5.220832e-02 5.224148e-02
#> [966] 5.227454e-02 5.230749e-02 5.234034e-02 5.237309e-02 5.240573e-02
#> [971] 5.243827e-02 5.247071e-02 5.250304e-02 5.253527e-02 5.256740e-02
#> [976] 5.259943e-02 5.263135e-02 5.266317e-02 5.269489e-02 5.272651e-02
#> [981] 5.275803e-02 5.278945e-02 5.282076e-02 5.285197e-02 5.288309e-02
#> [986] 5.291410e-02 5.294501e-02 5.297583e-02 5.300654e-02 5.303715e-02
#> [991] 5.306767e-02 5.309808e-02 5.312839e-02 5.315861e-02 5.318873e-02
#> [996] 5.321875e-02 5.324867e-02 5.327849e-02 5.330821e-02 5.333784e-02
#> [1001] 5.336737e-02 5.339680e-02 5.342614e-02 5.345537e-02 5.348451e-02
#> [1006] 5.351356e-02 5.354251e-02 5.357136e-02 5.360011e-02 5.362877e-02
#> [1011] 5.365733e-02 5.368580e-02 5.371417e-02 5.374245e-02 5.377063e-02
#> [1016] 5.379872e-02 5.382671e-02 5.385461e-02 5.388242e-02 5.391013e-02
#> [1021] 5.393774e-02 5.396527e-02 5.399270e-02 5.402003e-02 5.404727e-02
#> [1026] 5.407442e-02 5.410148e-02 5.412845e-02 5.415532e-02 5.418210e-02
#> [1031] 5.420879e-02 5.423538e-02 5.426189e-02 5.428830e-02 5.431462e-02
#> [1036] 5.434085e-02 5.436699e-02 5.439304e-02 5.441900e-02 5.444486e-02
#> [1041] 5.447064e-02 5.449633e-02 5.452193e-02 5.454743e-02 5.457285e-02
#> [1046] 5.459818e-02 5.462342e-02 5.464857e-02 5.467364e-02 5.469861e-02
#> [1051] 5.472349e-02 5.474829e-02 5.477300e-02 5.479762e-02 5.482215e-02
#> [1056] 5.484660e-02 5.487096e-02 5.489523e-02 5.491941e-02 5.494351e-02
#> [1061] 5.496752e-02 5.499144e-02 5.501528e-02 5.503903e-02 5.506270e-02
#> [1066] 5.508628e-02 5.510977e-02 5.513318e-02 5.515651e-02 5.517974e-02
#> [1071] 5.520290e-02 5.522597e-02 5.524895e-02 5.527185e-02 5.529467e-02
#> [1076] 5.531740e-02 5.534005e-02 5.536261e-02 5.538509e-02 5.540749e-02
#> [1081] 5.542980e-02 5.545203e-02 5.547418e-02 5.549624e-02 5.551823e-02
#> [1086] 5.554013e-02 5.556195e-02 5.558368e-02 5.560534e-02 5.562691e-02
#> [1091] 5.564840e-02 5.566981e-02 5.569114e-02 5.571239e-02 5.573355e-02
#> [1096] 5.575464e-02 5.577564e-02 5.579657e-02 5.581741e-02 5.583818e-02
#> [1101] 5.585886e-02 5.587947e-02 5.590000e-02 5.592044e-02 5.594081e-02
#> [1106] 5.596110e-02 5.598131e-02 5.600144e-02 5.602149e-02 5.604146e-02
#> [1111] 5.606136e-02 5.608118e-02 5.610092e-02 5.612058e-02 5.614016e-02
#> [1116] 5.615967e-02 5.617910e-02 5.619845e-02 5.621773e-02 5.623693e-02
#> [1121] 5.625605e-02 5.627510e-02 5.629407e-02 5.631296e-02 5.633178e-02
#> [1126] 5.635052e-02 5.636919e-02 5.638778e-02 5.640630e-02 5.642474e-02
#> [1131] 5.644310e-02 5.646139e-02 5.647961e-02 5.649775e-02 5.651582e-02
#> [1136] 5.653381e-02 5.655173e-02 5.656957e-02 5.658734e-02 5.660504e-02
#> [1141] 5.662266e-02 5.664022e-02 5.665769e-02 5.667510e-02 5.669243e-02
#> [1146] 5.670969e-02 5.672688e-02 5.674399e-02 5.676103e-02 5.677800e-02
#> [1151] 5.679490e-02 5.681173e-02 5.682848e-02 5.684516e-02 5.686178e-02
#> [1156] 5.687832e-02 5.689479e-02 5.691119e-02 5.692751e-02 5.694377e-02
#> [1161] 5.695996e-02 5.697608e-02 5.699212e-02 5.700810e-02 5.702401e-02
#> [1166] 5.703985e-02 5.705561e-02 5.707131e-02 5.708694e-02 5.710250e-02
#> [1171] 5.711800e-02 5.713342e-02 5.714877e-02 5.716406e-02 5.717928e-02
#> [1176] 5.719443e-02 5.720951e-02 5.722452e-02 5.723947e-02 5.725434e-02
#> [1181] 5.726915e-02 5.728390e-02 5.729857e-02 5.731318e-02 5.732773e-02
#> [1186] 5.734220e-02 5.735661e-02 5.737095e-02 5.738523e-02 5.739944e-02
#> [1191] 5.741358e-02 5.742766e-02 5.744167e-02 5.745562e-02 5.746950e-02
#> [1196] 5.748332e-02 5.749707e-02 5.751075e-02 5.752437e-02 5.753793e-02
#> [1201] 5.755142e-02 5.756485e-02 5.757821e-02 5.759151e-02 5.760474e-02
#> [1206] 5.761792e-02 5.763102e-02 5.764407e-02 5.765704e-02 5.766996e-02
#> [1211] 5.768281e-02 5.769560e-02 5.770833e-02 5.772099e-02 5.773360e-02
#> [1216] 5.774613e-02 5.775861e-02 5.777103e-02 5.778338e-02 5.779567e-02
#> [1221] 5.780790e-02 5.782006e-02 5.783217e-02 5.784421e-02 5.785619e-02
#> [1226] 5.786811e-02 5.787997e-02 5.789177e-02 5.790351e-02 5.791519e-02
#> [1231] 5.792680e-02 5.793836e-02 5.794985e-02 5.796129e-02 5.797267e-02
#> [1236] 5.798398e-02 5.799524e-02 5.800643e-02 5.801757e-02 5.802865e-02
#> [1241] 5.803967e-02 5.805063e-02 5.806153e-02 5.807237e-02 5.808315e-02
#> [1246] 5.809387e-02 5.810454e-02 5.811515e-02 5.812570e-02 5.813619e-02
#> [1251] 5.814662e-02 5.815699e-02 5.816731e-02 5.817757e-02 5.818777e-02
#> [1256] 5.819792e-02 5.820801e-02 5.821804e-02 5.822801e-02 5.823793e-02
#> [1261] 5.824779e-02 5.825759e-02 5.826734e-02 5.827703e-02 5.828666e-02
#> [1266] 5.829624e-02 5.830576e-02 5.831523e-02 5.832464e-02 5.833400e-02
#> [1271] 5.834330e-02 5.835254e-02 5.836173e-02 5.837086e-02 5.837994e-02
#> [1276] 5.838897e-02 5.839794e-02 5.840685e-02 5.841571e-02 5.842452e-02
#> [1281] 5.843327e-02 5.844197e-02 5.845061e-02 5.845920e-02 5.846773e-02
#> [1286] 5.847622e-02 5.848464e-02 5.849302e-02 5.850134e-02 5.850961e-02
#> [1291] 5.851783e-02 5.852599e-02 5.853410e-02 5.854215e-02 5.855016e-02
#> [1296] 5.855811e-02 5.856601e-02 5.857386e-02 5.858165e-02 5.858939e-02
#> [1301] 5.859708e-02 5.860472e-02 5.861231e-02 5.861985e-02 5.862733e-02
#> [1306] 5.863476e-02 5.864214e-02 5.864947e-02 5.865675e-02 5.866398e-02
#> [1311] 5.867116e-02 5.867829e-02 5.868536e-02 5.869239e-02 5.869937e-02
#> [1316] 5.870629e-02 5.871317e-02 5.871999e-02 5.872677e-02 5.873349e-02
#> [1321] 5.874017e-02 5.874680e-02 5.875337e-02 5.875990e-02 5.876638e-02
#> [1326] 5.877281e-02 5.877919e-02 5.878552e-02 5.879180e-02 5.879803e-02
#> [1331] 5.880422e-02 5.881036e-02 5.881644e-02 5.882248e-02 5.882848e-02
#> [1336] 5.883442e-02 5.884032e-02 5.884616e-02 5.885196e-02 5.885772e-02
#> [1341] 5.886342e-02 5.886908e-02 5.887469e-02 5.888025e-02 5.888577e-02
#> [1346] 5.889124e-02 5.889666e-02 5.890204e-02 5.890737e-02 5.891265e-02
#> [1351] 5.891788e-02 5.892307e-02 5.892822e-02 5.893331e-02 5.893836e-02
#> [1356] 5.894337e-02 5.894833e-02 5.895324e-02 5.895811e-02 5.896293e-02
#> [1361] 5.896771e-02 5.897244e-02 5.897713e-02 5.898177e-02 5.898636e-02
#> [1366] 5.899091e-02 5.899542e-02 5.899988e-02 5.900430e-02 5.900867e-02
#> [1371] 5.901300e-02 5.901728e-02 5.902152e-02 5.902572e-02 5.902987e-02
#> [1376] 5.903398e-02 5.903804e-02 5.904206e-02 5.904603e-02 5.904997e-02
#> [1381] 5.905386e-02 5.905770e-02 5.906150e-02 5.906526e-02 5.906898e-02
#> [1386] 5.907265e-02 5.907628e-02 5.907987e-02 5.908342e-02 5.908692e-02
#> [1391] 5.909038e-02 5.909380e-02 5.909717e-02 5.910050e-02 5.910379e-02
#> [1396] 5.910704e-02 5.911025e-02 5.911342e-02 5.911654e-02 5.911962e-02
#> [1401] 5.912266e-02 5.912566e-02 5.912862e-02 5.913153e-02 5.913441e-02
#> [1406] 5.913724e-02 5.914004e-02 5.914279e-02 5.914550e-02 5.914817e-02
#> [1411] 5.915080e-02 5.915339e-02 5.915594e-02 5.915845e-02 5.916092e-02
#> [1416] 5.916335e-02 5.916573e-02 5.916808e-02 5.917039e-02 5.917266e-02
#> [1421] 5.917489e-02 5.917708e-02 5.917923e-02 5.918134e-02 5.918341e-02
#> [1426] 5.918544e-02 5.918743e-02 5.918939e-02 5.919130e-02 5.919318e-02
#> [1431] 5.919502e-02 5.919681e-02 5.919857e-02 5.920029e-02 5.920198e-02
#> [1436] 5.920362e-02 5.920523e-02 5.920680e-02 5.920832e-02 5.920982e-02
#> [1441] 5.921127e-02 5.921269e-02 5.921406e-02 5.921540e-02 5.921671e-02
#> [1446] 5.921797e-02 5.921920e-02 5.922039e-02 5.922155e-02 5.922266e-02
#> [1451] 5.922374e-02 5.922478e-02 5.922579e-02 5.922676e-02 5.922769e-02
#> [1456] 5.922858e-02 5.922944e-02 5.923026e-02 5.923105e-02 5.923180e-02
#> [1461] 5.923251e-02 5.923319e-02 5.923383e-02 5.923443e-02 5.923500e-02
#> [1466] 5.923553e-02 5.923603e-02 5.923649e-02 5.923692e-02 5.923731e-02
#> [1471] 5.923766e-02 5.923798e-02 5.923827e-02 5.923852e-02 5.923873e-02
#> [1476] 5.923891e-02 5.923905e-02 5.923916e-02 5.923924e-02 5.923928e-02
#> [1481] 5.923928e-02 5.923925e-02 5.923919e-02 5.923909e-02 5.923896e-02
#> [1486] 5.923879e-02 5.923859e-02 5.923836e-02 5.923809e-02 5.923778e-02
#> [1491] 5.923745e-02 5.923708e-02 5.923667e-02 5.923624e-02 5.923576e-02
#> [1496] 5.923526e-02 5.923472e-02 5.923415e-02 5.923354e-02 5.923291e-02
#> [1501] 5.923224e-02 5.923153e-02 5.923080e-02 5.923003e-02 5.922922e-02
#> [1506] 5.922839e-02 5.922752e-02 5.922662e-02 5.922569e-02 5.922472e-02
#> [1511] 5.922372e-02 5.922270e-02 5.922163e-02 5.922054e-02 5.921941e-02
#> [1516] 5.921826e-02 5.921707e-02 5.921584e-02 5.921459e-02 5.921331e-02
#> [1521] 5.921199e-02 5.921064e-02 5.920926e-02 5.920785e-02 5.920641e-02
#> [1526] 5.920493e-02 5.920343e-02 5.920189e-02 5.920033e-02 5.919873e-02
#> [1531] 5.919710e-02 5.919544e-02 5.919375e-02 5.919203e-02 5.919028e-02
#> [1536] 5.918850e-02 5.918669e-02 5.918485e-02 5.918297e-02 5.918107e-02
#> [1541] 5.917914e-02 5.917717e-02 5.917518e-02 5.917316e-02 5.917110e-02
#> [1546] 5.916902e-02 5.916691e-02 5.916477e-02 5.916260e-02 5.916039e-02
#> [1551] 5.915816e-02 5.915590e-02 5.915361e-02 5.915130e-02 5.914895e-02
#> [1556] 5.914657e-02 5.914416e-02 5.914173e-02 5.913927e-02 5.913677e-02
#> [1561] 5.913425e-02 5.913170e-02 5.912912e-02 5.912651e-02 5.912388e-02
#> [1566] 5.912121e-02 5.911852e-02 5.911580e-02 5.911305e-02 5.911027e-02
#> [1571] 5.910747e-02 5.910463e-02 5.910177e-02 5.909888e-02 5.909596e-02
#> [1576] 5.909302e-02 5.909004e-02 5.908704e-02 5.908402e-02 5.908096e-02
#> [1581] 5.907788e-02 5.907477e-02 5.907163e-02 5.906846e-02 5.906527e-02
#> [1586] 5.906205e-02 5.905880e-02 5.905553e-02 5.905223e-02 5.904890e-02
#> [1591] 5.904555e-02 5.904217e-02 5.903876e-02 5.903532e-02 5.903186e-02
#> [1596] 5.902837e-02 5.902486e-02 5.902132e-02 5.901775e-02 5.901416e-02
#> [1601] 5.901054e-02 5.900689e-02 5.900322e-02 5.899952e-02 5.899580e-02
#> [1606] 5.899205e-02 5.898828e-02 5.898448e-02 5.898065e-02 5.897680e-02
#> [1611] 5.897292e-02 5.896901e-02 5.896508e-02 5.896113e-02 5.895715e-02
#> [1616] 5.895315e-02 5.894911e-02 5.894506e-02 5.894098e-02 5.893687e-02
#> [1621] 5.893274e-02 5.892859e-02 5.892441e-02 5.892020e-02 5.891597e-02
#> [1626] 5.891171e-02 5.890744e-02 5.890313e-02 5.889880e-02 5.889445e-02
#> [1631] 5.889007e-02 5.888567e-02 5.888124e-02 5.887679e-02 5.887232e-02
#> [1636] 5.886782e-02 5.886330e-02 5.885875e-02 5.885418e-02 5.884958e-02
#> [1641] 5.884497e-02 5.884032e-02 5.883566e-02 5.883097e-02 5.882625e-02
#> [1646] 5.882152e-02 5.881676e-02 5.881197e-02 5.880716e-02 5.880233e-02
#> [1651] 5.879748e-02 5.879260e-02 5.878770e-02 5.878278e-02 5.877783e-02
#> [1656] 5.877286e-02 5.876787e-02 5.876285e-02 5.875782e-02 5.875276e-02
#> [1661] 5.874767e-02 5.874257e-02 5.873744e-02 5.873228e-02 5.872711e-02
#> [1666] 5.872191e-02 5.871669e-02 5.871145e-02 5.870619e-02 5.870090e-02
#> [1671] 5.869560e-02 5.869027e-02 5.868491e-02 5.867954e-02 5.867414e-02
#> [1676] 5.866872e-02 5.866328e-02 5.865782e-02 5.865234e-02 5.864683e-02
#> [1681] 5.864130e-02 5.863576e-02 5.863019e-02 5.862459e-02 5.861898e-02
#> [1686] 5.861335e-02 5.860769e-02 5.860201e-02 5.859631e-02 5.859059e-02
#> [1691] 5.858485e-02 5.857909e-02 5.857331e-02 5.856750e-02 5.856168e-02
#> [1696] 5.855583e-02 5.854996e-02 5.854408e-02 5.853817e-02 5.853224e-02
