指数オプション GREEKS
library(derivmkts)
# 株式時価 ｓ、権利行使価格 ｋ
# ボラティリティ ｖ 利子率 ｒ
# 残存期間 ｔｔ 配当 ｄ
s=22920; k=22875; v=0.11; r=0; tt=7/365; d=0;
# コールの価格は以下のとおり
bscall(s, k, v, r, tt, d)## [1] 162.8083# プット価格は以下のとおり
bsput(s, k, v, r, tt, d)## [1] 117.8083s <- seq(22000, 24000, by=50)
gcall<-bscall(s, k, v, r, tt, d)
gput<-bsput(s, k, v, r, tt, d)
# コールとプットの価格曲線をグラフで示すと
plot(s,gcall,type="l")
plot(s,gput,type="l")
# 上記と同様の条件でグリークスを計算すると
greeks(bscall(s, k, v, r, tt, d), complete=FALSE, long=FALSE, initcaps=TRUE)
## bscall_22000 bscall_22050 bscall_22100 bscall_22150
## Premium 5.672404e-01 8.995214e-01 1.398441e+00 2.132130e+00
## Delta 5.344606e-03 8.115640e-03 1.206711e-02 1.757464e-02
## Gamma 4.568790e-05 6.622258e-05 9.322321e-05 1.284661e-04
## Vega 4.674630e-01 6.778329e-01 9.605509e-01 1.330477e+00
## Rho 2.244106e-02 3.414664e-02 5.087653e-02 7.424722e-02
## Theta -3.672939e-01 -5.325830e-01 -7.547162e-01 -1.045369e+00
## Psi -2.254984e-02 -3.431915e-02 -5.114472e-02 -7.465613e-02
## Elasticity 2.072866e+02 1.989390e+02 1.907004e+02 1.825772e+02
## bscall_22200 bscall_22250 bscall_22300 bscall_22350
## Premium 3.189151e+00 4.681533e+00 6.747131e+00 9.550829722
## Delta 2.507880e-02 3.507557e-02 4.809808e-02 0.064689060
## Gamma 1.733724e-04 2.307843e-04 2.967226e-04 0.000371756
## Vega 1.801563e+00 2.385133e+00 3.087891e+00 3.909868763
## Rho 1.061622e-01 1.487740e-01 2.044077e-01 0.275445146
## Theta -1.415505e+00 -1.874020e+00 -2.426184e+00 -3.072021120
## Psi -1.067739e-01 -1.496718e-01 -2.057017e-01 -0.277276812
## Elasticity 1.745761e+02 1.667043e+02 1.589694e+02 151.379569627
## bscall_22400 bscall_22450 bscall_22500 bscall_22550
## Premium 1.328415e+01 1.816286e+01 2.442234e+01 3.231061e+01
## Delta 8.536453e-02 1.105708e-01 1.406381e-01 1.757354e-01
## Gamma 4.558842e-04 5.434231e-04 6.525624e-04 7.366907e-04
## Vega 4.842585e+00 5.867739e+00 6.956741e+00 8.071328e+00
## Rho 3.641690e-01 4.725770e-01 6.021792e-01 7.537990e-01
## Theta -3.804869e+00 -4.610348e+00 -5.465996e+00 -6.341748e+00
## Psi -3.667167e-01 -4.760603e-01 -6.068629e-01 -7.599956e-01
## Elasticity 1.439434e+02 1.366698e+02 1.295681e+02 1.226481e+02
## bscall_22600 bscall_22650 bscall_22700 bscall_22750
## Premium 4.207933e+01 53.973045151 68.217578141 85.008406608
## Delta 2.158325e-01 0.260672678 0.309763823 0.362387109
## Gamma 8.458301e-04 0.000941327 0.001027729 0.001086846
## Vega 9.165375e+00 10.187863587 11.086761805 11.813417785
## Rho 9.274010e-01 1.121968293 1.335450611 1.564796932
## Theta -7.201364e+00 -8.004757062 -8.711043165 -9.281995152
## Psi -9.354711e-01 -1.132319288 -1.348533434 -1.581099914
## Elasticity 1.159195e+02 109.392311103 103.076640486 96.982252187
## bscall_22800 bscall_22850 bscall_22900 bscall_22950
## Premium 104.499982387 126.797021984 151.948560657 179.945334316
## Delta 0.417626998 0.474418939 0.531611422 0.588035973
## Gamma 0.001109584 0.001127773 0.001136868 0.001136868
## Vega 12.326952636 12.598092577 12.611939462 12.369313915
## Rho 1.806075821 2.054677500 2.305580008 2.553653709
## Theta -9.685492851 -9.898534628 -9.909414361 -9.718776835
## Psi -1.826116914 -2.078994737 -2.334720828 -2.588163773
## Elasticity 91.118633028 85.494695295 80.118571129 74.997363141
## bscall_23000 bscall_23050 bscall_23100 bscall_23150
## Premium 210.720716688 244.155080009 2.800831e+02 3.183034e+02
## Delta 0.642578107 0.694242181 7.422039e-01 7.858462e-01
## Gamma 0.001073204 0.001009539 9.276846e-04 8.367351e-04
## Vega 11.886504756 11.193483340 1.033085e+01 9.345953e+00
## Rho 2.793973380 3.022106544 3.234350e+00 3.427897e+00
## Theta -9.339420858 -8.794896154 -8.117105e+00 -7.343247e+00
## Psi -2.834385573 -3.068930806 -3.288065e+00 -3.488942e+00
## Elasticity 70.136893443 65.541467582 6.121365e+01 5.715409e+01
## bscall_23200 bscall_23250 bscall_23300 bscall_23350
## Premium 3.585891e+02 4.006995e+02 4.443904e+02 4.894241e+02
## Delta 8.247761e-01 8.588230e-01 8.880204e-01 9.125755e-01
## Gamma 7.275958e-04 6.184564e-04 4.911271e-04 4.547474e-04
## Vega 8.288653e+00 7.207309e+00 6.145351e+00 5.138774e+00
## Rho 3.600918e+00 3.752563e+00 3.882888e+00 3.992726e+00
## Theta -6.512504e+00 -5.662871e+00 -4.828472e+00 -4.037588e+00
## Psi -3.669689e+00 -3.829409e+00 -3.968113e+00 -4.086588e+00
## Elasticity 5.336138e+01 4.983195e+01 4.656013e+01 4.353819e+01
## bscall_23400 bscall_23450 bscall_23500 bscall_23550
## Premium 5.355763e+02 5.826426e+02 6.304418e+02 6.788174e+02
## Delta 9.328301e-01 9.492186e-01 9.622277e-01 9.723598e-01
## Gamma 3.637979e-04 2.728484e-04 2.000888e-04 2.000888e-04
## Vega 4.214696e+00 3.390948e+00 2.676565e+00 2.072954e+00
## Rho 4.083521e+00 4.157143e+00 4.215708e+00 4.261419e+00
## Theta -3.311527e+00 -2.664299e+00 -2.103001e+00 -1.628738e+00
## Psi -4.186234e+00 -4.268883e+00 -4.336615e+00 -4.391603e+00
## Elasticity 4.075652e+01 3.820382e+01 3.586747e+01 3.373378e+01
## bscall_23600 bscall_23650 bscall_23700 bscall_23750
## Premium 7.276380e+02 7.767956e+02 8.262037e+02 8.757946e+02
## Delta 9.801036e-01 9.859120e-01 9.901881e-01 9.932785e-01
## Gamma 1.455192e-04 1.273293e-04 7.275958e-05 3.637979e-05
## Vega 1.575468e+00 1.175141e+00 8.603657e-01 6.183588e-01
## Rho 4.296429e+00 4.322744e+00 4.342158e+00 4.356219e+00
## Theta -1.237860e+00 -9.233210e-01 -6.760003e-01 -4.858540e-01
## Psi -4.435976e+00 -4.471718e+00 -4.500608e+00 -4.524179e+00
## Elasticity 3.178840e+01 3.001667e+01 2.840396e+01 2.693595e+01
## bscall_23800 bscall_23850 bscall_23900 bscall_23950
## Premium 9.255166e+02 9.753307e+02 1.025208e+03 1.075129e+03
## Delta 9.954711e-01 9.969987e-01 9.980436e-01 9.987457e-01
## Gamma 5.456968e-05 1.818989e-05 3.637979e-05 1.818989e-05
## Vega 4.363286e-01 3.023106e-01 2.056885e-01 1.374466e-01
## Rho 4.366216e+00 4.373195e+00 4.377979e+00 4.381200e+00
## Theta -3.428316e-01 -2.375325e-01 -1.616154e-01 -1.079967e-01
## Psi -4.543712e+00 -4.560244e+00 -4.574594e+00 -4.587389e+00
## Elasticity 2.559891e+01 2.437985e+01 2.326673e+01 2.224845e+01
## bscall_24000
## Premium 1125.07904206
## Delta 0.99920901
## Gamma 0.00000000
## Vega 0.09021413
## Rho 4.38333036
## Theta -0.07088523
## Psi -4.59909894
## Elasticity 21.31496120
greeks(bsput(s, k, v, r, tt, d), complete=FALSE, long=FALSE, initcaps=TRUE)
