Moneyness formula implementation, for Black-Scholes-Merton model.
Arguments
- 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.
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.
Examples
bsmmoneyness(0:49, 1:50, 3, 0.1, 0)
#> [1] 1.00000000 0.32507060 0.10009413 -0.01239411 -0.07988705 -0.12488234
#> [7] -0.15702184 -0.18112646 -0.19987450 -0.21487293 -0.22714437 -0.23737057
#> [13] -0.24602351 -0.25344032 -0.25986822 -0.26549263 -0.27045535 -0.27486665
#> [19] -0.27881361 -0.28236587 -0.28557982 -0.28850159 -0.29116929 -0.29361469
#> [25] -0.29586446 -0.29794116 -0.29986404 -0.30164956 -0.30331195 -0.30486351
#> [31] -0.30631498 -0.30767572 -0.30895400 -0.31015708 -0.31129141 -0.31236273
#> [37] -0.31337614 -0.31433621 -0.31524704 -0.31611234 -0.31693542 -0.31771931
#> [43] -0.31846674 -0.31918020 -0.31986195 -0.32051405 -0.32113841 -0.32173675
#> [49] -0.32231067 -0.32286163
bsmmoneyness(10, 10, 1, 0.12, 0:1000 / 1000)
#> [1] -0.1274968516 -0.1263699183 -0.1252441114 -0.1241194297 -0.1229958721
#> [6] -0.1218734376 -0.1207521249 -0.1196319329 -0.1185128606 -0.1173949069
#> [11] -0.1162780705 -0.1151623503 -0.1140477454 -0.1129342545 -0.1118218765
#> [16] -0.1107106104 -0.1096004549 -0.1084914091 -0.1073834717 -0.1062766418
#> [21] -0.1051709181 -0.1040662996 -0.1029627851 -0.1018603736 -0.1007590640
#> [26] -0.0996588551 -0.0985597459 -0.0974617353 -0.0963648221 -0.0952690053
#> [31] -0.0941742837 -0.0930806563 -0.0919881220 -0.0908966797 -0.0898063283
#> [36] -0.0887170667 -0.0876288938 -0.0865418085 -0.0854558098 -0.0843708966
#> [41] -0.0832870677 -0.0822043221 -0.0811226587 -0.0800420764 -0.0789625742
#> [46] -0.0778841509 -0.0768068055 -0.0757305369 -0.0746553441 -0.0735812259
#> [51] -0.0725081813 -0.0714362091 -0.0703653085 -0.0692954782 -0.0682267172
#> [56] -0.0671590244 -0.0660923988 -0.0650268392 -0.0639623447 -0.0628989142
#> [61] -0.0618365465 -0.0607752407 -0.0597149957 -0.0586558104 -0.0575976837
#> [66] -0.0565406147 -0.0554846022 -0.0544296451 -0.0533757425 -0.0523228933
#> [71] -0.0512710964 -0.0502203507 -0.0491706553 -0.0481220091 -0.0470744110
#> [76] -0.0460278599 -0.0449823549 -0.0439378949 -0.0428944788 -0.0418521055
#> [81] -0.0408107742 -0.0397704837 -0.0387312329 -0.0376930208 -0.0366558465
#> [86] -0.0356197088 -0.0345846067 -0.0335505392 -0.0325175053 -0.0314855039
#> [91] -0.0304545340 -0.0294245945 -0.0283956844 -0.0273678028 -0.0263409485
#> [96] -0.0253151205 -0.0242903179 -0.0232665395 -0.0222437845 -0.0212220516
#> [101] -0.0202013400 -0.0191816486 -0.0181629764 -0.0171453223 -0.0161286854
#> [106] -0.0151130646 -0.0140984589 -0.0130848674 -0.0120722889 -0.0110607224
#> [111] -0.0100501671 -0.0090406218 -0.0080320855 -0.0070245573 -0.0060180361
#> [116] -0.0050125209 -0.0040080107 -0.0030045045 -0.0020020013 -0.0010005002
#> [121] 0.0000000000 0.0009995002 0.0019980013 0.0029955045 0.0039920107
#> [126] 0.0049875208 0.0059820359 0.0069755571 0.0079680852 0.0089596212
#> [131] 0.0099501663 0.0109397212 0.0119282871 0.0129158650 0.0139024557
#> [136] 0.0148880604 0.0158726799 0.0168563154 0.0178389676 0.0188206378
#> [141] 0.0198013267 0.0207810354 0.0217597649 0.0227375162 0.0237142902
#> [146] 0.0246900880 0.0256649104 0.0266387585 0.0276116332 0.0285835355
#> [151] 0.0295544665 0.0305244269 0.0314934179 0.0324614404 0.0334284954
#> [156] 0.0343945837 0.0353597065 0.0363238647 0.0372870591 0.0382492909
#> [161] 0.0392105608 0.0401708701 0.0411302194 0.0420886099 0.0430460425
#> [166] 0.0440025182 0.0449580378 0.0459126024 0.0468662129 0.0478188703
#> [171] 0.0487705755 0.0497213295 0.0506711332 0.0516199875 0.0525678935
#> [176] 0.0535148520 0.0544608641 0.0554059306 0.0563500526 0.0572932308
#> [181] 0.0582354664 0.0591767602 0.0601171132 0.0610565263 0.0619950005