#> [1701] 5.852629e-02 5.852032e-02 5.851433e-02 5.850831e-02 5.850228e-02
#> [1706] 5.849623e-02 5.849016e-02 5.848406e-02 5.847795e-02 5.847182e-02
#> [1711] 5.846566e-02 5.845949e-02 5.845330e-02 5.844708e-02 5.844085e-02
#> [1716] 5.843459e-02 5.842832e-02 5.842203e-02 5.841571e-02 5.840938e-02
#> [1721] 5.840303e-02 5.839666e-02 5.839026e-02 5.838385e-02 5.837742e-02
#> [1726] 5.837097e-02 5.836450e-02 5.835801e-02 5.835151e-02 5.834498e-02
#> [1731] 5.833843e-02 5.833186e-02 5.832528e-02 5.831868e-02 5.831205e-02
#> [1736] 5.830541e-02 5.829875e-02 5.829207e-02 5.828537e-02 5.827865e-02
#> [1741] 5.827192e-02 5.826516e-02 5.825839e-02 5.825160e-02 5.824479e-02
#> [1746] 5.823796e-02 5.823111e-02 5.822424e-02 5.821736e-02 5.821046e-02
#> [1751] 5.820353e-02 5.819660e-02 5.818964e-02 5.818266e-02 5.817567e-02
#> [1756] 5.816866e-02 5.816163e-02 5.815458e-02 5.814751e-02 5.814043e-02
#> [1761] 5.813333e-02 5.812621e-02 5.811907e-02 5.811192e-02 5.810474e-02
#> [1766] 5.809755e-02 5.809035e-02 5.808312e-02 5.807588e-02 5.806862e-02
#> [1771] 5.806134e-02 5.805405e-02 5.804673e-02 5.803941e-02 5.803206e-02
#> [1776] 5.802469e-02 5.801731e-02 5.800992e-02 5.800250e-02 5.799507e-02
#> [1781] 5.798762e-02 5.798015e-02 5.797267e-02 5.796517e-02 5.795765e-02
#> [1786] 5.795012e-02 5.794257e-02 5.793500e-02 5.792742e-02 5.791982e-02
#> [1791] 5.791220e-02 5.790457e-02 5.789692e-02 5.788925e-02 5.788157e-02
#> [1796] 5.787387e-02 5.786616e-02 5.785843e-02 5.785068e-02 5.784292e-02
#> [1801] 5.783514e-02 5.782734e-02 5.781953e-02 5.781170e-02 5.780385e-02
#> [1806] 5.779599e-02 5.778812e-02 5.778023e-02 5.777232e-02 5.776439e-02
#> [1811] 5.775646e-02 5.774850e-02 5.774053e-02 5.773254e-02 5.772454e-02
#> [1816] 5.771652e-02 5.770849e-02 5.770044e-02 5.769238e-02 5.768430e-02
#> [1821] 5.767620e-02 5.766809e-02 5.765997e-02 5.765183e-02 5.764367e-02
#> [1826] 5.763550e-02 5.762732e-02 5.761912e-02 5.761090e-02 5.760267e-02
#> [1831] 5.759442e-02 5.758616e-02 5.757788e-02 5.756959e-02 5.756129e-02
#> [1836] 5.755297e-02 5.754463e-02 5.753628e-02 5.752792e-02 5.751954e-02
#> [1841] 5.751115e-02 5.750274e-02 5.749431e-02 5.748588e-02 5.747742e-02
#> [1846] 5.746896e-02 5.746048e-02 5.745198e-02 5.744347e-02 5.743495e-02
#> [1851] 5.742641e-02 5.741786e-02 5.740929e-02 5.740071e-02 5.739212e-02
#> [1856] 5.738351e-02 5.737489e-02 5.736625e-02 5.735760e-02 5.734894e-02
#> [1861] 5.734026e-02 5.733157e-02 5.732286e-02 5.731414e-02 5.730541e-02
#> [1866] 5.729666e-02 5.728790e-02 5.727913e-02 5.727034e-02 5.726154e-02
#> [1871] 5.725272e-02 5.724389e-02 5.723505e-02 5.722620e-02 5.721733e-02
#> [1876] 5.720845e-02 5.719955e-02 5.719064e-02 5.718172e-02 5.717279e-02
#> [1881] 5.716384e-02 5.715488e-02 5.714590e-02 5.713691e-02 5.712791e-02
#> [1886] 5.711890e-02 5.710987e-02 5.710083e-02 5.709178e-02 5.708272e-02
#> [1891] 5.707364e-02 5.706455e-02 5.705544e-02 5.704633e-02 5.703720e-02
#> [1896] 5.702806e-02 5.701890e-02 5.700973e-02 5.700055e-02 5.699136e-02
#> [1901] 5.698216e-02 5.697294e-02 5.696371e-02 5.695447e-02 5.694522e-02
#> [1906] 5.693595e-02 5.692667e-02 5.691738e-02 5.690807e-02 5.689876e-02
#> [1911] 5.688943e-02 5.688009e-02 5.687074e-02 5.686137e-02 5.685200e-02
#> [1916] 5.684261e-02 5.683321e-02 5.682380e-02 5.681437e-02 5.680494e-02
#> [1921] 5.679549e-02 5.678603e-02 5.677656e-02 5.676707e-02 5.675758e-02
#> [1926] 5.674807e-02 5.673855e-02 5.672902e-02 5.671948e-02 5.670993e-02
#> [1931] 5.670036e-02 5.669079e-02 5.668120e-02 5.667160e-02 5.666199e-02
#> [1936] 5.665237e-02 5.664273e-02 5.663309e-02 5.662343e-02 5.661377e-02
#> [1941] 5.660409e-02 5.659440e-02 5.658470e-02 5.657498e-02 5.656526e-02
#> [1946] 5.655553e-02 5.654578e-02 5.653603e-02 5.652626e-02 5.651648e-02
#> [1951] 5.650669e-02 5.649689e-02 5.648708e-02 5.647726e-02 5.646742e-02
#> [1956] 5.645758e-02 5.644772e-02 5.643786e-02 5.642798e-02 5.641810e-02
#> [1961] 5.640820e-02 5.639829e-02 5.638837e-02 5.637844e-02 5.636850e-02
#> [1966] 5.635855e-02 5.634859e-02 5.633862e-02 5.632864e-02 5.631865e-02
#> [1971] 5.630865e-02 5.629863e-02 5.628861e-02 5.627858e-02 5.626853e-02
#> [1976] 5.625848e-02 5.624842e-02 5.623834e-02 5.622826e-02 5.621816e-02
#> [1981] 5.620806e-02 5.619795e-02 5.618782e-02 5.617769e-02 5.616754e-02
#> [1986] 5.615739e-02 5.614722e-02 5.613705e-02 5.612686e-02 5.611667e-02
#> [1991] 5.610647e-02 5.609625e-02 5.608603e-02 5.607580e-02 5.606555e-02
#> [1996] 5.605530e-02 5.604504e-02 5.603477e-02 5.602449e-02 5.601420e-02
#> [2001] 5.600389e-02
bsmtheta(c("call", "put"), c(50, 49, 48, 47), 45, 0.25, 0.13, 0.01, 0.2)
#> [1] -6.145512 -1.184449 -6.539154 -1.453346
bsmtheta("call", 50, 45, 0.25, 0.13, 0.01, 1:1000 / 1000)
#> [1] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [7] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [13] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [19] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [25] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [31] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [37] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [43] -5.164180 -5.164180 -5.164180 -5.164180 -5.164180 -5.164180
#> [49] -5.164180 -5.164180 -5.164180 -5.164180 -5.164181 -5.164182
#> [55] -5.164183 -5.164185 -5.164187 -5.164191 -5.164197 -5.164204
#> [61] -5.164214 -5.164228 -5.164246 -5.164269 -5.164299 -5.164337
#> [67] -5.164385 -5.164444 -5.164517 -5.164606 -5.164713 -5.164842
#> [73] -5.164994 -5.165174 -5.165384 -5.165628 -5.165909 -5.166233
#> [79] -5.166602 -5.167020 -5.167493 -5.168024 -5.168618 -5.169279
#> [85] -5.170013 -5.170822 -5.171713 -5.172690 -5.173756 -5.174918
#> [91] -5.176178 -5.177542 -5.179013 -5.180596 -5.182295 -5.184114
#> [97] -5.186057 -5.188126 -5.190326 -5.192661 -5.195132 -5.197744
#> [103] -5.200498 -5.203399 -5.206447 -5.209646 -5.212998 -5.216504
#> [109] -5.220167 -5.223988 -5.227968 -5.232109 -5.236412 -5.240879
#> [115] -5.245509 -5.250304 -5.255264 -5.260389 -5.265681 -5.271138
#> [121] -5.276761 -5.282550 -5.288505 -5.294626 -5.300911 -5.307361
#> [127] -5.313974 -5.320751 -5.327690 -5.334791 -5.342052 -5.349472
#> [133] -5.357051 -5.364787 -5.372679 -5.380726 -5.388926 -5.397278
#> [139] -5.405781 -5.414434 -5.423233 -5.432180 -5.441270 -5.450504
#> [145] -5.459880 -5.469395 -5.479048 -5.488839 -5.498764 -5.508822
#> [151] -5.519012 -5.529331 -5.539779 -5.550353 -5.561052 -5.571874
#> [157] -5.582817 -5.593880 -5.605060 -5.616357 -5.627769 -5.639293
#> [163] -5.650928 -5.662673 -5.674526 -5.686485 -5.698548 -5.710714
#> [169] -5.722982 -5.735349 -5.747815 -5.760377 -5.773034 -5.785784
#> [175] -5.798627 -5.811560 -5.824582 -5.837692 -5.850887 -5.864168
#> [181] -5.877531 -5.890977 -5.904503 -5.918108 -5.931791 -5.945550
#> [187] -5.959385 -5.973293 -5.987274 -6.001326 -6.015449 -6.029640
#> [193] -6.043899 -6.058225 -6.072616 -6.087071 -6.101589 -6.116170
#> [199] -6.130811 -6.145512 -6.160272 -6.175089 -6.189964 -6.204894
#> [205] -6.219879 -6.234917 -6.250009 -6.265152 -6.280346 -6.295591
#> [211] -6.310884 -6.326226 -6.341615 -6.357050 -6.372532 -6.388058
#> [217] -6.403628 -6.419242 -6.434898 -6.450596 -6.466334 -6.482114
#> [223] -6.497932 -6.513790 -6.529685 -6.545618 -6.561588 -6.577594
#> [229] -6.593635 -6.609711 -6.625821 -6.641965 -6.658142 -6.674351
#> [235] -6.690591 -6.706863 -6.723166 -6.739498 -6.755860 -6.772251
#> [241] -6.788671 -6.805118 -6.821593 -6.838095 -6.854623 -6.871177
#> [247] -6.887756 -6.904361 -6.920990 -6.937643 -6.954320 -6.971020
#> [253] -6.987743 -7.004488 -7.021255 -7.038044 -7.054854 -7.071685
#> [259] -7.088536 -7.105407 -7.122298 -7.139208 -7.156137 -7.173085
#> [265] -7.190051 -7.207035 -7.224036 -7.241055 -7.258091 -7.275143
#> [271] -7.292212 -7.309296 -7.326397 -7.343513 -7.360644 -7.377789
#> [277] -7.394950 -7.412125 -7.429314 -7.446516 -7.463732 -7.480962
#> [283] -7.498204 -7.515460 -7.532727 -7.550008 -7.567300 -7.584604
#> [289] -7.601920 -7.619247 -7.636585 -7.653934 -7.671295 -7.688665
#> [295] -7.706046 -7.723438 -7.740839 -7.758250 -7.775670 -7.793100
#> [301] -7.810540 -7.827988 -7.845445 -7.862911 -7.880386 -7.897868
#> [307] -7.915359 -7.932858 -7.950365 -7.967880 -7.985402 -8.002932
#> [313] -8.020469 -8.038013 -8.055565 -8.073123 -8.090687 -8.108259
#> [319] -8.125836 -8.143420 -8.161011 -8.178607 -8.196209 -8.213817
#> [325] -8.231431 -8.249051 -8.266675 -8.284306 -8.301941 -8.319582
#> [331] -8.337227 -8.354878 -8.372533 -8.390193 -8.407857 -8.425526
#> [337] -8.443200 -8.460878 -8.478559 -8.496245 -8.513936 -8.531629
#> [343] -8.549327 -8.567029 -8.584734 -8.602443 -8.620155 -8.637871
#> [349] -8.655590 -8.673312 -8.691037 -8.708766 -8.726498 -8.744232
#> [355] -8.761969 -8.779709 -8.797452 -8.815198 -8.832946 -8.850696
#> [361] -8.868449 -8.886205 -8.903962 -8.921722 -8.939484 -8.957249
#> [367] -8.975015 -8.992783 -9.010554 -9.028326 -9.046100 -9.063875
#> [373] -9.081653 -9.099432 -9.117213 -9.134995 -9.152779 -9.170564
#> [379] -9.188350 -9.206138 -9.223927 -9.241718 -9.259510 -9.277302
#> [385] -9.295096 -9.312891 -9.330687 -9.348484 -9.366282 -9.384081
#> [391] -9.401880 -9.419681 -9.437482 -9.455284 -9.473086 -9.490890
#> [397] -9.508693 -9.526498 -9.544303 -9.562108 -9.579914 -9.597720
#> [403] -9.615526 -9.633333 -9.651141 -9.668948 -9.686756 -9.704564
#> [409] -9.722372 -9.740180 -9.757988 -9.775797 -9.793605 -9.811414
#> [415] -9.829222 -9.847030 -9.864839 -9.882647 -9.900455 -9.918263
#> [421] -9.936071 -9.953878 -9.971686 -9.989493 -10.007299 -10.025106
#> [427] -10.042912 -10.060717 -10.078523 -10.096328 -10.114132 -10.131936
#> [433] -10.149739 -10.167542 -10.185345 -10.203146 -10.220948 -10.238748
#> [439] -10.256548 -10.274348 -10.292146 -10.309944 -10.327742 -10.345538
#> [445] -10.363334 -10.381129 -10.398923 -10.416717 -10.434509 -10.452301
#> [451] -10.470092 -10.487882 -10.505671 -10.523459 -10.541246 -10.559033
#> [457] -10.576818 -10.594602 -10.612386 -10.630168 -10.647949 -10.665729
#> [463] -10.683508 -10.701286 -10.719063 -10.736839 -10.754614 -10.772387
#> [469] -10.790160 -10.807931 -10.825701 -10.843470 -10.861237 -10.879003
#> [475] -10.896768 -10.914532 -10.932295 -10.950056 -10.967816 -10.985575
#> [481] -11.003332 -11.021088 -11.038842 -11.056596 -11.074347 -11.092098
#> [487] -11.109847 -11.127595 -11.145341 -11.163086 -11.180829 -11.198571
#> [493] -11.216311 -11.234050 -11.251787 -11.269523 -11.287258 -11.304990
#> [499] -11.322722 -11.340452 -11.358180 -11.375906 -11.393631 -11.411355
#> [505] -11.429077 -11.446797 -11.464516 -11.482233 -11.499948 -11.517662
#> [511] -11.535374 -11.553084 -11.570793 -11.588500 -11.606206 -11.623909
#> [517] -11.641611 -11.659311 -11.677010 -11.694707 -11.712402 -11.730095
#> [523] -11.747787 -11.765476 -11.783164 -11.800851 -11.818535 -11.836218
#> [529] -11.853898 -11.871577 -11.889255 -11.906930 -11.924603 -11.942275
#> [535] -11.959945 -11.977613 -11.995279 -12.012943 -12.030605 -12.048266
#> [541] -12.065924 -12.083581 -12.101236 -12.118888 -12.136539 -12.154188