## bsput_22000 bsput_22050 bsput_22100 bsput_22150
## Premium 8.755672e+02 8.258995e+02 7.763984e+02 7.271321e+02
## Delta -9.946554e-01 -9.918844e-01 -9.879329e-01 -9.824254e-01
## Gamma 5.456968e-05 7.275958e-05 9.094947e-05 1.273293e-04
## Vega 4.674630e-01 6.778329e-01 9.605509e-01 1.330477e+00
## Rho -4.364545e+00 -4.352840e+00 -4.336110e+00 -4.312739e+00
## Theta -3.672939e-01 -5.325830e-01 -7.547162e-01 -1.045369e+00
## Psi 4.196628e+00 4.194448e+00 4.187211e+00 4.173289e+00
## Elasticity -2.499228e+01 -2.648149e+01 -2.812128e+01 -2.992678e+01
## bsput_22200 bsput_22250 bsput_22300 bsput_22350
## Premium 6.781892e+02 6.296815e+02 5.817471e+02 5.345508e+02
## Delta -9.749212e-01 -9.649244e-01 -9.519019e-01 -9.353109e-01
## Gamma 1.818989e-04 2.182787e-04 2.910383e-04 3.637979e-04
## Vega 1.801563e+00 2.385133e+00 3.087891e+00 3.909869e+00
## Rho -4.280824e+00 -4.238212e+00 -4.182579e+00 -4.111541e+00
## Theta -1.415505e+00 -1.874020e+00 -2.426184e+00 -3.072021e+00
## Psi 4.150760e+00 4.117452e+00 4.071011e+00 4.009025e+00
## Elasticity -3.191330e+01 -3.409592e+01 -3.648907e+01 -3.910610e+01
## bsput_22400 bsput_22450 bsput_22500 bsput_22550
## Premium 4.882842e+02 4.431629e+02 3.994223e+02 3.573106e+02
## Delta -9.146355e-01 -8.894292e-01 -8.593619e-01 -8.242646e-01
## Gamma 4.729372e-04 5.275069e-04 6.548362e-04 7.275958e-04
## Vega 4.842585e+00 5.867739e+00 6.956741e+00 8.071328e+00
## Rho -4.022817e+00 -3.914409e+00 -3.784807e+00 -3.633187e+00
## Theta -3.804869e+00 -4.610348e+00 -5.465996e+00 -6.341748e+00
## Psi 3.929174e+00 3.829419e+00 3.708206e+00 3.564662e+00
## Elasticity -4.195884e+01 -4.505722e+01 -4.840902e+01 -5.201963e+01
## bsput_22600 bsput_22650 bsput_22700 bsput_22750
## Premium 317.079334375 2.789730e+02 243.217578141 210.008406608
## Delta -0.784167551 -7.393273e-01 -0.690236193 -0.637612902
## Gamma 0.000854925 9.458745e-04 0.001055014 0.001091394
## Vega 9.165374661 1.018786e+01 11.086761805 11.813417785
## Rho -3.459585255 -3.265018e+00 -3.051535690 -2.822189369
## Theta -7.201364147 -8.004757e+00 -8.711043165 -9.281995152
## Psi 3.398775520 3.211516e+00 3.004891223 2.781913784
## Elasticity -55.891963689 -6.002646e+01 -64.421172592 -69.071966021
## bsput_22800 bsput_22850 bsput_22900 bsput_22950
## Premium 179.499982387 151.797021984 126.948560657 104.945334316
## Delta -0.582373032 -0.525581054 -0.468388571 -0.411964029
## Gamma 0.001109584 0.001127773 0.001127773 0.001127773
## Vega 12.326952636 12.598092577 12.611939462 12.369313915
## Rho -2.580910480 -2.332308802 -2.081406293 -1.833332592
## Theta -9.685492851 -9.898534628 -9.909414361 -9.718776835
## Psi 2.546485826 2.303197044 2.057059994 1.813206090
## Elasticity -73.972737741 -79.115696227 -84.491688741 -90.090469718
## bsput_23000 bsput_23050 bsput_23100 bsput_23150
## Premium 85.720716688 6.915508e+01 5.508311e+01 4.330336e+01
## Delta -0.357421904 -3.057578e-01 -2.577961e-01 -2.141538e-01
## Gamma 0.001073204 1.018634e-03 9.276846e-04 8.367351e-04