#> [186] 0.0629325366 0.0638691357 0.0648047987 0.0657395264 0.0666733199
#> [191] 0.0676061801 0.0685381079 0.0694691042 0.0703991700 0.0713283062
#> [196] 0.0722565137 0.0731837934 0.0741101464 0.0750355735 0.0759600756
#> [201] 0.0768836536 0.0778063086 0.0787280413 0.0796488528 0.0805687439
#> [206] 0.0814877156 0.0824057688 0.0833229044 0.0842391233 0.0851544264
#> [211] 0.0860688147 0.0869822891 0.0878948505 0.0888064997 0.0897172378
#> [216] 0.0906270655 0.0915359839 0.0924439939 0.0933510962 0.0942572920
#> [221] 0.0951625820 0.0960669671 0.0969704483 0.0978730265 0.0987747026
#> [226] 0.0996754774 0.1005753519 0.1014743270 0.1023724036 0.1032695825
#> [231] 0.1041658647 0.1050612511 0.1059557425 0.1068493399 0.1077420441
#> [236] 0.1086338561 0.1095247767 0.1104148068 0.1113039474 0.1121921992
#> [241] 0.1130795633 0.1139660404 0.1148516315 0.1157363374 0.1166201591
#> [246] 0.1175030974 0.1183851532 0.1192663274 0.1201466209 0.1210260345
#> [251] 0.1219045691 0.1227822256 0.1236590049 0.1245349079 0.1254099354
#> [256] 0.1262840883 0.1271573675 0.1280297739 0.1289013083 0.1297719715
#> [261] 0.1306417646 0.1315106883 0.1323787435 0.1332459311 0.1341122519
#> [266] 0.1349777069 0.1358422968 0.1367060226 0.1375688851 0.1384308851
#> [271] 0.1392920236 0.1401523013 0.1410117193 0.1418702782 0.1427279790
#> [276] 0.1435848225 0.1444408096 0.1452959412 0.1461502180 0.1470036410
#> [281] 0.1478562110 0.1487079289 0.1495587955 0.1504088116 0.1512579781
#> [286] 0.1521062959 0.1529537658 0.1538003887 0.1546461653 0.1554910966
#> [291] 0.1563351834 0.1571784265 0.1580208268 0.1588623852 0.1597031023
#> [296] 0.1605429792 0.1613820167 0.1622202155 0.1630575765 0.1638941006
#> [301] 0.1647297886 0.1655646413 0.1663986596 0.1672318443 0.1680641962
#> [306] 0.1688957161 0.1697264050 0.1705562636 0.1713852928 0.1722134933
#> [311] 0.1730408661 0.1738674118 0.1746931315 0.1755180259 0.1763420957
#> [316] 0.1771653419 0.1779877653 0.1788093667 0.1796301469 0.1804501067
#> [321] 0.1812692469 0.1820875684 0.1829050721 0.1837217586 0.1845376288
#> [326] 0.1853526836 0.1861669237 0.1869803500 0.1877929633 0.1886047644
#> [331] 0.1894157540 0.1902259331 0.1910353024 0.1918438628 0.1926516150
#> [336] 0.1934585598 0.1942646981 0.1950700307 0.1958745583 0.1966782818
#> [341] 0.1974812020 0.1982833197 0.1990846357 0.1998851507 0.2006848656
#> [346] 0.2014837812 0.2022818983 0.2030792177 0.2038757402 0.2046714665
#> [351] 0.2054663975 0.2062605340 0.2070538767 0.2078464265 0.2086381841
#> [356] 0.2094291504 0.2102193261 0.2110087120 0.2117973089 0.2125851176
#> [361] 0.2133721389 0.2141583736 0.2149438224 0.2157284862 0.2165123657
#> [366] 0.2172954618 0.2180777751 0.2188593065 0.2196400567 0.2204200266
#> [371] 0.2211992169 0.2219776284 0.2227552619 0.2235321182 0.2243081980
#> [376] 0.2250835020 0.2258580312 0.2266317862 0.2274047679 0.2281769770
#> [381] 0.2289484142 0.2297190804 0.2304889763 0.2312581027 0.2320264603
#> [386] 0.2327940500 0.2335608725 0.2343269285 0.2350922189 0.2358567444
#> [391] 0.2366205057 0.2373835036 0.2381457389 0.2389072124 0.2396679247
#> [396] 0.2404278768 0.2411870692 0.2419455029 0.2427031785 0.2434600968
#> [401] 0.2442162585 0.2449716645 0.2457263155 0.2464802121 0.2472333553
#> [406] 0.2479857457 0.2487373841 0.2494882712 0.2502384078 0.2509877946
#> [411] 0.2517364324 0.2524843220 0.2532314640 0.2539778593 0.2547235086
#> [416] 0.2554684125 0.2562125720 0.2569559876 0.2576986603 0.2584405906
#> [421] 0.2591817793 0.2599222273 0.2606619351 0.2614009036 0.2621391335
#> [426] 0.2628766256 0.2636133805 0.2643493991 0.2650846820 0.2658192300
#> [431] 0.2665530438 0.2672861241 0.2680184718 0.2687500874 0.2694809718
#> [436] 0.2702111257 0.2709405498 0.2716692449 0.2723972116 0.2731244507