#> [547] -12.171835 -12.189480 -12.207123 -12.224765 -12.242404 -12.260041
#> [553] -12.277676 -12.295310 -12.312941 -12.330570 -12.348197 -12.365823
#> [559] -12.383446 -12.401067 -12.418687 -12.436304 -12.453919 -12.471532
#> [565] -12.489143 -12.506752 -12.524359 -12.541964 -12.559567 -12.577168
#> [571] -12.594766 -12.612363 -12.629958 -12.647550 -12.665140 -12.682729
#> [577] -12.700315 -12.717899 -12.735481 -12.753060 -12.770638 -12.788213
#> [583] -12.805787 -12.823358 -12.840927 -12.858494 -12.876059 -12.893621
#> [589] -12.911181 -12.928740 -12.946296 -12.963849 -12.981401 -12.998951
#> [595] -13.016498 -13.034043 -13.051586 -13.069126 -13.086665 -13.104201
#> [601] -13.121735 -13.139266 -13.156796 -13.174323 -13.191848 -13.209371
#> [607] -13.226891 -13.244410 -13.261925 -13.279439 -13.296951 -13.314460
#> [613] -13.331967 -13.349471 -13.366973 -13.384473 -13.401971 -13.419467
#> [619] -13.436960 -13.454450 -13.471939 -13.489425 -13.506909 -13.524390
#> [625] -13.541870 -13.559346 -13.576821 -13.594293 -13.611763 -13.629230
#> [631] -13.646696 -13.664158 -13.681619 -13.699077 -13.716532 -13.733986
#> [637] -13.751437 -13.768885 -13.786331 -13.803775 -13.821217 -13.838656
#> [643] -13.856092 -13.873526 -13.890958 -13.908387 -13.925814 -13.943239
#> [649] -13.960661 -13.978081 -13.995498 -14.012913 -14.030325 -14.047735
#> [655] -14.065143 -14.082548 -14.099951 -14.117351 -14.134749 -14.152144
#> [661] -14.169537 -14.186927 -14.204315 -14.221700 -14.239083 -14.256464
#> [667] -14.273842 -14.291217 -14.308590 -14.325961 -14.343329 -14.360694
#> [673] -14.378058 -14.395418 -14.412776 -14.430132 -14.447485 -14.464835
#> [679] -14.482183 -14.499528 -14.516871 -14.534212 -14.551549 -14.568885
#> [685] -14.586217 -14.603548 -14.620875 -14.638200 -14.655523 -14.672843
#> [691] -14.690160 -14.707475 -14.724788 -14.742097 -14.759405 -14.776709
#> [697] -14.794011 -14.811311 -14.828607 -14.845902 -14.863193 -14.880482
#> [703] -14.897769 -14.915053 -14.932334 -14.949613 -14.966889 -14.984162
#> [709] -15.001433 -15.018701 -15.035967 -15.053230 -15.070490 -15.087748
#> [715] -15.105003 -15.122255 -15.139505 -15.156752 -15.173997 -15.191238
#> [721] -15.208478 -15.225714 -15.242948 -15.260179 -15.277408 -15.294634
#> [727] -15.311857 -15.329077 -15.346295 -15.363511 -15.380723 -15.397933
#> [733] -15.415140 -15.432344 -15.449546 -15.466745 -15.483942 -15.501135
#> [739] -15.518326 -15.535514 -15.552700 -15.569883 -15.587063 -15.604240
#> [745] -15.621415 -15.638587 -15.655756 -15.672923 -15.690086 -15.707247
#> [751] -15.724406 -15.741561 -15.758714 -15.775864 -15.793011 -15.810156
#> [757] -15.827297 -15.844436 -15.861573 -15.878706 -15.895837 -15.912965
#> [763] -15.930090 -15.947212 -15.964332 -15.981449 -15.998563 -16.015674
#> [769] -16.032783 -16.049888 -16.066991 -16.084091 -16.101188 -16.118283
#> [775] -16.135375 -16.152463 -16.169549 -16.186633 -16.203713 -16.220791
#> [781] -16.237865 -16.254937 -16.272006 -16.289073 -16.306136 -16.323197
#> [787] -16.340255 -16.357309 -16.374361 -16.391411 -16.408457 -16.425501
#> [793] -16.442541 -16.459579 -16.476614 -16.493646 -16.510675 -16.527702
#> [799] -16.544725 -16.561746 -16.578763 -16.595778 -16.612790 -16.629799
#> [805] -16.646805 -16.663808 -16.680809 -16.697806 -16.714801 -16.731792
#> [811] -16.748781 -16.765767 -16.782750 -16.799730 -16.816707 -16.833681
#> [817] -16.850652 -16.867621 -16.884586 -16.901549 -16.918508 -16.935465
#> [823] -16.952418 -16.969369 -16.986317 -17.003262 -17.020203 -17.037142
#> [829] -17.054078 -17.071011 -17.087941 -17.104868 -17.121793 -17.138714
#> [835] -17.155632 -17.172547 -17.189459 -17.206368 -17.223275 -17.240178
#> [841] -17.257078 -17.273976 -17.290870 -17.307761 -17.324649 -17.341535
#> [847] -17.358417 -17.375296 -17.392173 -17.409046 -17.425916 -17.442783
#> [853] -17.459647 -17.476509 -17.493367 -17.510222 -17.527074 -17.543923
#> [859] -17.560769 -17.577612 -17.594452 -17.611289 -17.628123 -17.644954
#> [865] -17.661781 -17.678606 -17.695428 -17.712246 -17.729062 -17.745874
#> [871] -17.762683 -17.779490 -17.796293 -17.813093 -17.829890 -17.846684
#> [877] -17.863475 -17.880263 -17.897048 -17.913829 -17.930608 -17.947383
#> [883] -17.964156 -17.980925 -17.997691 -18.014454 -18.031214 -18.047971
#> [889] -18.064724 -18.081475 -18.098222 -18.114967 -18.131708 -18.148446
#> [895] -18.165181 -18.181913 -18.198641 -18.215367 -18.232089 -18.248808
#> [901] -18.265524 -18.282237 -18.298947 -18.315654 -18.332357 -18.349057
#> [907] -18.365754 -18.382448 -18.399139 -18.415827 -18.432511 -18.449192
#> [913] -18.465870 -18.482545 -18.499217 -18.515886 -18.532551 -18.549213
#> [919] -18.565872 -18.582528 -18.599180 -18.615830 -18.632476 -18.649119
#> [925] -18.665758 -18.682395 -18.699028 -18.715658 -18.732285 -18.748908
#> [931] -18.765529 -18.782146 -18.798760 -18.815370 -18.831978 -18.848582
#> [937] -18.865183 -18.881781 -18.898375 -18.914966 -18.931554 -18.948139
#> [943] -18.964720 -18.981298 -18.997873 -19.014445 -19.031013 -19.047578
#> [949] -19.064140 -19.080699 -19.097254 -19.113806 -19.130355 -19.146900
#> [955] -19.163442 -19.179981 -19.196516 -19.213048 -19.229577 -19.246103
#> [961] -19.262625 -19.279144 -19.295660 -19.312172 -19.328681 -19.345187
#> [967] -19.361689 -19.378188 -19.394684 -19.411176 -19.427665 -19.444151
#> [973] -19.460634 -19.477113 -19.493588 -19.510061 -19.526530 -19.542995
#> [979] -19.559458 -19.575916 -19.592372 -19.608824 -19.625273 -19.641719
#> [985] -19.658161 -19.674599 -19.691035 -19.707467 -19.723895 -19.740320
#> [991] -19.756742 -19.773161 -19.789576 -19.805987 -19.822396 -19.838801
#> [997] -19.855202 -19.871600 -19.887995 -19.904386
bsmtheta("put", 20, 30, 0:2000 / 1000, 0.15, 0, 0.25)
#> [1] NaN 4.499325 4.498650 4.497975 4.497301 4.496626 4.495952 4.495277
#> [9] 4.494603 4.493929 4.493255 4.492581 4.491907 4.491234 4.490560 4.489886
#> [17] 4.489213 4.488540 4.487866 4.487193 4.486520 4.485847 4.485174 4.484502
#> [25] 4.483829 4.483157 4.482484 4.481812 4.481140 4.480468 4.479795 4.479124
#> [33] 4.478452 4.477780 4.477108 4.476437 4.475765 4.475094 4.474423 4.473752
#> [41] 4.473081 4.472410 4.471739 4.471068 4.470398 4.469727 4.469057 4.468387
#> [49] 4.467716 4.467046 4.466376 4.465706 4.465037 4.464367 4.463697 4.463028
#> [57] 4.462358 4.461689 4.461020 4.460351 4.459682 4.459013 4.458344 4.457675
#> [65] 4.457007 4.456338 4.455670 4.455001 4.454333 4.453665 4.452997 4.452329
#> [73] 4.451661 4.450994 4.450326 4.449658 4.448991 4.448324 4.447656 4.446989
#> [81] 4.446322 4.445655 4.444988 4.444321 4.443654 4.442987 4.442320 4.441653
#> [89] 4.440987 4.440320 4.439653 4.438986 4.438320 4.437653 4.436986 4.436319
#> [97] 4.435652 4.434985 4.434318 4.433650 4.432983 4.432315 4.431647 4.430979
#> [105] 4.430311 4.429642 4.428973 4.428304 4.427634 4.426964 4.426294 4.425622
#> [113] 4.424951 4.424279 4.423606 4.422932 4.422258 4.421583 4.420908 4.420231
#> [121] 4.419554 4.418875 4.418196 4.417515 4.416834 4.416151 4.415467 4.414781
#> [129] 4.414095 4.413406 4.412717 4.412026 4.411333 4.410638 4.409942 4.409243
#> [137] 4.408543 4.407841 4.407137 4.406430 4.405722 4.405011 4.404297 4.403581
#> [145] 4.402863 4.402142 4.401418 4.400692 4.399962 4.399230 4.398495 4.397756
#> [153] 4.397015 4.396270 4.395521 4.394769 4.394014 4.393255 4.392492 4.391726
#> [161] 4.390956 4.390181 4.389403 4.388620 4.387834 4.387043 4.386247 4.385448
#> [169] 4.384643 4.383834 4.383020 4.382202 4.381379 4.380550 4.379717 4.378879
#> [177] 4.378035 4.377186 4.376332 4.375473 4.374608 4.373737 4.372861 4.371979
#> [185] 4.371091 4.370198 4.369299 4.368393 4.367482 4.366565 4.365641 4.364711
#> [193] 4.363775 4.362833 4.361884 4.360929 4.359967 4.358998 4.358023 4.357042
#> [201] 4.356053 4.355058 4.354056 4.353047 4.352031 4.351008 4.349978 4.348941
#> [209] 4.347897 4.346846 4.345788 4.344722 4.343649 4.342569 4.341481 4.340386
#> [217] 4.339284 4.338174 4.337056 4.335931 4.334799 4.333659 4.332511 4.331356
#> [225] 4.330193 4.329023 4.327844 4.326658 4.325465 4.324263 4.323054 4.321837
#> [233] 4.320612 4.319379 4.318139 4.316891 4.315634 4.314370 4.313098 4.311819
#> [241] 4.310531 4.309235 4.307932 4.306621 4.305301 4.303974 4.302639 4.301296
#> [249] 4.299945 4.298586 4.297219 4.295845 4.294462 4.293072 4.291673 4.290267
#> [257] 4.288853 4.287431 4.286001 4.284564 4.283118 4.281665 4.280204 4.278735
#> [265] 4.277258 4.275773 4.274281 4.272781 4.271274 4.269758 4.268235 4.266704
#> [273] 4.265166 4.263620 4.262066 4.260505 4.258936 4.257360 4.255776 4.254184
#> [281] 4.252585 4.250979 4.249365 4.247744 4.246116 4.244480 4.242837 4.241186
#> [289] 4.239528 4.237863 4.236191 4.234512 4.232825 4.231131 4.229431 4.227723
#> [297] 4.226008 4.224286 4.222557 4.220821 4.219079 4.217329 4.215573 4.213810
#> [305] 4.212040 4.210263 4.208479 4.206689 4.204893 4.203089 4.201279 4.199463
#> [313] 4.197640 4.195811 4.193975 4.192133 4.190284 4.188429 4.186568 4.184701
#> [321] 4.182827 4.180947 4.179062 4.177170 4.175272 4.173367 4.171457 4.169541
#> [329] 4.167620 4.165692 4.163758 4.161819 4.159874 4.157923 4.155967 4.154005
#> [337] 4.152037 4.150064 4.148085 4.146101 4.144111 4.142116 4.140115 4.138110
#> [345] 4.136099 4.134082 4.132061 4.130034 4.128002 4.125966 4.123924 4.121877
#> [353] 4.119825 4.117768 4.115707 4.113640 4.111569 4.109493 4.107412 4.105326
#> [361] 4.103236 4.101141 4.099042 4.096938 4.094829 4.092717 4.090599 4.088478
#> [369] 4.086352 4.084221 4.082087 4.079948 4.077805 4.075658 4.073506 4.071351
#> [377] 4.069192 4.067028 4.064861 4.062690 4.060514 4.058335 4.056152 4.053966
#> [385] 4.051776 4.049581 4.047384 4.045182 4.042977 4.040769 4.038557 4.036341
#> [393] 4.034123 4.031900 4.029674 4.027445 4.025213 4.022977 4.020739 4.018496
#> [401] 4.016251 4.014003 4.011751 4.009497 4.007239 4.004979 4.002715 4.000449
#> [409] 3.998180 3.995908 3.993633 3.991355 3.989075 3.986791 3.984506 3.982217
#> [417] 3.979926 3.977632 3.975336 3.973037 3.970736 3.968432 3.966126 3.963818
#> [425] 3.961507 3.959193 3.956878 3.954560 3.952240 3.949918 3.947593 3.945267
#> [433] 3.942938 3.940608 3.938275 3.935940 3.933603 3.931264 3.928924 3.926581
#> [441] 3.924237 3.921890 3.919542 3.917192 3.914841 3.912487 3.910132 3.907775
#> [449] 3.905417 3.903057 3.900695 3.898332 3.895967 3.893601 3.891233 3.888864
#> [457] 3.886494 3.884122 3.881748 3.879373 3.876997 3.874620 3.872242 3.869862
#> [465] 3.867481 3.865098 3.862715 3.860330 3.857945 3.855558 3.853170 3.850781
#> [473] 3.848391 3.846000 3.843608 3.841216 3.838822 3.836427 3.834032 3.831635
#> [481] 3.829238 3.826840 3.824441 3.822041 3.819641 3.817240 3.814838 3.812436
#> [489] 3.810033 3.807629 3.805225 3.802820 3.800415 3.798009 3.795602 3.793195
#> [497] 3.790787 3.788379 3.785971 3.783562 3.781153 3.778743 3.776333 3.773923
#> [505] 3.771512 3.769101 3.766690 3.764279 3.761867 3.759455 3.757043 3.754631
#> [513] 3.752218 3.749805 3.747393 3.744980 3.742567 3.740154 3.737740 3.735327
#> [521] 3.732914 3.730501 3.728088 3.725674 3.723261 3.720848 3.718435 3.716022
#> [529] 3.713610 3.711197 3.708784 3.706372 3.703960 3.701548 3.699136 3.696724
#> [537] 3.694313 3.691902 3.689491 3.687081 3.684671 3.682261 3.679851 3.677442
#> [545] 3.675033 3.672625 3.670217 3.667809 3.665402 3.662995 3.660588 3.658182
#> [553] 3.655777 3.653372 3.650968 3.648564 3.646160 3.643757 3.641355 3.638953
#> [561] 3.636552 3.634151 3.631751 3.629352 3.626953 3.624555 3.622158 3.619761
#> [569] 3.617365 3.614970 3.612575 3.610181 3.607788 3.605395 3.603003 3.600612
#> [577] 3.598222 3.595833 3.593444 3.591056 3.588669 3.586283 3.583898 3.581513
#> [585] 3.579130 3.576747 3.574365 3.571984 3.569604 3.567225 3.564847 3.562469
#> [593] 3.560093 3.557718 3.555343 3.552970 3.550597 3.548226 3.545855 3.543486
#> [601] 3.541117 3.538750 3.536383 3.534018 3.531654 3.529291 3.526928 3.524567
#> [609] 3.522207 3.519849 3.517491 3.515134 3.512779 3.510424 3.508071 3.505719
#> [617] 3.503368 3.501018 3.498669 3.496322 3.493976 3.491631 3.489287 3.486944
#> [625] 3.484603 3.482263 3.479924 3.477586 3.475250 3.472914 3.470580 3.468248
#> [633] 3.465916 3.463586 3.461257 3.458930 3.456604 3.454279 3.451955 3.449633
#> [641] 3.447312 3.444992 3.442674 3.440357 3.438041 3.435727 3.433414 3.431103
#> [649] 3.428793 3.426484 3.424177 3.421871 3.419566 3.417263 3.414961 3.412661
#> [657] 3.410362 3.408065 3.405769 3.403474 3.401181 3.398889 3.396599 3.394310
#> [665] 3.392023 3.389737 3.387453 3.385170 3.382889 3.380609 3.378330 3.376053
#> [673] 3.373778 3.371504 3.369232 3.366961 3.364691 3.362423 3.360157 3.357892
#> [681] 3.355629 3.353367 3.351107 3.348849 3.346592 3.344336 3.342082 3.339830
#> [689] 3.337579 3.335330 3.333082 3.330836 3.328591 3.326348 3.324107 3.321867
#> [697] 3.319629 3.317393 3.315158 3.312925 3.310693 3.308463 3.306234 3.304007
#> [705] 3.301782 3.299558 3.297337 3.295116 3.292897 3.290680 3.288465 3.286251
#> [713] 3.284039 3.281828 3.279620 3.277412 3.275207 3.273003 3.270801 3.268600
#> [721] 3.266401 3.264204 3.262009 3.259815 3.257623 3.255432 3.253243 3.251056
#> [729] 3.248871 3.246687 3.244505 3.242324 3.240146 3.237969 3.235794 3.233620
#> [737] 3.231448 3.229278 3.227109 3.224943 3.222778 3.220614 3.218453 3.216293
#> [745] 3.214135 3.211978 3.209823 3.207670 3.205519 3.203369 3.201222 3.199075
#> [753] 3.196931 3.194788 3.192647 3.190508 3.188371 3.186235 3.184101 3.181969
#> [761] 3.179838 3.177710 3.175583 3.173457 3.171334 3.169212 3.167092 3.164974
#> [769] 3.162857 3.160742 3.158629 3.156518 3.154409 3.152301 3.150195 3.148091
#> [777] 3.145988 3.143887 3.141788 3.139691 3.137596 3.135502 3.133410 3.131320
#> [785] 3.129232 3.127145 3.125060 3.122977 3.120896 3.118816 3.116738 3.114662
#> [793] 3.112588 3.110516 3.108445 3.106376 3.104309 3.102243 3.100180 3.098118
#> [801] 3.096058 3.093999 3.091943 3.089888 3.087835 3.085784 3.083734 3.081687
#> [809] 3.079641 3.077597 3.075554 3.073514 3.071475 3.069438 3.067403 3.065369
#> [817] 3.063338 3.061308 3.059279 3.057253 3.055228 3.053206 3.051185 3.049165
#> [825] 3.047148 3.045132 3.043118 3.041106 3.039096 3.037087 3.035080 3.033075
#> [833] 3.031072 3.029070 3.027070 3.025072 3.023076 3.021082 3.019089 3.017098
#> [841] 3.015109 3.013122 3.011136 3.009152 3.007170 3.005190 3.003212 3.001235
#> [849] 2.999260 2.997287 2.995315 2.993346 2.991378 2.989412 2.987447 2.985485
#> [857] 2.983524 2.981565 2.979608 2.977652 2.975698 2.973746 2.971796 2.969848
#> [865] 2.967901 2.965956 2.964013 2.962071 2.960132 2.958194 2.956258 2.954323
#> [873] 2.952391 2.950460 2.948531 2.946603 2.944678 2.942754 2.940831 2.938911
#> [881] 2.936992 2.935076 2.933160 2.931247 2.929335 2.927426 2.925517 2.923611
#> [889] 2.921706 2.919803 2.917902 2.916003 2.914105 2.912209 2.910315 2.908422
#> [897] 2.906532 2.904643 2.902755 2.900870 2.898986 2.897104 2.895224 2.893345
#> [905] 2.891468 2.889593 2.887719 2.885848 2.883978 2.882109 2.880243 2.878378
#> [913] 2.876515 2.874654 2.872794 2.870936 2.869080 2.867225 2.865372 2.863521
#> [921] 2.861672 2.859824 2.857978 2.856134 2.854291 2.852451 2.850611 2.848774
#> [929] 2.846938 2.845104 2.843272 2.841441 2.839612 2.837785 2.835960 2.834136
#> [937] 2.832314 2.830493 2.828674 2.826857 2.825042 2.823228 2.821416 2.819606
#> [945] 2.817797 2.815990 2.814185 2.812381 2.810579 2.808779 2.806980 2.805184
#> [953] 2.803388 2.801595 2.799803 2.798013 2.796224 2.794437 2.792652 2.790868
#> [961] 2.789086 2.787306 2.785528 2.783751 2.781975 2.780202 2.778430 2.776660
#> [969] 2.774891 2.773124 2.771359 2.769595 2.767833 2.766072 2.764314 2.762557
#> [977] 2.760801 2.759047 2.757295 2.755545 2.753796 2.752048 2.750303 2.748559
#> [985] 2.746816 2.745075 2.743336 2.741599 2.739863 2.738129 2.736396 2.734665
#> [993] 2.732935 2.731208 2.729481 2.727757 2.726034 2.724313 2.722593 2.720875
#> [1001] 2.719158 2.717443 2.715730 2.714018 2.712308 2.710600 2.708893 2.707187
#> [1009] 2.705484 2.703782 2.702081 2.700382 2.698685 2.696989 2.695295 2.693602
#> [1017] 2.691911 2.690222 2.688534 2.686848 2.685163 2.683480 2.681798 2.680118
#> [1025] 2.678440 2.676763 2.675088 2.673414 2.671742 2.670071 2.668402 2.666735
#> [1033] 2.665069 2.663405 2.661742 2.660081 2.658421 2.656763 2.655106 2.653451
#> [1041] 2.651798 2.650146 2.648495 2.646847 2.645199 2.643553 2.641909 2.640267
#> [1049] 2.638625 2.636986 2.635348 2.633711 2.632076 2.630443 2.628811 2.627180
#> [1057] 2.625551 2.623924 2.622298 2.620673 2.619051 2.617429 2.615809 2.614191
#> [1065] 2.612574 2.610959 2.609345 2.607733 2.606122 2.604513 2.602905 2.601299
#> [1073] 2.599694 2.598091 2.596489 2.594888 2.593290 2.591692 2.590096 2.588502
#> [1081] 2.586909 2.585318 2.583728 2.582139 2.580552 2.578967 2.577383 2.575800
#> [1089] 2.574219 2.572640 2.571062 2.569485 2.567910 2.566336 2.564764 2.563193
#> [1097] 2.561624 2.560056 2.558489 2.556924 2.555361 2.553799 2.552238 2.550679
#> [1105] 2.549121 2.547565 2.546010 2.544457 2.542905 2.541354 2.539805 2.538257
#> [1113] 2.536711 2.535166 2.533623 2.532081 2.530541 2.529002 2.527464 2.525928
#> [1121] 2.524393 2.522860 2.521328 2.519797 2.518268 2.516740 2.515214 2.513689
#> [1129] 2.512166 2.510644 2.509123 2.507604 2.506086 2.504569 2.503054 2.501541
#> [1137] 2.500028 2.498518 2.497008 2.495500 2.493993 2.492488 2.490984 2.489481
#> [1145] 2.487980 2.486481 2.484982 2.483485 2.481990 2.480495 2.479002 2.477511
#> [1153] 2.476021 2.474532 2.473045 2.471559 2.470074 2.468591 2.467109 2.465628
#> [1161] 2.464149 2.462671 2.461195 2.459719 2.458246 2.456773 2.455302 2.453832
#> [1169] 2.452364 2.450897 2.449431 2.447967 2.446504 2.445042 2.443582 2.442123
#> [1177] 2.440665 2.439209 2.437754 2.436300 2.434848 2.433397 2.431947 2.430499
#> [1185] 2.429051 2.427606 2.426161 2.424718 2.423276 2.421836 2.420397 2.418959
#> [1193] 2.417522 2.416087 2.414653 2.413221 2.411789 2.410359 2.408931 2.407503
#> [1201] 2.406077 2.404652 2.403229 2.401806 2.400386 2.398966 2.397548 2.396130
#> [1209] 2.394715 2.393300 2.391887 2.390475 2.389064 2.387655 2.386247 2.384840
#> [1217] 2.383434 2.382030 2.380627 2.379225 2.377825 2.376426 2.375028 2.373631
#> [1225] 2.372236 2.370842 2.369449 2.368057 2.366667 2.365278 2.363890 2.362503
#> [1233] 2.361118 2.359734 2.358351 2.356969 2.355589 2.354209 2.352832 2.351455
#> [1241] 2.350079 2.348705 2.347332 2.345961 2.344590 2.343221 2.341853 2.340486
#> [1249] 2.339120 2.337756 2.336393 2.335031 2.333670 2.332311 2.330953 2.329596
#> [1257] 2.328240 2.326885 2.325532 2.324180 2.322829 2.321479 2.320130 2.318783
#> [1265] 2.317437 2.316092 2.314748 2.313406 2.312064 2.310724 2.309385 2.308047
#> [1273] 2.306711 2.305376 2.304041 2.302708 2.301377 2.300046 2.298716 2.297388
#> [1281] 2.296061 2.294735 2.293410 2.292087 2.290765 2.289443 2.288123 2.286804
#> [1289] 2.285487 2.284170 2.282855 2.281541 2.280228 2.278916 2.277605 2.276296
#> [1297] 2.274987 2.273680 2.272374 2.271069 2.269765 2.268463 2.267161 2.265861
#> [1305] 2.264562 2.263264 2.261967 2.260671 2.259377 2.258083 2.256791 2.255500
#> [1313] 2.254210 2.252921 2.251633 2.250346 2.249061 2.247776 2.246493 2.245211
#> [1321] 2.243930 2.242650 2.241371 2.240094 2.238817 2.237542 2.236268 2.234995
#> [1329] 2.233723 2.232452 2.231182 2.229913 2.228646 2.227379 2.226114 2.224849
#> [1337] 2.223586 2.222324 2.221063 2.219803 2.218545 2.217287 2.216030 2.214775
#> [1345] 2.213521 2.212267 2.211015 2.209764 2.208514 2.207265 2.206017 2.204770
#> [1353] 2.203525 2.202280 2.201037 2.199794 2.198553 2.197313 2.196073 2.194835
#> [1361] 2.193598 2.192362 2.191127 2.189894 2.188661 2.187429 2.186198 2.184969
#> [1369] 2.183740 2.182513 2.181287 2.180061 2.178837 2.177614 2.176392 2.175170
#> [1377] 2.173950 2.172731 2.171513 2.170296 2.169081 2.167866 2.166652 2.165439
#> [1385] 2.164228 2.163017 2.161807 2.160599 2.159391 2.158185 2.156979 2.155775
#> [1393] 2.154572 2.153369 2.152168 2.150968 2.149768 2.148570 2.147373 2.146177
#> [1401] 2.144981 2.143787 2.142594 2.141402 2.140211 2.139021 2.137832 2.136644
#> [1409] 2.135457 2.134271 2.133086 2.131902 2.130719 2.129537 2.128356 2.127176
#> [1417] 2.125997 2.124819 2.123642 2.122466 2.121291 2.120117 2.118944 2.117772
#> [1425] 2.116601 2.115431 2.114262 2.113094 2.111927 2.110761 2.109596 2.108432
#> [1433] 2.107269 2.106107 2.104945 2.103785 2.102626 2.101468 2.100311 2.099155
#> [1441] 2.097999 2.096845 2.095692 2.094539 2.093388 2.092238 2.091088 2.089940
#> [1449] 2.088792 2.087646 2.086500 2.085356 2.084212 2.083069 2.081927 2.080787
#> [1457] 2.079647 2.078508 2.077370 2.076233 2.075097 2.073962 2.072828 2.071695
#> [1465] 2.070563 2.069431 2.068301 2.067172 2.066043 2.064916 2.063789 2.062664
#> [1473] 2.061539 2.060415 2.059293 2.058171 2.057050 2.055930 2.054811 2.053693
#> [1481] 2.052575 2.051459 2.050344 2.049229 2.048116 2.047003 2.045892 2.044781
#> [1489] 2.043671 2.042562 2.041454 2.040347 2.039241 2.038136 2.037032 2.035928
#> [1497] 2.034826 2.033724 2.032624 2.031524 2.030425 2.029327 2.028230 2.027134
#> [1505] 2.026039 2.024945 2.023851 2.022759 2.021667 2.020576 2.019486 2.018398
#> [1513] 2.017310 2.016222 2.015136 2.014051 2.012966 2.011883 2.010800 2.009718
#> [1521] 2.008637 2.007557 2.006478 2.005400 2.004323 2.003246 2.002171 2.001096
#> [1529] 2.000022 1.998949 1.997877 1.996806 1.995735 1.994666 1.993597 1.992530
#> [1537] 1.991463 1.990397 1.989332 1.988267 1.987204 1.986142 1.985080 1.984019
#> [1545] 1.982959 1.981900 1.980842 1.979785 1.978728 1.977672 1.976618 1.975564
#> [1553] 1.974511 1.973458 1.972407 1.971357 1.970307 1.969258 1.968210 1.967163
#> [1561] 1.966117 1.965071 1.964027 1.962983 1.961940 1.960898 1.959857 1.958816
#> [1569] 1.957777 1.956738 1.955700 1.954663 1.953627 1.952592 1.951557 1.950523
#> [1577] 1.949490 1.948458 1.947427 1.946397 1.945367 1.944339 1.943311 1.942284
#> [1585] 1.941257 1.940232 1.939207 1.938183 1.937160 1.936138 1.935117 1.934096
#> [1593] 1.933077 1.932058 1.931040 1.930022 1.929006 1.927990 1.926975 1.925961
#> [1601] 1.924948 1.923936 1.922924 1.921913 1.920903 1.919894 1.918886 1.917878