#> [441] 0.2738509629 0.2745767490 0.2753018097 0.2760261456 0.2767497576
#> [446] 0.2774726464 0.2781948126 0.2789162570 0.2796369803 0.2803569833
#> [451] 0.2810762666 0.2817948310 0.2825126771 0.2832298058 0.2839462178
#> [456] 0.2846619136 0.2853768942 0.2860911601 0.2868047121 0.2875175509
#> [461] 0.2882296772 0.2889410918 0.2896517953 0.2903617884 0.2910710720
#> [466] 0.2917796465 0.2924875129 0.2931946717 0.2939011238 0.2946068697
#> [471] 0.2953119103 0.2960162461 0.2967198780 0.2974228066 0.2981250326
#> [476] 0.2988265568 0.2995273798 0.3002275023 0.3009269250 0.3016256486
#> [481] 0.3023236739 0.3030210015 0.3037176322 0.3044135665 0.3051088053
#> [486] 0.3058033491 0.3064971988 0.3071903550 0.3078828183 0.3085745895
#> [491] 0.3092656694 0.3099560584 0.3106457575 0.3113347672 0.3120230882
#> [496] 0.3127107212 0.3133976670 0.3140839261 0.3147694993 0.3154543873
#> [501] 0.3161385908 0.3168221104 0.3175049468 0.3181871007 0.3188685728
#> [506] 0.3195493638 0.3202294743 0.3209089051 0.3215876567 0.3222657300
#> [511] 0.3229431255 0.3236198440 0.3242958860 0.3249712524 0.3256459438
#> [516] 0.3263199608 0.3269933041 0.3276659744 0.3283379723 0.3290092986
#> [521] 0.3296799540 0.3303499390 0.3310192543 0.3316879007 0.3323558787
#> [526] 0.3330231891 0.3336898326 0.3343558097 0.3350211212 0.3356857677
#> [531] 0.3363497499 0.3370130684 0.3376757239 0.3383377172 0.3389990487
#> [536] 0.3396597193 0.3403197295 0.3409790801 0.3416377716 0.3422958047
#> [541] 0.3429531802 0.3436098986 0.3442659606 0.3449213669 0.3455761181
#> [546] 0.3462302149 0.3468836579 0.3475364478 0.3481885852 0.3488400708
#> [551] 0.3494909053 0.3501410892 0.3507906233 0.3514395082 0.3520877445
#> [556] 0.3527353329 0.3533822741 0.3540285686 0.3546742171 0.3553192204
#> [561] 0.3559635789 0.3566072934 0.3572503645 0.3578927929 0.3585345792
#> [566] 0.3591757240 0.3598162279 0.3604560917 0.3610953160 0.3617339013
#> [571] 0.3623718484 0.3630091578 0.3636458303 0.3642818664 0.3649172668
#> [576] 0.3655520321 0.3661861629 0.3668196599 0.3674525238 0.3680847551
#> [581] 0.3687163545 0.3693473226 0.3699776601 0.3706073675 0.3712364455
#> [586] 0.3718648948 0.3724927160 0.3731199096 0.3737464763 0.3743724168
#> [591] 0.3749977317 0.3756224216 0.3762464871 0.3768699288 0.3774927474
#> [596] 0.3781149435 0.3787365178 0.3793574707 0.3799778030 0.3805975153
#> [601] 0.3812166082 0.3818350823 0.3824529382 0.3830701766 0.3836867981
#> [606] 0.3843028032 0.3849181927 0.3855329671 0.3861471270 0.3867606730
#> [611] 0.3873736058 0.3879859260 0.3885976342 0.3892087309 0.3898192169
#> [616] 0.3904290927 0.3910383589 0.3916470162 0.3922550651 0.3928625063
#> [621] 0.3934693403 0.3940755678 0.3946811894 0.3952862056 0.3958906171
#> [626] 0.3964944246 0.3970976285 0.3977002295 0.3983022282 0.3989036253
#> [631] 0.3995044212 0.4001046166 0.4007042122 0.4013032084 0.4019016059
#> [636] 0.4024994054 0.4030966073 0.4036932124 0.4042892211 0.4048846341
#> [641] 0.4054794520 0.4060736754 0.4066673049 0.4072603410 0.4078527844
#> [646] 0.4084446356 0.4090358953 0.4096265640 0.4102166424 0.4108061310
#> [651] 0.4113950303 0.4119833411 0.4125710638 0.4131581992 0.4137447476
#> [656] 0.4143307099 0.4149160864 0.4155008779 0.4160850848 0.4166687079
#> [661] 0.4172517476 0.4178342046 0.4184160794 0.4189973726 0.4195780849
#> [666] 0.4201582167 0.4207377686 0.4213167413 0.4218951353 0.4224729512
#> [671] 0.4230501896 0.4236268511 0.4242029361 0.4247784454 0.4253533794
#> [676] 0.4259277388 0.4265015241 0.4270747359 0.4276473748 0.4282194414
#> [681] 0.4287909362 0.4293618597 0.4299322126 0.4305019955 0.4310712088
#> [686] 0.4316398532 0.4322079293 0.4327754376 0.4333423786 0.4339087530
#> [691] 0.4344745613 0.4350398041 0.4356044819 0.4361685953 0.4367321449
#> [696] 0.4372951312 0.4378575548 0.4384194163 0.4389807162 0.4395414550
#> [701] 0.4401016334 0.4406612519 0.4412203111 0.4417788115 0.4423367537
#> [706] 0.4428941382 0.4434509656 0.4440072364 0.4445629513 0.4451181107
#> [711] 0.4456727153 0.4462267655 0.4467802619 0.4473332051 0.4478855957
#> [716] 0.4484374341 0.4489887210 0.4495394569 0.4500896423 0.4506392778
#> [721] 0.4511883639 0.4517369012 0.4522848903 0.4528323316 0.4533792258
#> [726] 0.4539255734 0.4544713748 0.4550166308 0.4555613418 0.4561055083
#> [731] 0.4566491309 0.4571922102 0.4577347467 0.4582767409 0.4588181934
#> [736] 0.4593591047 0.4598994754 0.4604393059 0.4609785969 0.4615173489
#> [741] 0.4620555624 0.4625932380 0.4631303761 0.4636669774 0.4642030423
#> [746] 0.4647385715 0.4652735654 0.4658080245 0.4663419495 0.4668753408
#> [751] 0.4674081990 0.4679405246 0.4684723181 0.4690035801 0.4695343111
#> [756] 0.4700645117 0.4705941823 0.4711233235 0.4716519358 0.4721800198
#> [761] 0.4727075760 0.4732346048 0.4737611069 0.4742870828 0.4748125329
#> [766] 0.4753374579 0.4758618582 0.4763857344 0.4769090869 0.4774319164
#> [771] 0.4779542232 0.4784760081 0.4789972714 0.4795180137 0.4800382355
#> [776] 0.4805579374 0.4810771198 0.4815957833 0.4821139284 0.4826315557
#> [781] 0.4831486655 0.4836652585 0.4841813352 0.4846968960 0.4852119415
#> [786] 0.4857264723 0.4862404888 0.4867539915 0.4872669810 0.4877794577
#> [791] 0.4882914222 0.4888028750 0.4893138166 0.4898242476 0.4903341683
#> [796] 0.4908435794 0.4913524813 0.4918608746 0.4923687597 0.4928761372
#> [801] 0.4933830076 0.4938893714 0.4943952291 0.4949005811 0.4954054281
#> [806] 0.4959097704 0.4964136087 0.4969169434 0.4974197750 0.4979221040
#> [811] 0.4984239309 0.4989252563 0.4994260806 0.4999264043 0.5004262279
#> [816] 0.5009255520 0.5014243770 0.5019227034 0.5024205318 0.5029178625
#> [821] 0.5034146962 0.5039110333 0.5044068743 0.5049022197 0.5053970700
#> [826] 0.5058914257 0.5063852873 0.5068786553 0.5073715302 0.5078639124
#> [831] 0.5083558025 0.5088472010 0.5093381083 0.5098285249 0.5103184514
#> [836] 0.5108078882 0.5112968358 0.5117852947 0.5122732654 0.5127607483
#> [841] 0.5132477440 0.5137342530 0.5142202757 0.5147058126 0.5151908642
#> [846] 0.5156754310 0.5161595135 0.5166431122 0.5171262275 0.5176088599
#> [851] 0.5180910099 0.5185726780 0.5190538647 0.5195345705 0.5200147957
#> [856] 0.5204945410 0.5209738068 0.5214525936 0.5219309018 0.5224087319
#> [861] 0.5228860845 0.5233629599 0.5238393587 0.5243152814 0.5247907283
#> [866] 0.5252657001 0.5257401971 0.5262142198 0.5266877688 0.5271608444
#> [871] 0.5276334473 0.5281055777 0.5285772363 0.5290484234 0.5295191396
#> [876] 0.5299893853 0.5304591610 0.5309284671 0.5313973042 0.5318656727
#> [881] 0.5323335730 0.5328010057 0.5332679711 0.5337344699 0.5342005024
#> [886] 0.5346660690 0.5351311704 0.5355958068 0.5360599789 0.5365236870
#> [891] 0.5369869317 0.5374497133 0.5379120324 0.5383738894 0.5388352848
#> [896] 0.5392962190 0.5397566925 0.5402167058 0.5406762592 0.5411353534
#> [901] 0.5415939887 0.5420521656 0.5425098845 0.5429671460 0.5434239504
#> [906] 0.5438802982 0.5443361899 0.5447916260 0.5452466068 0.5457011329
#> [911] 0.5461552047 0.5466088227 0.5470619872 0.5475146988 0.5479669580
#> [916] 0.5484187651 0.5488701206 0.5493210250 0.5497714787 0.5502214822
#> [921] 0.5506710359 0.5511201403 0.5515687958 0.5520170028 0.5524647619
#> [926] 0.5529120734 0.5533589379 0.5538053557 0.5542513273 0.5546968532
#> [931] 0.5551419338 0.5555865695 0.5560307608 0.5564745081 0.5569178119
#> [936] 0.5573606726 0.5578030907 0.5582450666 0.5586866007 0.5591276936
#> [941] 0.5595683455 0.5600085570 0.5604483285 0.5608876605 0.5613265534