#> [1609] 1.916871 1.915865 1.914860 1.913856 1.912852 1.911849 1.910847 1.909846
#> [1617] 1.908845 1.907846 1.906847 1.905849 1.904851 1.903855 1.902859 1.901864
#> [1625] 1.900870 1.899877 1.898884 1.897893 1.896902 1.895911 1.894922 1.893933
#> [1633] 1.892945 1.891958 1.890972 1.889986 1.889002 1.888018 1.887034 1.886052
#> [1641] 1.885070 1.884089 1.883109 1.882130 1.881151 1.880173 1.879196 1.878220
#> [1649] 1.877244 1.876270 1.875296 1.874322 1.873350 1.872378 1.871407 1.870437
#> [1657] 1.869467 1.868499 1.867531 1.866563 1.865597 1.864631 1.863666 1.862702
#> [1665] 1.861739 1.860776 1.859814 1.858853 1.857892 1.856933 1.855974 1.855015
#> [1673] 1.854058 1.853101 1.852145 1.851190 1.850236 1.849282 1.848329 1.847376
#> [1681] 1.846425 1.845474 1.844524 1.843575 1.842626 1.841678 1.840731 1.839785
#> [1689] 1.838839 1.837894 1.836950 1.836006 1.835063 1.834121 1.833180 1.832239
#> [1697] 1.831299 1.830360 1.829422 1.828484 1.827547 1.826611 1.825675 1.824740
#> [1705] 1.823806 1.822873 1.821940 1.821008 1.820077 1.819146 1.818217 1.817288
#> [1713] 1.816359 1.815431 1.814504 1.813578 1.812653 1.811728 1.810803 1.809880
#> [1721] 1.808957 1.808035 1.807114 1.806193 1.805273 1.804354 1.803435 1.802518
#> [1729] 1.801600 1.800684 1.799768 1.798853 1.797939 1.797025 1.796112 1.795200
#> [1737] 1.794288 1.793377 1.792467 1.791558 1.790649 1.789741 1.788833 1.787926
#> [1745] 1.787020 1.786115 1.785210 1.784306 1.783403 1.782500 1.781598 1.780697
#> [1753] 1.779796 1.778896 1.777997 1.777098 1.776200 1.775303 1.774406 1.773511
#> [1761] 1.772615 1.771721 1.770827 1.769934 1.769041 1.768149 1.767258 1.766367
#> [1769] 1.765478 1.764588 1.763700 1.762812 1.761925 1.761038 1.760152 1.759267
#> [1777] 1.758383 1.757499 1.756616 1.755733 1.754851 1.753970 1.753089 1.752209
#> [1785] 1.751330 1.750451 1.749573 1.748696 1.747819 1.746943 1.746068 1.745193
#> [1793] 1.744319 1.743446 1.742573 1.741701 1.740829 1.739959 1.739088 1.738219
#> [1801] 1.737350 1.736482 1.735614 1.734747 1.733881 1.733015 1.732150 1.731286
#> [1809] 1.730422 1.729559 1.728696 1.727835 1.726973 1.726113 1.725253 1.724394
#> [1817] 1.723535 1.722677 1.721819 1.720963 1.720107 1.719251 1.718396 1.717542
#> [1825] 1.716688 1.715835 1.714983 1.714131 1.713280 1.712429 1.711580 1.710730
#> [1833] 1.709882 1.709034 1.708186 1.707340 1.706493 1.705648 1.704803 1.703959
#> [1841] 1.703115 1.702272 1.701430 1.700588 1.699746 1.698906 1.698066 1.697226
#> [1849] 1.696388 1.695550 1.694712 1.693875 1.693039 1.692203 1.691368 1.690533
#> [1857] 1.689700 1.688866 1.688034 1.687202 1.686370 1.685539 1.684709 1.683879
#> [1865] 1.683050 1.682222 1.681394 1.680567 1.679740 1.678914 1.678088 1.677264
#> [1873] 1.676439 1.675616 1.674792 1.673970 1.673148 1.672327 1.671506 1.670686
#> [1881] 1.669866 1.669047 1.668229 1.667411 1.666594 1.665778 1.664962 1.664146
#> [1889] 1.663331 1.662517 1.661704 1.660890 1.660078 1.659266 1.658455 1.657644
#> [1897] 1.656834 1.656024 1.655215 1.654407 1.653599 1.652792 1.651985 1.651179
#> [1905] 1.650373 1.649568 1.648764 1.647960 1.647157 1.646354 1.645552 1.644751
#> [1913] 1.643950 1.643150 1.642350 1.641550 1.640752 1.639954 1.639156 1.638359
#> [1921] 1.637563 1.636767 1.635972 1.635177 1.634383 1.633589 1.632796 1.632004
#> [1929] 1.631212 1.630421 1.629630 1.628840 1.628050 1.627261 1.626473 1.625685
#> [1937] 1.624897 1.624110 1.623324 1.622538 1.621753 1.620968 1.620184 1.619401
#> [1945] 1.618618 1.617835 1.617054 1.616272 1.615492 1.614711 1.613932 1.613153
#> [1953] 1.612374 1.611596 1.610818 1.610042 1.609265 1.608489 1.607714 1.606939
#> [1961] 1.606165 1.605391 1.604618 1.603846 1.603074 1.602302 1.601531 1.600761
#> [1969] 1.599991 1.599222 1.598453 1.597684 1.596917 1.596150 1.595383 1.594617
#> [1977] 1.593851 1.593086 1.592322 1.591558 1.590794 1.590031 1.589269 1.588507
#> [1985] 1.587746 1.586985 1.586225 1.585465 1.584706 1.583947 1.583189 1.582431
#> [1993] 1.581674 1.580917 1.580161 1.579406 1.578651 1.577896 1.577142 1.576389
#> [2001] 1.575636
bsmrho(c("call", "put"), c(50, 49, 48, 47), 45, 0.25, 0.13, 0.01, 0.2)
#> [1] 9.842783 -1.473697 8.872391 -2.686832
bsmrho("call", 50, 45, 0.25, 0.13, 0.01, 1:1000 / 1000)
#> [1] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253
#> [8] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253
#> [15] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253
#> [22] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253
#> [29] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253
#> [36] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253 10.890253
#> [43] 10.890253 10.890253 10.890253 10.890253 10.890253 10.890252 10.890252
#> [50] 10.890252 10.890252 10.890251 10.890251 10.890249 10.890248 10.890245
#> [57] 10.890241 10.890235 10.890226 10.890215 10.890200 10.890179 10.890151
#> [64] 10.890116 10.890070 10.890013 10.889941 10.889852 10.889742 10.889609
#> [71] 10.889449 10.889259 10.889033 10.888767 10.888458 10.888099 10.887687
#> [78] 10.887215 10.886677 10.886070 10.885386 10.884620 10.883766 10.882818
#> [85] 10.881770 10.880617 10.879353 10.877972 10.876469 10.874837 10.873073
#> [92] 10.871170 10.869124 10.866930 10.864584 10.862081 10.859417 10.856590
#> [99] 10.853595 10.850428 10.847088 10.843571 10.839876 10.835999 10.831939
#> [106] 10.827695 10.823265 10.818648 10.813844 10.808851 10.803669 10.798299
#> [113] 10.792740 10.786993 10.781059 10.774937 10.768630 10.762138 10.755463
#> [120] 10.748605 10.741567 10.734351 10.726958 10.719390 10.711650 10.703740
#> [127] 10.695662 10.687419 10.679013 10.670447 10.661724 10.652846 10.643816
#> [134] 10.634637 10.625313 10.615845 10.606238 10.596494 10.586616 10.576607
#> [141] 10.566471 10.556210 10.545828 10.535328 10.524712 10.513985 10.503148
#> [148] 10.492205 10.481160 10.470015 10.458773 10.447437 10.436011 10.424496
#> [155] 10.412897 10.401216 10.389455 10.377618 10.365708 10.353727 10.341677
#> [162] 10.329562 10.317384 10.305146 10.292850 10.280499 10.268095 10.255641
#> [169] 10.243139 10.230591 10.218000 10.205368 10.192697 10.179989 10.167246
#> [176] 10.154471 10.141666 10.128832 10.115971 10.103086 10.090178 10.077249
#> [183] 10.064301 10.051335 10.038353 10.025358 10.012350 9.999331 9.986303
#> [190] 9.973267 9.960225 9.947177 9.934127 9.921074 9.908020 9.894967
#> [197] 9.881915 9.868867 9.855822 9.842783 9.829751 9.816725 9.803709
#> [204] 9.790702 9.777706 9.764722 9.751750 9.738791 9.725848 9.712919
#> [211] 9.700006 9.687111 9.674233 9.661374 9.648534 9.635715 9.622915
#> [218] 9.610138 9.597382 9.584649 9.571939 9.559254 9.546593 9.533956
#> [225] 9.521346 9.508761 9.496203 9.483672 9.471169 9.458694 9.446247
#> [232] 9.433829 9.421440 9.409081 9.396752 9.384453 9.372185 9.359948
#> [239] 9.347742 9.335568 9.323426 9.311316 9.299238 9.287193 9.275181
#> [246] 9.263203 9.251257 9.239346 9.227468 9.215624 9.203814 9.192039
#> [253] 9.180298 9.168592 9.156920 9.145283 9.133682 9.122115 9.110584
#> [260] 9.099088 9.087628 9.076203 9.064814 9.053460 9.042142 9.030860
#> [267] 9.019613 9.008403 8.997228 8.986089 8.974987 8.963920 8.952889
#> [274] 8.941894 8.930936 8.920013 8.909126 8.898276 8.887461 8.876682
#> [281] 8.865939 8.855232 8.844561 8.833926 8.823326 8.812763 8.802235
#> [288] 8.791742 8.781286 8.770865 8.760479 8.750129 8.739814 8.729535
#> [295] 8.719290 8.709081 8.698907 8.688768 8.678664 8.668595 8.658561
#> [302] 8.648561 8.638596 8.628665 8.618769 8.608907 8.599080 8.589286
#> [309] 8.579527 8.569801 8.560110 8.550452 8.540827 8.531236 8.521679
#> [316] 8.512155 8.502664 8.493206 8.483781 8.474390 8.465030 8.455704
#> [323] 8.446410 8.437148 8.427919 8.418722 8.409556 8.400423 8.391322
#> [330] 8.382252 8.373214 8.364208 8.355232 8.346288 8.337375 8.328493
#> [337] 8.319642 8.310822 8.302032 8.293273 8.284544 8.275845 8.267176
#> [344] 8.258538 8.249929 8.241350 8.232800 8.224281 8.215790 8.207329
#> [351] 8.198896 8.190493 8.182119 8.173773 8.165456 8.157167 8.148907
#> [358] 8.140675 8.132471 8.124295 8.116147 8.108027 8.099934 8.091869
#> [365] 8.083831 8.075820 8.067837 8.059880 8.051951 8.044048 8.036172
#> [372] 8.028322 8.020498 8.012701 8.004930 7.997185 7.989466 7.981773
#> [379] 7.974105 7.966463 7.958847 7.951255 7.943689 7.936148 7.928632
#> [386] 7.921141 7.913674 7.906232 7.898815 7.891421 7.884053 7.876708
#> [393] 7.869387 7.862090 7.854817 7.847568 7.840342 7.833140 7.825961
#> [400] 7.818805 7.811672 7.804562 7.797476 7.790412 7.783370 7.776352
#> [407] 7.769356 7.762382 7.755430 7.748501 7.741593 7.734707 7.727844
#> [414] 7.721002 7.714181 7.707383 7.700605 7.693849 7.687114 7.680400
#> [421] 7.673707 7.667035 7.660384 7.653753 7.647143 7.640554 7.633985
#> [428] 7.627436 7.620908 7.614399 7.607911 7.601442 7.594994 7.588565
#> [435] 7.582155 7.575765 7.569395 7.563044 7.556712 7.550399 7.544105
#> [442] 7.537831 7.531575 7.525338 7.519120 7.512920 7.506739 7.500576
#> [449] 7.494431 7.488305 7.482197 7.476107 7.470035 7.463981 7.457944
#> [456] 7.451926 7.445925 7.439941 7.433975 7.428027 7.422095 7.416181
#> [463] 7.410285 7.404405 7.398542 7.392696 7.386867 7.381054 7.375258
#> [470] 7.369479 7.363716 7.357970 7.352240 7.346526 7.340829 7.335147
#> [477] 7.329482 7.323833 7.318199 7.312581 7.306979 7.301393 7.295822
#> [484] 7.290267 7.284727 7.279202 7.273693 7.268199 7.262720 7.257256
#> [491] 7.251807 7.246373 7.240954 7.235550 7.230160 7.224785 7.219425
#> [498] 7.214079 7.208748 7.203431 7.198128 7.192840 7.187565 7.182305
#> [505] 7.177059 7.171827 7.166609 7.161404 7.156214 7.151037 7.145873
#> [512] 7.140724 7.135588 7.130465 7.125356 7.120260 7.115177 7.110108
#> [519] 7.105052 7.100009 7.094979 7.089961 7.084957 7.079966 7.074987
#> [526] 7.070022 7.065068 7.060128 7.055200 7.050285 7.045382 7.040491
#> [533] 7.035613 7.030747 7.025893 7.021052 7.016223 7.011405 7.006600
#> [540] 7.001807 6.997025 6.992256 6.987498 6.982752 6.978017 6.973295
#> [547] 6.968583 6.963884 6.959196 6.954519 6.949854 6.945200 6.940557
#> [554] 6.935925 6.931305 6.926696 6.922098 6.917511 6.912935 6.908370
#> [561] 6.903815 6.899272 6.894739 6.890217 6.885706 6.881206 6.876716
#> [568] 6.872236 6.867767 6.863309 6.858861 6.854423 6.849996 6.845579
#> [575] 6.841172 6.836775 6.832389 6.828012 6.823646 6.819290 6.814944
#> [582] 6.810607 6.806281 6.801964 6.797657 6.793360 6.789073 6.784795
#> [589] 6.780527 6.776268 6.772019 6.767780 6.763550 6.759329 6.755118
#> [596] 6.750916 6.746724 6.742541 6.738367 6.734202 6.730046 6.725900
#> [603] 6.721762 6.717634 6.713514 6.709404 6.705302 6.701210 6.697126
#> [610] 6.693051 6.688985 6.684927 6.680878 6.676838 6.672807 6.668784
#> [617] 6.664769 6.660763 6.656766 6.652777 6.648797 6.644825 6.640861
#> [624] 6.636905 6.632958 6.629019 6.625089 6.621166 6.617252 6.613345
#> [631] 6.609447 6.605557 6.601675 6.597801 6.593934 6.590076 6.586226
#> [638] 6.582383 6.578548 6.574721 6.570902 6.567091 6.563287 6.559491
#> [645] 6.555702 6.551921 6.548148 6.544382 6.540623 6.536873 6.533129