#> [946] 0.5617650075 0.5622030235 0.5626406016 0.5630777424 0.5635144463
#> [951] 0.5639507137 0.5643865450 0.5648219407 0.5652569013 0.5656914271
#> [956] 0.5661255186 0.5665591762 0.5669924004 0.5674251915 0.5678575501
#> [961] 0.5682894766 0.5687209713 0.5691520348 0.5695826674 0.5700128696
#> [966] 0.5704426418 0.5708719844 0.5713008980 0.5717293828 0.5721574393
#> [971] 0.5725850681 0.5730122693 0.5734390437 0.5738653914 0.5742913130
#> [976] 0.5747168089 0.5751418795 0.5755665253 0.5759907466 0.5764145439
#> [981] 0.5768379177 0.5772608683 0.5776833961 0.5781055016 0.5785271852
#> [986] 0.5789484474 0.5793692885 0.5797897089 0.5802097092 0.5806292897
#> [991] 0.5810484508 0.5814671929 0.5818855165 0.5823034220 0.5827209098
#> [996] 0.5831379803 0.5835546340 0.5839708712 0.5843866924 0.5848020979
#> [1001] 0.5852170883
bsmmoneyness(10, 10, 1, 0:1000 / 1000, 0)
#> [1] 0.000000000 -0.001000500 -0.002002001 -0.003004505 -0.004008011
#> [6] -0.005012521 -0.006018036 -0.007024557 -0.008032086 -0.009040622
#> [11] -0.010050167 -0.011060722 -0.012072289 -0.013084867 -0.014098459
#> [16] -0.015113065 -0.016128685 -0.017145322 -0.018162976 -0.019181649
#> [21] -0.020201340 -0.021222052 -0.022243784 -0.023266540 -0.024290318
#> [26] -0.025315121 -0.026340948 -0.027367803 -0.028395684 -0.029424594
#> [31] -0.030454534 -0.031485504 -0.032517505 -0.033550539 -0.034584607
#> [36] -0.035619709 -0.036655846 -0.037693021 -0.038731233 -0.039770484
#> [41] -0.040810774 -0.041852106 -0.042894479 -0.043937895 -0.044982355
#> [46] -0.046027860 -0.047074411 -0.048122009 -0.049170655 -0.050220351
#> [51] -0.051271096 -0.052322893 -0.053375743 -0.054429645 -0.055484602
#> [56] -0.056540615 -0.057597684 -0.058655810 -0.059714996 -0.060775241
#> [61] -0.061836547 -0.062898914 -0.063962345 -0.065026839 -0.066092399
#> [66] -0.067159024 -0.068226717 -0.069295478 -0.070365308 -0.071436209
#> [71] -0.072508181 -0.073581226 -0.074655344 -0.075730537 -0.076806805
#> [76] -0.077884151 -0.078962574 -0.080042076 -0.081122659 -0.082204322
#> [81] -0.083287068 -0.084370897 -0.085455810 -0.086541809 -0.087628894
#> [86] -0.088717067 -0.089806328 -0.090896680 -0.091988122 -0.093080656
#> [91] -0.094174284 -0.095269005 -0.096364822 -0.097461735 -0.098559746
#> [96] -0.099658855 -0.100759064 -0.101860374 -0.102962785 -0.104066300
#> [101] -0.105170918 -0.106276642 -0.107383472 -0.108491409 -0.109600455
#> [106] -0.110710610 -0.111821877 -0.112934254 -0.114047745 -0.115162350
#> [111] -0.116278070 -0.117394907 -0.118512861 -0.119631933 -0.120752125
#> [116] -0.121873438 -0.122995872 -0.124119430 -0.125244111 -0.126369918
#> [121] -0.127496852 -0.128624912 -0.129754102 -0.130884421 -0.132015871
#> [126] -0.133148453 -0.134282168 -0.135417018 -0.136553003 -0.137690124
#> [131] -0.138828383 -0.139967781 -0.141108319 -0.142249998 -0.143392820
#> [136] -0.144536784 -0.145681894 -0.146828149 -0.147975550 -0.149124100
#> [141] -0.150273799 -0.151424648 -0.152576649 -0.153729802 -0.154884109
#> [146] -0.156039570 -0.157196188 -0.158353963 -0.159512896 -0.160672989
#> [151] -0.161834243 -0.162996658 -0.164160236 -0.165324979 -0.166490887
#> [156] -0.167657961 -0.168826203 -0.169995614 -0.171166195 -0.172337947
#> [161] -0.173510871 -0.174684969 -0.175860241 -0.177036690 -0.178214315
#> [166] -0.179393119 -0.180573102 -0.181754265 -0.182936611 -0.184120139
#> [171] -0.185304851 -0.186490749 -0.187677833 -0.188866105 -0.190055566
#> [176] -0.191246217 -0.192438059 -0.193631093 -0.194825321 -0.196020744
#> [181] -0.197217363 -0.198415179 -0.199614194 -0.200814408 -0.202015823
#> [186] -0.203218440 -0.204422260 -0.205627285 -0.206833515 -0.208040952
#> [191] -0.209249598 -0.210459452 -0.211670517 -0.212882794 -0.214096283
#> [196] -0.215310986 -0.216526905 -0.217744041 -0.218962394 -0.220181966