#> [652] 6.529393 6.525665 6.521943 6.518229 6.514523 6.510823 6.507131
#> [659] 6.503446 6.499769 6.496098 6.492435 6.488778 6.485129 6.481487
#> [666] 6.477851 6.474223 6.470602 6.466988 6.463380 6.459780 6.456186
#> [673] 6.452599 6.449019 6.445446 6.441879 6.438319 6.434766 6.431220
#> [680] 6.427680 6.424146 6.420620 6.417100 6.413586 6.410079 6.406579
#> [687] 6.403085 6.399597 6.396116 6.392641 6.389172 6.385710 6.382254
#> [694] 6.378805 6.375362 6.371925 6.368494 6.365069 6.361651 6.358239
#> [701] 6.354832 6.351432 6.348038 6.344651 6.341269 6.337893 6.334523
#> [708] 6.331159 6.327801 6.324449 6.321103 6.317763 6.314428 6.311100
#> [715] 6.307777 6.304460 6.301149 6.297843 6.294544 6.291250 6.287961
#> [722] 6.284679 6.281402 6.278130 6.274864 6.271604 6.268350 6.265100
#> [729] 6.261857 6.258619 6.255386 6.252159 6.248937 6.245721 6.242510
#> [736] 6.239305 6.236104 6.232910 6.229720 6.226536 6.223357 6.220183
#> [743] 6.217015 6.213852 6.210694 6.207541 6.204393 6.201251 6.198113
#> [750] 6.194981 6.191854 6.188732 6.185615 6.182503 6.179396 6.176294
#> [757] 6.173197 6.170105 6.167018 6.163936 6.160859 6.157787 6.154719
#> [764] 6.151657 6.148599 6.145546 6.142498 6.139455 6.136417 6.133383
#> [771] 6.130354 6.127330 6.124310 6.121296 6.118286 6.115280 6.112279
#> [778] 6.109283 6.106292 6.103305 6.100322 6.097345 6.094371 6.091403
#> [785] 6.088438 6.085479 6.082524 6.079573 6.076627 6.073685 6.070747
#> [792] 6.067814 6.064886 6.061962 6.059042 6.056126 6.053215 6.050309
#> [799] 6.047406 6.044508 6.041614 6.038724 6.035839 6.032958 6.030081
#> [806] 6.027208 6.024340 6.021475 6.018615 6.015759 6.012907 6.010060
#> [813] 6.007216 6.004376 6.001541 5.998710 5.995882 5.993059 5.990240
#> [820] 5.987424 5.984613 5.981806 5.979003 5.976203 5.973408 5.970617
#> [827] 5.967829 5.965045 5.962266 5.959490 5.956718 5.953950 5.951186
#> [834] 5.948425 5.945669 5.942916 5.940167 5.937422 5.934681 5.931943
#> [841] 5.929209 5.926479 5.923752 5.921030 5.918311 5.915595 5.912884
#> [848] 5.910176 5.907472 5.904771 5.902074 5.899380 5.896691 5.894004
#> [855] 5.891322 5.888643 5.885967 5.883295 5.880627 5.877962 5.875300
#> [862] 5.872643 5.869988 5.867337 5.864690 5.862046 5.859405 5.856768
#> [869] 5.854135 5.851505 5.848878 5.846254 5.843634 5.841018 5.838404
#> [876] 5.835794 5.833188 5.830585 5.827985 5.825388 5.822795 5.820205
#> [883] 5.817618 5.815034 5.812454 5.809877 5.807303 5.804733 5.802166
#> [890] 5.799602 5.797041 5.794483 5.791929 5.789377 5.786829 5.784284
#> [897] 5.781742 5.779204 5.776668 5.774135 5.771606 5.769080 5.766557
#> [904] 5.764037 5.761519 5.759005 5.756495 5.753987 5.751482 5.748980
#> [911] 5.746481 5.743985 5.741492 5.739003 5.736516 5.734032 5.731551
#> [918] 5.729073 5.726598 5.724126 5.721657 5.719190 5.716727 5.714266
#> [925] 5.711809 5.709354 5.706902 5.704453 5.702007 5.699564 5.697124
#> [932] 5.694686 5.692251 5.689819 5.687390 5.684964 5.682540 5.680119
#> [939] 5.677701 5.675286 5.672874 5.670464 5.668057 5.665653 5.663251
#> [946] 5.660852 5.658456 5.656063 5.653672 5.651284 5.648899 5.646516
#> [953] 5.644136 5.641759 5.639384 5.637012 5.634642 5.632276 5.629911
#> [960] 5.627550 5.625191 5.622834 5.620481 5.618129 5.615781 5.613435
#> [967] 5.611091 5.608750 5.606412 5.604076 5.601742 5.599412 5.597083
#> [974] 5.594757 5.592434 5.590113 5.587795 5.585479 5.583166 5.580855
#> [981] 5.578546 5.576240 5.573937 5.571636 5.569337 5.567041 5.564747
#> [988] 5.562455 5.560166 5.557880 5.555596 5.553314 5.551034 5.548757
#> [995] 5.546482 5.544210 5.541940 5.539672 5.537407 5.535144
bsmrho("put", 20, 30, 0:2000 / 1000, 0.15, 0, 0.25)
#> [1] 0.00000000 -0.02999550 -0.05998200 -0.08995951 -0.11992802
#> [6] -0.14988754 -0.17983807 -0.20977962 -0.23971217 -0.26963575
#> [11] -0.29955034 -0.32945595 -0.35935258 -0.38924024 -0.41911893
#> [16] -0.44898864 -0.47884938 -0.50870116 -0.53854397 -0.56837781
#> [21] -0.59820270 -0.62801862 -0.65782559 -0.68762360 -0.71741266
#> [26] -0.74719277 -0.77696392 -0.80672613 -0.83647940 -0.86622372
#> [31] -0.89595910 -0.92568554 -0.95540304 -0.98511161 -1.01481124
#> [36] -1.04450195 -1.07418372 -1.10385656 -1.13352048 -1.16317548
#> [41] -1.19282156 -1.22245871 -1.25208695 -1.28170628 -1.31131669
#> [46] -1.34091819 -1.37051078 -1.40009446 -1.42966924 -1.45923511
#> [51] -1.48879208 -1.51834016 -1.54787933 -1.57740961 -1.60693100
#> [56] -1.63644350 -1.66594710 -1.69544182 -1.72492766 -1.75440461
#> [61] -1.78387268 -1.81333187 -1.84278219 -1.87222363 -1.90165619
#> [66] -1.93107989 -1.96049471 -1.98990067 -2.01929776 -2.04868599
#> [71] -2.07806536 -2.10743586 -2.13679752 -2.16615031 -2.19549425
#> [76] -2.22482934 -2.25415558 -2.28347298 -2.31278152 -2.34208123
#> [81] -2.37137209 -2.40065411 -2.42992729 -2.45919163 -2.48844714
#> [86] -2.51769382 -2.54693166 -2.57616067 -2.60538086 -2.63459221
#> [91] -2.66379475 -2.69298845 -2.72217334 -2.75134940 -2.78051664
#> [96] -2.80967506 -2.83882465 -2.86796544 -2.89709740 -2.92622054
#> [101] -2.95533487 -2.98444038 -3.01353708 -3.04262495 -3.07170401
#> [106] -3.10077425 -3.12983568 -3.15888828 -3.18793206 -3.21696702
#> [111] -3.24599315 -3.27501046 -3.30401895 -3.33301860 -3.36200942
#> [116] -3.39099140 -3.41996454 -3.44892884 -3.47788430 -3.50683090
#> [121] -3.53576865 -3.56469753 -3.59361756 -3.62252870 -3.65143098
#> [126] -3.68032436 -3.70920886 -3.73808446 -3.76695115 -3.79580893
#> [131] -3.82465778 -3.85349770 -3.88232868 -3.91115071 -3.93996378
#> [136] -3.96876787 -3.99756298 -4.02634909 -4.05512619 -4.08389427
#> [141] -4.11265331 -4.14140330 -4.17014422 -4.19887607 -4.22759882
#> [146] -4.25631246 -4.28501697 -4.31371233 -4.34239853 -4.37107554
#> [151] -4.39974336 -4.42840195 -4.45705130 -4.48569138 -4.51432218
#> [156] -4.54294368 -4.57155584 -4.60015866 -4.62875209 -4.65733613
#> [161] -4.68591074 -4.71447590 -4.74303159 -4.77157777 -4.80011442
#> [166] -4.82864151 -4.85715901 -4.88566690 -4.91416514 -4.94265371
#> [171] -4.97113257 -4.99960169 -5.02806104 -5.05651059 -5.08495031
#> [176] -5.11338016 -5.14180010 -5.17021011 -5.19861014 -5.22700017
#> [181] -5.25538016 -5.28375006 -5.31210985 -5.34045948 -5.36879891
#> [186] -5.39712812 -5.42544705 -5.45375567 -5.48205395 -5.51034182
#> [191] -5.53861927 -5.56688624 -5.59514270 -5.62338860 -5.65162389
#> [196] -5.67984854 -5.70806251 -5.73626574 -5.76445819 -5.79263982
#> [201] -5.82081058 -5.84897043 -5.87711933 -5.90525721 -5.93338405
#> [206] -5.96149978 -5.98960437 -6.01769777 -6.04577992 -6.07385078
#> [211] -6.10191030 -6.12995843 -6.15799513 -6.18602033 -6.21403400
#> [216] -6.24203609 -6.27002653 -6.29800528 -6.32597230 -6.35392752
#> [221] -6.38187091 -6.40980240 -6.43772194 -6.46562949 -6.49352498
#> [226] -6.52140838 -6.54927962 -6.57713865 -6.60498542 -6.63281988
#> [231] -6.66064197 -6.68845164 -6.71624884 -6.74403351 -6.77180560
#> [236] -6.79956505 -6.82731182 -6.85504584 -6.88276707 -6.91047545
#> [241] -6.93817092 -6.96585343 -6.99352293 -7.02117935 -7.04882266
#> [246] -7.07645279 -7.10406968 -7.13167329 -7.15926355 -7.18684042
#> [251] -7.21440384 -7.24195375 -7.26949011 -7.29701284 -7.32452191
#> [256] -7.35201725 -7.37949882 -7.40696655 -7.43442039 -7.46186029
#> [261] -7.48928619 -7.51669804 -7.54409578 -7.57147936 -7.59884873
#> [266] -7.62620383 -7.65354461 -7.68087101 -7.70818298 -7.73548047
#> [271] -7.76276342 -7.79003178 -7.81728549 -7.84452451 -7.87174877
#> [276] -7.89895823 -7.92615283 -7.95333252 -7.98049725 -8.00764696
#> [281] -8.03478160 -8.06190112 -8.08900548 -8.11609460 -8.14316845
#> [286] -8.17022697 -8.19727012 -8.22429783 -8.25131006 -8.27830676
#> [291] -8.30528787 -8.33225335 -8.35920315 -8.38613721 -8.41305548
#> [296] -8.43995792 -8.46684448 -8.49371510 -8.52056974 -8.54740835
#> [301] -8.57423088 -8.60103727 -8.62782749 -8.65460149 -8.68135921
#> [306] -8.70810060 -8.73482563 -8.76153424 -8.78822639 -8.81490203
#> [311] -8.84156111 -8.86820358 -8.89482941 -8.92143854 -8.94803093
#> [316] -8.97460653 -9.00116530 -9.02770719 -9.05423216 -9.08074017
#> [321] -9.10723116 -9.13370510 -9.16016195 -9.18660165 -9.21302416
#> [326] -9.23942945 -9.26581747 -9.29218817 -9.31854152 -9.34487747
#> [331] -9.37119598 -9.39749701 -9.42378052 -9.45004647 -9.47629481
#> [336] -9.50252551 -9.52873853 -9.55493382 -9.58111135 -9.60727108
#> [341] -9.63341297 -9.65953697 -9.68564306 -9.71173119 -9.73780132
#> [346] -9.76385342 -9.78988745 -9.81590337 -9.84190115 -9.86788074
#> [351] -9.89384212 -9.91978524 -9.94571007 -9.97161658 -9.99750473
#> [356] -10.02337448 -10.04922580 -10.07505865 -10.10087300 -10.12666882
#> [361] -10.15244608 -10.17820473 -10.20394475 -10.22966610 -10.25536875
#> [366] -10.28105267 -10.30671783 -10.33236418 -10.35799172 -10.38360039
#> [371] -10.40919017 -10.43476103 -10.46031294 -10.48584587 -10.51135979
#> [376] -10.53685466 -10.56233047 -10.58778717 -10.61322475 -10.63864316
#> [381] -10.66404239 -10.68942241 -10.71478319 -10.74012469 -10.76544690
#> [386] -10.79074978 -10.81603331 -10.84129747 -10.86654222 -10.89176753
#> [391] -10.91697340 -10.94215978 -10.96732665 -10.99247399 -11.01760178
#> [396] -11.04270998 -11.06779858 -11.09286755 -11.11791686 -11.14294650
#> [401] -11.16795643 -11.19294664 -11.21791711 -11.24286780 -11.26779870
#> [406] -11.29270979 -11.31760105 -11.34247245 -11.36732396 -11.39215558
#> [411] -11.41696728 -11.44175904 -11.46653083 -11.49128265 -11.51601446
#> [416] -11.54072625 -11.56541800 -11.59008969 -11.61474130 -11.63937281
#> [421] -11.66398421 -11.68857547 -11.71314657 -11.73769751 -11.76222826
#> [426] -11.78673880 -11.81122912 -11.83569920 -11.86014902 -11.88457857
#> [431] -11.90898784 -11.93337679 -11.95774542 -11.98209372 -12.00642166
#> [436] -12.03072924 -12.05501643 -12.07928323 -12.10352961 -12.12775557
#> [441] -12.15196109 -12.17614615 -12.20031075 -12.22445486 -12.24857848
#> [446] -12.27268159 -12.29676418 -12.32082624 -12.34486775 -12.36888870
#> [451] -12.39288908 -12.41686888 -12.44082808 -12.46476668 -12.48868467
#> [456] -12.51258202 -12.53645874 -12.56031480 -12.58415021 -12.60796495
#> [461] -12.63175900 -12.65553237 -12.67928503 -12.70301699 -12.72672823
#> [466] -12.75041873 -12.77408851 -12.79773753 -12.82136580 -12.84497331
#> [471] -12.86856004 -12.89212600 -12.91567117 -12.93919554 -12.96269911
#> [476] -12.98618187 -13.00964382 -13.03308494 -13.05650522 -13.07990467
#> [481] -13.10328328 -13.12664103 -13.14997793 -13.17329396 -13.19658913
#> [486] -13.21986342 -13.24311683 -13.26634935 -13.28956099 -13.31275173
#> [491] -13.33592156 -13.35907050 -13.38219852 -13.40530563 -13.42839182
#> [496] -13.45145708 -13.47450142 -13.49752483 -13.52052731 -13.54350884
#> [501] -13.56646944 -13.58940909 -13.61232780 -13.63522556 -13.65810236
#> [506] -13.68095821 -13.70379310 -13.72660703 -13.74940000 -13.77217200
#> [511] -13.79492304 -13.81765311 -13.84036221 -13.86305034 -13.88571750
#> [516] -13.90836369 -13.93098890 -13.95359313 -13.97617639 -13.99873868
#> [521] -14.02127998 -14.04380031 -14.06629966 -14.08877804 -14.11123543