#> [201] -0.221402758 -0.222624772 -0.223848008 -0.225072468 -0.226298153
#> [206] -0.227525065 -0.228753204 -0.229982572 -0.231213170 -0.232444999
#> [211] -0.233678060 -0.234912355 -0.236147885 -0.237384651 -0.238622655
#> [216] -0.239861897 -0.241102379 -0.242344102 -0.243587068 -0.244831277
#> [221] -0.246076731 -0.247323431 -0.248571378 -0.249820574 -0.251071019
#> [226] -0.252322716 -0.253575665 -0.254829868 -0.256085325 -0.257342039
#> [231] -0.258600010 -0.259859239 -0.261119729 -0.262381479 -0.263644492
#> [236] -0.264908769 -0.266174310 -0.267441118 -0.268709193 -0.269978537
#> [241] -0.271249150 -0.272521035 -0.273794193 -0.275068624 -0.276344330
#> [246] -0.277621313 -0.278899574 -0.280179113 -0.281459932 -0.282742033
#> [251] -0.284025417 -0.285310084 -0.286596037 -0.287883277 -0.289171804
#> [256] -0.290461621 -0.291752728 -0.293045127 -0.294338819 -0.295633805
#> [261] -0.296930087 -0.298227665 -0.299526542 -0.300826719 -0.302128196
#> [266] -0.303430976 -0.304735059 -0.306040446 -0.307347140 -0.308655141
#> [271] -0.309964451 -0.311275070 -0.312587001 -0.313900245 -0.315214802
#> [276] -0.316530675 -0.317847864 -0.319166371 -0.320486197 -0.321807344
#> [281] -0.323129812 -0.324453604 -0.325778720 -0.327105162 -0.328432931
#> [286] -0.329762028 -0.331092455 -0.332424213 -0.333757304 -0.335091729
#> [291] -0.336427488 -0.337764584 -0.339103018 -0.340442790 -0.341783904
#> [296] -0.343126359 -0.344470157 -0.345815299 -0.347161788 -0.348509623
#> [301] -0.349858808 -0.351209342 -0.352561227 -0.353914464 -0.355269056
#> [306] -0.356625003 -0.357982307 -0.359340968 -0.360700989 -0.362062371
#> [311] -0.363425114 -0.364789221 -0.366154693 -0.367521531 -0.368889737
#> [316] -0.370259311 -0.371630256 -0.373002572 -0.374376261 -0.375751325
#> [321] -0.377127764 -0.378505581 -0.379884776 -0.381265351 -0.382647307
#> [326] -0.384030646 -0.385415369 -0.386801477 -0.388188972 -0.389577856
#> [331] -0.390968128 -0.392359792 -0.393752849 -0.395147298 -0.396543144
#> [336] -0.397940385 -0.399339025 -0.400739064 -0.402140503 -0.403543345
#> [341] -0.404947591 -0.406353241 -0.407760298 -0.409168762 -0.410578636
#> [346] -0.411989920 -0.413402616 -0.414816725 -0.416232250 -0.417649190
#> [351] -0.419067549 -0.420487326 -0.421908524 -0.423331143 -0.424755186
#> [356] -0.426180654 -0.427607548 -0.429035870 -0.430465620 -0.431896802
#> [361] -0.433329415 -0.434763461 -0.436198942 -0.437635859 -0.439074214
#> [366] -0.440514008 -0.441955243 -0.443397919 -0.444842039 -0.446287604
#> [371] -0.447734615 -0.449183073 -0.450632981 -0.452084340 -0.453537150
#> [376] -0.454991415 -0.456447134 -0.457904309 -0.459362943 -0.460823036
#> [381] -0.462284589 -0.463747605 -0.465212085 -0.466678030 -0.468145442
#> [386] -0.469614321 -0.471084671 -0.472556491 -0.474029784 -0.475504551
#> [391] -0.476980794 -0.478458513 -0.479937711 -0.481418389 -0.482900549
#> [396] -0.484384191 -0.485869318 -0.487355930 -0.488844030 -0.490333619
#> [401] -0.491824698 -0.493317268 -0.494811333 -0.496306892 -0.497803947
#> [406] -0.499302500 -0.500802552 -0.502304106 -0.503807161 -0.505311720
#> [411] -0.506817785 -0.508325357 -0.509834436 -0.511345026 -0.512857127
#> [416] -0.514370741 -0.515885869 -0.517402513 -0.518920674 -0.520440355
#> [421] -0.521961556 -0.523484278 -0.525008525 -0.526534296 -0.528061594
#> [426] -0.529590420 -0.531120775 -0.532652662 -0.534186081 -0.535721034
#> [431] -0.537257524 -0.538795550 -0.540335115 -0.541876221 -0.543418868
#> [436] -0.544963059 -0.546508795 -0.548056077 -0.549604907 -0.551155287
#> [441] -0.552707219 -0.554260702 -0.555815740 -0.557372334 -0.558930486
#> [446] -0.560490196 -0.562051467 -0.563614299 -0.565178696 -0.566744657