#> [526] -14.13367185 -14.15608729 -14.17848176 -14.20085524 -14.22320775
#> [531] -14.24553929 -14.26784985 -14.29013944 -14.31240806 -14.33465571
#> [536] -14.35688239 -14.37908810 -14.40127284 -14.42343662 -14.44557944
#> [541] -14.46770130 -14.48980220 -14.51188214 -14.53394113 -14.55597917
#> [546] -14.57799626 -14.59999240 -14.62196760 -14.64392186 -14.66585518
#> [551] -14.68776756 -14.70965902 -14.73152955 -14.75337915 -14.77520783
#> [556] -14.79701560 -14.81880245 -14.84056839 -14.86231343 -14.88403756
#> [561] -14.90574080 -14.92742314 -14.94908459 -14.97072516 -14.99234485
#> [566] -15.01394366 -15.03552160 -15.05707868 -15.07861489 -15.10013025
#> [571] -15.12162476 -15.14309842 -15.16455125 -15.18598323 -15.20739439
#> [576] -15.22878472 -15.25015424 -15.27150294 -15.29283084 -15.31413793
#> [581] -15.33542423 -15.35668974 -15.37793447 -15.39915842 -15.42036160
#> [586] -15.44154402 -15.46270568 -15.48384659 -15.50496676 -15.52606619
#> [591] -15.54714489 -15.56820286 -15.58924012 -15.61025667 -15.63125252
#> [596] -15.65222767 -15.67318214 -15.69411592 -15.71502904 -15.73592148
#> [601] -15.75679327 -15.77764441 -15.79847491 -15.81928477 -15.84007401
#> [606] -15.86084263 -15.88159063 -15.90231804 -15.92302485 -15.94371108
#> [611] -15.96437672 -15.98502180 -16.00564632 -16.02625028 -16.04683371
#> [616] -16.06739659 -16.08793895 -16.10846079 -16.12896213 -16.14944296
#> [621] -16.16990331 -16.19034317 -16.21076256 -16.23116148 -16.25153995
#> [626] -16.27189798 -16.29223557 -16.31255273 -16.33284948 -16.35312582
#> [631] -16.37338176 -16.39361732 -16.41383249 -16.43402730 -16.45420175
#> [636] -16.47435585 -16.49448961 -16.51460304 -16.53469615 -16.55476895
#> [641] -16.57482146 -16.59485367 -16.61486561 -16.63485728 -16.65482869
#> [646] -16.67477985 -16.69471078 -16.71462148 -16.73451196 -16.75438224
#> [651] -16.77423232 -16.79406222 -16.81387195 -16.83366151 -16.85343092
#> [656] -16.87318019 -16.89290934 -16.91261836 -16.93230727 -16.95197609
#> [661] -16.97162482 -16.99125348 -17.01086207 -17.03045061 -17.05001911
#> [666] -17.06956758 -17.08909604 -17.10860448 -17.12809293 -17.14756140
#> [671] -17.16700989 -17.18643843 -17.20584701 -17.22523566 -17.24460438
#> [676] -17.26395319 -17.28328209 -17.30259110 -17.32188024 -17.34114951
#> [681] -17.36039892 -17.37962849 -17.39883823 -17.41802815 -17.43719826
#> [686] -17.45634858 -17.47547911 -17.49458988 -17.51368089 -17.53275215
#> [691] -17.55180367 -17.57083548 -17.58984757 -17.60883997 -17.62781268
#> [696] -17.64676573 -17.66569911 -17.68461284 -17.70350695 -17.72238142
#> [701] -17.74123629 -17.76007157 -17.77888725 -17.79768337 -17.81645993
#> [706] -17.83521694 -17.85395442 -17.87267237 -17.89137082 -17.91004978
#> [711] -17.92870925 -17.94734925 -17.96596980 -17.98457090 -18.00315258
#> [716] -18.02171483 -18.04025768 -18.05878114 -18.07728522 -18.09576994
#> [721] -18.11423530 -18.13268133 -18.15110803 -18.16951541 -18.18790350
#> [726] -18.20627230 -18.22462183 -18.24295210 -18.26126312 -18.27955491
#> [731] -18.29782748 -18.31608085 -18.33431502 -18.35253001 -18.37072583
#> [736] -18.38890251 -18.40706004 -18.42519845 -18.44331774 -18.46141794
#> [741] -18.47949905 -18.49756109 -18.51560407 -18.53362801 -18.55163292
#> [746] -18.56961881 -18.58758570 -18.60553359 -18.62346252 -18.64137247
#> [751] -18.65926348 -18.67713556 -18.69498871 -18.71282296 -18.73063831
#> [756] -18.74843479 -18.76621240 -18.78397115 -18.80171107 -18.81943216
#> [761] -18.83713444 -18.85481793 -18.87248263 -18.89012857 -18.90775575
#> [766] -18.92536419 -18.94295390 -18.96052490 -18.97807720 -18.99561081
#> [771] -19.01312575 -19.03062204 -19.04809968 -19.06555870 -19.08299910
#> [776] -19.10042090 -19.11782411 -19.13520875 -19.15257483 -19.16992237
#> [781] -19.18725138 -19.20456187 -19.22185386 -19.23912736 -19.25638239
#> [786] -19.27361896 -19.29083708 -19.30803677 -19.32521805 -19.34238092
#> [791] -19.35952541 -19.37665152 -19.39375927 -19.41084867 -19.42791975
#> [796] -19.44497250 -19.46200696 -19.47902312 -19.49602101 -19.51300064
#> [801] -19.52996203 -19.54690518 -19.56383012 -19.58073685 -19.59762539
#> [806] -19.61449577 -19.63134798 -19.64818204 -19.66499798 -19.68179580
#> [811] -19.69857551 -19.71533714 -19.73208069 -19.74880619 -19.76551364
#> [816] -19.78220306 -19.79887446 -19.81552787 -19.83216328 -19.84878073
#> [821] -19.86538021 -19.88196175 -19.89852536 -19.91507106 -19.93159885
#> [826] -19.94810876 -19.96460080 -19.98107498 -19.99753131 -20.01396982
#> [831] -20.03039052 -20.04679341 -20.06317852 -20.07954586 -20.09589544
#> [836] -20.11222728 -20.12854140 -20.14483780 -20.16111650 -20.17737752
#> [841] -20.19362087 -20.20984657 -20.22605462 -20.24224505 -20.25841787
#> [846] -20.27457309 -20.29071073 -20.30683080 -20.32293331 -20.33901829
#> [851] -20.35508574 -20.37113568 -20.38716813 -20.40318310 -20.41918060
#> [856] -20.43516064 -20.45112325 -20.46706844 -20.48299622 -20.49890660
#> [861] -20.51479961 -20.53067525 -20.54653353 -20.56237449 -20.57819812
#> [866] -20.59400444 -20.60979347 -20.62556522 -20.64131971 -20.65705695
#> [871] -20.67277695 -20.68847974 -20.70416531 -20.71983370 -20.73548491
#> [876] -20.75111896 -20.76673585 -20.78233562 -20.79791827 -20.81348381
#> [881] -20.82903226 -20.84456363 -20.86007795 -20.87557521 -20.89105545
#> [886] -20.90651867 -20.92196488 -20.93739410 -20.95280635 -20.96820164
#> [891] -20.98357999 -20.99894140 -21.01428589 -21.02961349 -21.04492419
#> [896] -21.06021802 -21.07549499 -21.09075512 -21.10599842 -21.12122490
#> [901] -21.13643458 -21.15162747 -21.16680359 -21.18196295 -21.19710556
#> [906] -21.21223145 -21.22734062 -21.24243309 -21.25750887 -21.27256798
#> [911] -21.28761043 -21.30263624 -21.31764542 -21.33263799 -21.34761395
#> [916] -21.36257333 -21.37751613 -21.39244238 -21.40735208 -21.42224526
#> [921] -21.43712192 -21.45198208 -21.46682576 -21.48165296 -21.49646370
#> [926] -21.51125800 -21.52603588 -21.54079733 -21.55554239 -21.57027106
#> [931] -21.58498336 -21.59967930 -21.61435890 -21.62902216 -21.64366912
#> [936] -21.65829977 -21.67291413 -21.68751223 -21.70209406 -21.71665965
#> [941] -21.73120901 -21.74574216 -21.76025910 -21.77475985 -21.78924444
#> [946] -21.80371286 -21.81816514 -21.83260128 -21.84702131 -21.86142524
#> [951] -21.87581308 -21.89018485 -21.90454055 -21.91888021 -21.93320384
#> [956] -21.94751144 -21.96180305 -21.97607866 -21.99033830 -22.00458198
#> [961] -22.01880971 -22.03302150 -22.04721738 -22.06139735 -22.07556143
#> [966] -22.08970963 -22.10384197 -22.11795845 -22.13205911 -22.14614394
#> [971] -22.16021296 -22.17426619 -22.18830364 -22.20232532 -22.21633125
#> [976] -22.23032145 -22.24429592 -22.25825468 -22.27219774 -22.28612512
#> [981] -22.30003683 -22.31393289 -22.32781331 -22.34167810 -22.35552728
#> [986] -22.36936086 -22.38317885 -22.39698127 -22.41076813 -22.42453945
#> [991] -22.43829524 -22.45203552 -22.46576029 -22.47946957 -22.49316338
#> [996] -22.50684173 -22.52050463 -22.53415209 -22.54778414 -22.56140078
#> [1001] -22.57500202 -22.58858789 -22.60215839 -22.61571355 -22.62925336
#> [1006] -22.64277785 -22.65628703 -22.66978091 -22.68325951 -22.69672284
#> [1011] -22.71017092 -22.72360375 -22.73702136 -22.75042374 -22.76381093
#> [1016] -22.77718293 -22.79053976 -22.80388142 -22.81720794 -22.83051933
#> [1021] -22.84381559 -22.85709675 -22.87036281 -22.88361380 -22.89684972
#> [1026] -22.91007058 -22.92327641 -22.93646721 -22.94964300 -22.96280380
#> [1031] -22.97594960 -22.98908044 -23.00219631 -23.01529724 -23.02838324
#> [1036] -23.04145432 -23.05451050 -23.06755179 -23.08057819 -23.09358974
#> [1041] -23.10658643 -23.11956828 -23.13253531 -23.14548752 -23.15842494
#> [1046] -23.17134758 -23.18425544 -23.19714854 -23.21002690 -23.22289053
#> [1051] -23.23573944 -23.24857364 -23.26139316 -23.27419799 -23.28698816
#> [1056] -23.29976367 -23.31252455 -23.32527079 -23.33800243 -23.35071947
#> [1061] -23.36342192 -23.37610979 -23.38878311 -23.40144188 -23.41408611
#> [1066] -23.42671583 -23.43933103 -23.45193174 -23.46451797 -23.47708973
#> [1071] -23.48964704 -23.50218990 -23.51471833 -23.52723234 -23.53973196
#> [1076] -23.55221718 -23.56468802 -23.57714450 -23.58958662 -23.60201441
#> [1081] -23.61442787 -23.62682702 -23.63921187 -23.65158243 -23.66393871
#> [1086] -23.67628074 -23.68860851 -23.70092205 -23.71322137 -23.72550648
#> [1091] -23.73777739 -23.75003412 -23.76227667 -23.77450507 -23.78671932
#> [1096] -23.79891943 -23.81110543 -23.82327732 -23.83543511 -23.84757882
#> [1101] -23.85970846 -23.87182405 -23.88392559 -23.89601309 -23.90808659
#> [1106] -23.92014607 -23.93219156 -23.94422307 -23.95624061 -23.96824420
#> [1111] -23.98023384 -23.99220956 -24.00417135 -24.01611924 -24.02805324
#> [1116] -24.03997336 -24.05187961 -24.06377201 -24.07565056 -24.08751528
#> [1121] -24.09936619 -24.11120329 -24.12302660 -24.13483613 -24.14663189
#> [1126] -24.15841390 -24.17018216 -24.18193670 -24.19367752 -24.20540463
#> [1131] -24.21711805 -24.22881779 -24.24050386 -24.25217627 -24.26383504
#> [1136] -24.27548018 -24.28711171 -24.29872962 -24.31033394 -24.32192468
#> [1141] -24.33350186 -24.34506547 -24.35661554 -24.36815207 -24.37967509
#> [1146] -24.39118460 -24.40268061 -24.41416314 -24.42563219 -24.43708779
#> [1151] -24.44852994 -24.45995866 -24.47137395 -24.48277583 -24.49416432
#> [1156] -24.50553941 -24.51690114 -24.52824950 -24.53958451 -24.55090618
#> [1161] -24.56221453 -24.57350956 -24.58479130 -24.59605974 -24.60731490
#> [1166] -24.61855680 -24.62978545 -24.64100085 -24.65220303 -24.66339198
#> [1171] -24.67456773 -24.68573029 -24.69687966 -24.70801587 -24.71913892
#> [1176] -24.73024882 -24.74134559 -24.75242923 -24.76349976 -24.77455720
#> [1181] -24.78560155 -24.79663282 -24.80765104 -24.81865620 -24.82964832
#> [1186] -24.84062741 -24.85159349 -24.86254656 -24.87348665 -24.88441375
#> [1191] -24.89532788 -24.90622906 -24.91711729 -24.92799258 -24.93885496
#> [1196] -24.94970442 -24.96054099 -24.97136467 -24.98217547 -24.99297341
#> [1201] -25.00375850 -25.01453075 -25.02529017 -25.03603678 -25.04677058
#> [1206] -25.05749158 -25.06819980 -25.07889525 -25.08957795 -25.10024789
#> [1211] -25.11090510 -25.12154959 -25.13218136 -25.14280043 -25.15340681
#> [1216] -25.16400051 -25.17458154 -25.18514992 -25.19570566 -25.20624876
#> [1221] -25.21677924 -25.22729711 -25.23780238 -25.24829507 -25.25877518
#> [1226] -25.26924272 -25.27969771 -25.29014016 -25.30057008 -25.31098748
#> [1231] -25.32139238 -25.33178477 -25.34216468 -25.35253212 -25.36288710
#> [1236] -25.37322962 -25.38355970 -25.39387736 -25.40418260 -25.41447543
#> [1241] -25.42475586 -25.43502391 -25.44527959 -25.45552291 -25.46575388
#> [1246] -25.47597250 -25.48617880 -25.49637279 -25.50655446 -25.51672384
#> [1251] -25.52688094 -25.53702577 -25.54715833 -25.55727864 -25.56738672
#> [1256] -25.57748256 -25.58756619 -25.59763761 -25.60769684 -25.61774388
#> [1261] -25.62777875 -25.63780146 -25.64781201 -25.65781043 -25.66779671
#> [1266] -25.67777088 -25.68773294 -25.69768290 -25.70762078 -25.71754658
#> [1271] -25.72746032 -25.73736201 -25.74725165 -25.75712926 -25.76699485
#> [1276] -25.77684843 -25.78669002 -25.79651961 -25.80633723 -25.81614288
#> [1281] -25.82593657 -25.83571832 -25.84548814 -25.85524603 -25.86499201
#> [1286] -25.87472609 -25.88444828 -25.89415858 -25.90385702 -25.91354360
#> [1291] -25.92321832 -25.93288122 -25.94253228 -25.95217153 -25.96179897
#> [1296] -25.97141462 -25.98101848 -25.99061056 -26.00019089 -26.00975946
#> [1301] -26.01931629 -26.02886139 -26.03839476 -26.04791643 -26.05742640
#> [1306] -26.06692467 -26.07641127 -26.08588620 -26.09534947 -26.10480109
#> [1311] -26.11424108 -26.12366944 -26.13308618 -26.14249132 -26.15188486
#> [1316] -26.16126682 -26.17063720 -26.17999602 -26.18934328 -26.19867900
#> [1321] -26.20800319 -26.21731586 -26.22661701 -26.23590666 -26.24518482
#> [1326] -26.25445150 -26.26370671 -26.27295045 -26.28218275 -26.29140361
#> [1331] -26.30061303 -26.30981104 -26.31899764 -26.32817284 -26.33733665
#> [1336] -26.34648908 -26.35563014 -26.36475984 -26.37387820 -26.38298522
#> [1341] -26.39208091 -26.40116528 -26.41023834 -26.41930011 -26.42835059
#> [1346] -26.43738979 -26.44641773 -26.45543441 -26.46443984 -26.47343404
#> [1351] -26.48241700 -26.49138876 -26.50034930 -26.50929865 -26.51823681
#> [1356] -26.52716380 -26.53607962 -26.54498428 -26.55387780 -26.56276018
#> [1361] -26.57163143 -26.58049157 -26.58934060 -26.59817853 -26.60700537
#> [1366] -26.61582114 -26.62462585 -26.63341949 -26.64220209 -26.65097365
#> [1371] -26.65973418 -26.66848369 -26.67722220 -26.68594971 -26.69466623
#> [1376] -26.70337177 -26.71206635 -26.72074996 -26.72942263 -26.73808436
#> [1381] -26.74673515 -26.75537503 -26.76400400 -26.77262207 -26.78122924
#> [1386] -26.78982554 -26.79841097 -26.80698553 -26.81554924 -26.82410211
#> [1391] -26.83264415 -26.84117537 -26.84969577 -26.85820537 -26.86670418
#> [1396] -26.87519220 -26.88366945 -26.89213593 -26.90059166 -26.90903664
#> [1401] -26.91747088 -26.92589440 -26.93430720 -26.94270930 -26.95110069
#> [1406] -26.95948140 -26.96785143 -26.97621079 -26.98455949 -26.99289754
#> [1411] -27.00122495 -27.00954173 -27.01784788 -27.02614343 -27.03442837
#> [1416] -27.04270271 -27.05096647 -27.05921966 -27.06746228 -27.07569435
#> [1421] -27.08391587 -27.09212685 -27.10032731 -27.10851724 -27.11669667
#> [1426] -27.12486560 -27.13302403 -27.14117199 -27.14930947 -27.15743649
#> [1431] -27.16555306 -27.17365918 -27.18175487 -27.18984013 -27.19791498
#> [1436] -27.20597942 -27.21403346 -27.22207712 -27.23011039 -27.23813330
#> [1441] -27.24614584 -27.25414803 -27.26213988 -27.27012140 -27.27809259
#> [1446] -27.28605347 -27.29400404 -27.30194431 -27.30987430 -27.31779401
#> [1451] -27.32570345 -27.33360263 -27.34149156 -27.34937024 -27.35723869
#> [1456] -27.36509692 -27.37294494 -27.38078274 -27.38861036 -27.39642778
#> [1461] -27.40423502 -27.41203210 -27.41981901 -27.42759578 -27.43536239
#> [1466] -27.44311888 -27.45086524 -27.45860149 -27.46632762 -27.47404366
#> [1471] -27.48174961 -27.48944548 -27.49713128 -27.50480702 -27.51247270
#> [1476] -27.52012834 -27.52777395 -27.53540952 -27.54303508 -27.55065063
#> [1481] -27.55825618 -27.56585174 -27.57343731 -27.58101291 -27.58857855
#> [1486] -27.59613423 -27.60367996 -27.61121575 -27.61874162 -27.62625756
#> [1491] -27.63376359 -27.64125972 -27.64874595 -27.65622229 -27.66368876
#> [1496] -27.67114536 -27.67859210 -27.68602898 -27.69345603 -27.70087324
#> [1501] -27.70828063 -27.71567819 -27.72306595 -27.73044392 -27.73781209
#> [1506] -27.74517047 -27.75251909 -27.75985794 -27.76718703 -27.77450638
#> [1511] -27.78181598 -27.78911586 -27.79640601 -27.80368645 -27.81095719
#> [1516] -27.81821823 -27.82546958 -27.83271125 -27.83994325 -27.84716559
#> [1521] -27.85437827 -27.86158131 -27.86877471 -27.87595849 -27.88313264
#> [1526] -27.89029718 -27.89745212 -27.90459747 -27.91173322 -27.91885940
#> [1531] -27.92597602 -27.93308307 -27.94018056 -27.94726852 -27.95434693
#> [1536] -27.96141582 -27.96847519 -27.97552505 -27.98256541 -27.98959627
#> [1541] -27.99661765 -28.00362955 -28.01063198 -28.01762495 -28.02460847
#> [1546] -28.03158254 -28.03854718 -28.04550239 -28.05244818 -28.05938456
#> [1551] -28.06631153 -28.07322911 -28.08013731 -28.08703612 -28.09392557
#> [1556] -28.10080565 -28.10767638 -28.11453777 -28.12138982 -28.12823253
#> [1561] -28.13506593 -28.14189002 -28.14870480 -28.15551028 -28.16230648
#> [1566] -28.16909339 -28.17587103 -28.18263941 -28.18939853 -28.19614841
#> [1571] -28.20288904 -28.20962045 -28.21634263 -28.22305559 -28.22975934
#> [1576] -28.23645390 -28.24313927 -28.24981545 -28.25648245 -28.26314029
#> [1581] -28.26978897 -28.27642850 -28.28305889 -28.28968013 -28.29629226
#> [1586] -28.30289526 -28.30948915 -28.31607393 -28.32264963 -28.32921623
#> [1591] -28.33577375 -28.34232220 -28.34886159 -28.35539192 -28.36191321
#> [1596] -28.36842545 -28.37492866 -28.38142284 -28.38790801 -28.39438417
#> [1601] -28.40085133 -28.40730950 -28.41375868 -28.42019888 -28.42663011
#> [1606] -28.43305238 -28.43946570 -28.44587007 -28.45226550 -28.45865200
#> [1611] -28.46502958 -28.47139824 -28.47775800 -28.48410886 -28.49045082
#> [1616] -28.49678390 -28.50310810 -28.50942343 -28.51572991 -28.52202753
#> [1621] -28.52831630 -28.53459623 -28.54086734 -28.54712962 -28.55338309
#> [1626] -28.55962775 -28.56586361 -28.57209068 -28.57830896 -28.58451847
#> [1631] -28.59071920 -28.59691118 -28.60309440 -28.60926887 -28.61543461
#> [1636] -28.62159161 -28.62773990 -28.63387946 -28.64001032 -28.64613247
#> [1641] -28.65224593 -28.65835071 -28.66444681 -28.67053423 -28.67661299
#> [1646] -28.68268310 -28.68874456 -28.69479738 -28.70084156 -28.70687712
#> [1651] -28.71290406 -28.71892239 -28.72493211 -28.73093324 -28.73692578
#> [1656] -28.74290974 -28.74888513 -28.75485194 -28.76081020 -28.76675991
#> [1661] -28.77270108 -28.77863370 -28.78455780 -28.79047338 -28.79638044
#> [1666] -28.80227899 -28.80816904 -28.81405060 -28.81992368 -28.82578828
#> [1671] -28.83164440 -28.83749207 -28.84333127 -28.84916203 -28.85498435
#> [1676] -28.86079823 -28.86660369 -28.87240073 -28.87818935 -28.88396957
#> [1681] -28.88974139 -28.89550482 -28.90125987 -28.90700654 -28.91274484
#> [1686] -28.91847478 -28.92419637 -28.92990961 -28.93561451 -28.94131107
#> [1691] -28.94699931 -28.95267924 -28.95835085 -28.96401415 -28.96966916
#> [1696] -28.97531588 -28.98095432 -28.98658448 -28.99220637 -28.99782000
#> [1701] -29.00342538 -29.00902251 -29.01461140 -29.02019206 -29.02576449
#> [1706] -29.03132870 -29.03688470 -29.04243250 -29.04797209 -29.05350350
#> [1711] -29.05902673 -29.06454177 -29.07004865 -29.07554737 -29.08103793
#> [1716] -29.08652034 -29.09199461 -29.09746075 -29.10291876 -29.10836864
#> [1721] -29.11381042 -29.11924409 -29.12466966 -29.13008713 -29.13549652
#> [1726] -29.14089784 -29.14629108 -29.15167625 -29.15705337 -29.16242244
#> [1731] -29.16778346 -29.17313645 -29.17848140 -29.18381833 -29.18914725
#> [1736] -29.19446815 -29.19978106 -29.20508596 -29.21038288 -29.21567182
#> [1741] -29.22095278 -29.22622577 -29.23149080 -29.23674788 -29.24199700
#> [1746] -29.24723819 -29.25247144 -29.25769677 -29.26291417 -29.26812366
#> [1751] -29.27332524 -29.27851892 -29.28370471 -29.28888261 -29.29405263
#> [1756] -29.29921478 -29.30436906 -29.30951548 -29.31465405 -29.31978477
#> [1761] -29.32490765 -29.33002270 -29.33512992 -29.34022932 -29.34532091
#> [1766] -29.35040469 -29.35548067 -29.36054886 -29.36560926 -29.37066188
#> [1771] -29.37570673 -29.38074382 -29.38577314 -29.39079471 -29.39580853
#> [1776] -29.40081462 -29.40581297 -29.41080359 -29.41578649 -29.42076168
#> [1781] -29.42572916 -29.43068895 -29.43564104 -29.44058544 -29.44552216
#> [1786] -29.45045120 -29.45537258 -29.46028630 -29.46519236 -29.47009078
#> [1791] -29.47498155 -29.47986469 -29.48474020 -29.48960809 -29.49446836
#> [1796] -29.49932102 -29.50416608 -29.50900355 -29.51383342 -29.51865572
#> [1801] -29.52347043 -29.52827758 -29.53307716 -29.53786918 -29.54265366
#> [1806] -29.54743059 -29.55219998 -29.55696184 -29.56171617 -29.56646299
#> [1811] -29.57120229 -29.57593409 -29.58065839 -29.58537519 -29.59008451
#> [1816] -29.59478635 -29.59948071 -29.60416761 -29.60884704 -29.61351902
#> [1821] -29.61818355 -29.62284064 -29.62749029 -29.63213251 -29.63676731
#> [1826] -29.64139469 -29.64601466 -29.65062723 -29.65523239 -29.65983017
#> [1831] -29.66442056 -29.66900357 -29.67357921 -29.67814748 -29.68270839
#> [1836] -29.68726195 -29.69180815 -29.69634702 -29.70087855 -29.70540275
#> [1841] -29.70991963 -29.71442919 -29.71893144 -29.72342638 -29.72791403
#> [1846] -29.73239438 -29.73686745 -29.74133324 -29.74579176 -29.75024300
#> [1851] -29.75468699 -29.75912372 -29.76355320 -29.76797544 -29.77239044
#> [1856] -29.77679821 -29.78119876 -29.78559209 -29.78997821 -29.79435712
#> [1861] -29.79872883 -29.80309334 -29.80745067 -29.81180082 -29.81614379
#> [1866] -29.82047959 -29.82480822 -29.82912970 -29.83344403 -29.83775121
#> [1871] -29.84205126 -29.84634417 -29.85062995 -29.85490861 -29.85918016
#> [1876] -29.86344460 -29.86770193 -29.87195217 -29.87619531 -29.88043137
#> [1881] -29.88466035 -29.88888226 -29.89309710 -29.89730488 -29.90150560
#> [1886] -29.90569928 -29.90988591 -29.91406550 -29.91823806 -29.92240360
#> [1891] -29.92656212 -29.93071362 -29.93485812 -29.93899561 -29.94312611
#> [1896] -29.94724961 -29.95136614 -29.95547568 -29.95957825 -29.96367386
#> [1901] -29.96776251 -29.97184420 -29.97591894 -29.97998674 -29.98404760
#> [1906] -29.98810153 -29.99214853 -29.99618862 -30.00022179 -30.00424805
#> [1911] -30.00826741 -30.01227988 -30.01628545 -30.02028414 -30.02427595
#> [1916] -30.02826089 -30.03223896 -30.03621017 -30.04017452 -30.04413202
#> [1921] -30.04808268 -30.05202650 -30.05596349 -30.05989365 -30.06381699
#> [1926] -30.06773351 -30.07164323 -30.07554614 -30.07944225 -30.08333157
#> [1931] -30.08721410 -30.09108985 -30.09495883 -30.09882104 -30.10267648
#> [1936] -30.10652516 -30.11036709 -30.11420228 -30.11803072 -30.12185243
#> [1941] -30.12566741 -30.12947566 -30.13327720 -30.13707202 -30.14086013
#> [1946] -30.14464154 -30.14841626 -30.15218429 -30.15594563 -30.15970029
#> [1951] -30.16344828 -30.16718960 -30.17092426 -30.17465226 -30.17837361
#> [1956] -30.18208831 -30.18579638 -30.18949781 -30.19319261 -30.19688079
#> [1961] -30.20056235 -30.20423729 -30.20790563 -30.21156737 -30.21522252
#> [1966] -30.21887107 -30.22251304 -30.22614843 -30.22977725 -30.23339950
#> [1971] -30.23701519 -30.24062432 -30.24422689 -30.24782293 -30.25141242
#> [1976] -30.25499537 -30.25857180 -30.26214171 -30.26570509 -30.26926196
#> [1981] -30.27281233 -30.27635619 -30.27989355 -30.28342443 -30.28694881
#> [1986] -30.29046672 -30.29397815 -30.29748312 -30.30098161 -30.30447365
#> [1991] -30.30795924 -30.31143838 -30.31491108 -30.31837733 -30.32183716
#> [1996] -30.32529056 -30.32873754 -30.33217811 -30.33561226 -30.33904001
#> [2001] -30.34246136