#> [451] -0.568312185 -0.569881282 -0.571451949 -0.573024187 -0.574597997
#> [456] -0.576173383 -0.577750345 -0.579328884 -0.580909003 -0.582490703
#> [461] -0.584073985 -0.585658851 -0.587245303 -0.588833342 -0.590422970
#> [466] -0.592014189 -0.593606999 -0.595201403 -0.596797403 -0.598394999
#> [471] -0.599994193 -0.601594988 -0.603197384 -0.604801383 -0.606406987
#> [476] -0.608014197 -0.609623016 -0.611233444 -0.612845483 -0.614459136
#> [481] -0.616074402 -0.617691285 -0.619309785 -0.620929905 -0.622551646
#> [486] -0.624175009 -0.625799996 -0.627426609 -0.629054850 -0.630684720
#> [491] -0.632316220 -0.633949353 -0.635584119 -0.637220521 -0.638858561
#> [496] -0.640498239 -0.642139558 -0.643782519 -0.645427123 -0.647073374
#> [501] -0.648721271 -0.650370817 -0.652022013 -0.653674861 -0.655329363
#> [506] -0.656985520 -0.658643335 -0.660302808 -0.661963941 -0.663626736
#> [511] -0.665291195 -0.666957319 -0.668625110 -0.670294570 -0.671965700
#> [516] -0.673638502 -0.675312977 -0.676989128 -0.678666956 -0.680346463
#> [521] -0.682027650 -0.683710519 -0.685395071 -0.687081309 -0.688769234
#> [526] -0.690458848 -0.692150153 -0.693843149 -0.695537840 -0.697234225
#> [531] -0.698932309 -0.700632091 -0.702333573 -0.704036758 -0.705741647
#> [536] -0.707448242 -0.709156545 -0.710866556 -0.712578278 -0.714291713
#> [541] -0.716006862 -0.717723727 -0.719442310 -0.721162613 -0.722884636
#> [546] -0.724608382 -0.726333853 -0.728061051 -0.729789976 -0.731520631
#> [551] -0.733253018 -0.734987138 -0.736722993 -0.738460584 -0.740199914
#> [556] -0.741940985 -0.743683797 -0.745428353 -0.747174654 -0.748922703
#> [561] -0.750672500 -0.752424048 -0.754177349 -0.755932404 -0.757689214
#> [566] -0.759447783 -0.761208111 -0.762970200 -0.764734052 -0.766499668
#> [571] -0.768267051 -0.770036203 -0.771807124 -0.773579818 -0.775354285
#> [576] -0.777130527 -0.778908546 -0.780688345 -0.782469924 -0.784253285
#> [581] -0.786038431 -0.787825362 -0.789614082 -0.791404591 -0.793196892
#> [586] -0.794990986 -0.796786874 -0.798584560 -0.800384044 -0.802185329
#> [591] -0.803988415 -0.805793306 -0.807600003 -0.809408507 -0.811218820
#> [596] -0.813030945 -0.814844883 -0.816660635 -0.818478205 -0.820297592
#> [601] -0.822118800 -0.823941831 -0.825766685 -0.827593365 -0.829421872
#> [606] -0.831252209 -0.833084377 -0.834918378 -0.836754214 -0.838591887
#> [611] -0.840431399 -0.842272751 -0.844115945 -0.845960983 -0.847807867
#> [616] -0.849656600 -0.851507181 -0.853359615 -0.855213901 -0.857070043
#> [621] -0.858928042 -0.860787900 -0.862649618 -0.864513200 -0.866378645
#> [626] -0.868245957 -0.870115138 -0.871986188 -0.873859111 -0.875733907
#> [631] -0.877610579 -0.879489129 -0.881369558 -0.883251869 -0.885136063
#> [636] -0.887022141 -0.888910107 -0.890799962 -0.892691708 -0.894585346
#> [641] -0.896480879 -0.898378309 -0.900277637 -0.902178865 -0.904081995
#> [646] -0.905987029 -0.907893970 -0.909802818 -0.911713576 -0.913626246
#> [651] -0.915540829 -0.917457328 -0.919375744 -0.921296080 -0.923218337
#> [656] -0.925142517 -0.927068623 -0.928996655 -0.930926617 -0.932858509
#> [661] -0.934792334 -0.936728094 -0.938665791 -0.940605427 -0.942547003
#> [666] -0.944490521 -0.946435984 -0.948383394 -0.950332752 -0.952284060
#> [671] -0.954237321 -0.956192535 -0.958149706 -0.960108835 -0.962069925
#> [676] -0.964032976 -0.965997991 -0.967964973 -0.969933922 -0.971904841
#> [681] -0.973877732 -0.975852597 -0.977829438 -0.979808257 -0.981789055
#> [686] -0.983771836 -0.985756600 -0.987743349 -0.989732087 -0.991722814
#> [691] -0.993715533 -0.995710246 -0.997706954 -0.999705661 -1.001706366
#> [696] -1.003709074 -1.005713785 -1.007720502 -1.009729227 -1.011739961
#> [701] -1.013752707 -1.015767467 -1.017784243 -1.019803037 -1.021823850
#> [706] -1.023846685 -1.025871544 -1.027898429 -1.029927341 -1.031958284
#> [711] -1.033991259 -1.036026267 -1.038063312 -1.040102395 -1.042143517
#> [716] -1.044186682 -1.046231891 -1.048279147 -1.050328450 -1.052379804
#> [721] -1.054433211 -1.056488671 -1.058546189 -1.060605764 -1.062667401
#> [726] -1.064731100 -1.066796864 -1.068864694 -1.070934594 -1.073006564
#> [731] -1.075080608 -1.077156726 -1.079234922 -1.081315197 -1.083397553
#> [736] -1.085481993 -1.087568518 -1.089657130 -1.091747833 -1.093840627
#> [741] -1.095935514 -1.098032498 -1.100131580 -1.102232762 -1.104336046
#> [746] -1.106441435 -1.108548930 -1.110658534 -1.112770248 -1.114884075
#> [751] -1.117000017 -1.119118075 -1.121238253 -1.123360553 -1.125484975
#> [756] -1.127611523 -1.129740199 -1.131871004 -1.134003942 -1.136139013
#> [761] -1.138276220 -1.140415566 -1.142557052 -1.144700681 -1.146846454
#> [766] -1.148994375 -1.151144444 -1.153296664 -1.155451038 -1.157607567
#> [771] -1.159766254 -1.161927100 -1.164090109 -1.166255281 -1.168422620
#> [776] -1.170592127 -1.172763805 -1.174937656 -1.177113681 -1.179291884
#> [781] -1.181472265 -1.183654829 -1.185839576 -1.188026509 -1.190215630
#> [786] -1.192406941 -1.194600444 -1.196796142 -1.198994037 -1.201194131
#> [791] -1.203396426 -1.205600925 -1.207807629 -1.210016541 -1.212227663
#> [796] -1.214440997 -1.216656545 -1.218874311 -1.221094295 -1.223316500
#> [801] -1.225540928 -1.227767583 -1.229996464 -1.232227576 -1.234460920
#> [806] -1.236696499 -1.238934314 -1.241174368 -1.243416664 -1.245661202
#> [811] -1.247907987 -1.250157019 -1.252408301 -1.254661836 -1.256917626
#> [816] -1.259175672 -1.261435978 -1.263698545 -1.265963376 -1.268230473
#> [821] -1.270499838 -1.272771473 -1.275045381 -1.277321565 -1.279600025
#> [826] -1.281880765 -1.284163787 -1.286449094 -1.288736686 -1.291026568
#> [831] -1.293318740 -1.295613206 -1.297909967 -1.300209027 -1.302510386
#> [836] -1.304814048 -1.307120015 -1.309428289 -1.311738872 -1.314051768
#> [841] -1.316366977 -1.318684502 -1.321004347 -1.323326512 -1.325651000
#> [846] -1.327977815 -1.330306957 -1.332638429 -1.334972234 -1.337308375
#> [851] -1.339646852 -1.341987669 -1.344330828 -1.346676331 -1.349024181
#> [856] -1.351374381 -1.353726931 -1.356081835 -1.358439095 -1.360798714
#> [861] -1.363160694 -1.365525036 -1.367891745 -1.370260821 -1.372632267
#> [866] -1.375006086 -1.377382280 -1.379760851 -1.382141802 -1.384525136
#> [871] -1.386910854 -1.389298958 -1.391689452 -1.394082338 -1.396477618
#> [876] -1.398875294 -1.401275369 -1.403677846 -1.406082726 -1.408490012
#> [881] -1.410899706 -1.413311812 -1.415726331 -1.418143265 -1.420562618
#> [886] -1.422984391 -1.425408588 -1.427835209 -1.430264259 -1.432695739
#> [891] -1.435129651 -1.437565999 -1.440004784 -1.442446009 -1.444889677
#> [896] -1.447335789 -1.449784349 -1.452235359 -1.454688821 -1.457144737
#> [901] -1.459603111 -1.462063944 -1.464527240 -1.466993000 -1.469461227
#> [906] -1.471931923 -1.474405091 -1.476880734 -1.479358854 -1.481839453
#> [911] -1.484322533 -1.486808098 -1.489296150 -1.491786692 -1.494279725
#> [916] -1.496775252 -1.499273276 -1.501773799 -1.504276824 -1.506782354
#> [921] -1.509290390 -1.511800935 -1.514313993 -1.516829564 -1.519347653
#> [926] -1.521868260 -1.524391390 -1.526917044 -1.529445225 -1.531975935
#> [931] -1.534509178 -1.537044954 -1.539583268 -1.542124122 -1.544667517
#> [936] -1.547213458 -1.549761945 -1.552312982 -1.554866572 -1.557422716
#> [941] -1.559981418 -1.562542680 -1.565106505 -1.567672894 -1.570241851
#> [946] -1.572813379 -1.575387479 -1.577964154 -1.580543408 -1.583125242
#> [951] -1.585709659 -1.588296662 -1.590886254 -1.593478436 -1.596073211
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#> [1001] -1.718281828