## Vega 11.886504756 1.119348e+01 1.033085e+01 9.345953e+00
## Rho -1.593012921 -1.364880e+00 -1.152636e+00 -9.590889e-01
## Theta -9.339420858 -8.794896e+00 -8.117105e+00 -7.343247e+00
## Psi 1.576573331 1.351617e+00 1.142072e+00 9.507841e-01
## Elasticity -95.901015772 -1.019118e+02 -1.081110e+02 -1.144867e+02
## bsput_23200 bsput_23250 bsput_23300 bsput_23350
## Premium 3.358907e+01 2.569947e+01 1.939044e+01 1.442406e+01
## Delta -1.752239e-01 -1.411770e-01 -1.119796e-01 -8.742451e-02
## Gamma 7.275958e-04 6.184564e-04 4.911271e-04 4.547474e-04
## Vega 8.288653e+00 7.207309e+00 6.145351e+00 5.138774e+00
## Rho -7.860681e-01 -6.344236e-01 -5.040987e-01 -3.942603e-01
## Theta -6.512504e+00 -5.662871e+00 -4.828472e+00 -4.037588e+00
## Psi 7.796263e-01 6.294949e-01 5.003800e-01 3.914941e-01
## Elasticity -1.210273e+02 -1.277212e+02 -1.345572e+02 -1.415248e+02
## bsput_23400 bsput_23450 bsput_23500 bsput_23550
## Premium 1.057627e+01 7.642601e+00 5.441790e+00 3.817427e+00
## Delta -6.716995e-02 -5.078145e-02 -3.777233e-02 -2.764016e-02
## Gamma 3.637979e-04 2.728484e-04 2.000888e-04 2.000888e-04
## Vega 4.214696e+00 3.390948e+00 2.676565e+00 2.072954e+00
## Rho -3.034651e-01 -2.298432e-01 -1.712778e-01 -1.255673e-01
## Theta -3.311527e+00 -2.664299e+00 -2.103001e+00 -1.628738e+00
## Psi 3.014368e-01 2.283775e-01 1.702342e-01 1.248352e-01
## Elasticity -1.486136e+02 -1.558141e+02 -1.631173e+02 -1.705143e+02
## bsput_23600 bsput_23650 bsput_23700 bsput_23750
## Premium 2.637986e+00 1.795557e+00 1.203675e+00 7.946363e-01
## Delta -1.989642e-02 -1.408805e-02 -9.811902e-03 -6.721530e-03
## Gamma 1.455192e-04 1.273293e-04 7.275958e-05 3.637979e-05
## Vega 1.575468e+00 1.175141e+00 8.603657e-01 6.183588e-01
## Rho -9.055762e-02 -6.424241e-02 -4.482794e-02 -3.076759e-02
## Theta -1.237860e+00 -9.233210e-01 -6.760003e-01 -4.858540e-01
## Psi 9.005170e-02 6.389806e-02 4.459709e-02 3.061520e-02
## Elasticity -1.779977e+02 -1.855594e+02 -1.931933e+02 -2.008923e+02
## bsput_23800 bsput_23850 bsput_23900 bsput_23950
## Premium 5.165914e-01 3.306907e-01 2.084367e-01 1.293569e-01
## Delta -4.528883e-03 -3.001351e-03 -1.956378e-03 -1.254302e-03
## Gamma 5.456968e-05 1.818989e-05 3.637979e-05 1.818989e-05
## Vega 4.363286e-01 3.023106e-01 2.056885e-01 1.374466e-01
## Rho -2.077061e-02 -1.379157e-02 -9.007185e-03 -5.786036e-03
## Theta -3.428316e-01 -2.375325e-01 -1.616154e-01 -1.079967e-01
## Psi 2.067154e-02 1.372815e-02 8.967210e-03 5.761228e-03
## Elasticity -2.086512e+02 -2.164627e+02 -2.243243e+02 -2.322299e+02
## bsput_24000
## Premium 7.904206e-02
## Delta -7.910057e-04
## Gamma 0.000000e+00
## Vega 9.021413e-02
## Rho -3.655940e-03
## Theta -7.088523e-02
## Psi 3.640782e-03
## Elasticity -2.401777e+02
#######原資産価格別のgreeksのグラフ表示
S <- seq(22000, 24000, by=50)
Call <- greeks(bscall(S, k, v, r, tt, d))
Put <- greeks(bsput(S, k, v, r, tt, d))
y <- list(Call=Call, Put=Put)
par(mfrow=c(1, 2))
for (i in names(y)) {
for (j in rownames(y[[i]])) {
plot(S, y[[i]][j, ], main=paste(i, j), ylab=j, type='l')
}
}
##原資産価格別のgreeksを印刷
(yy<-as.data.frame(y)
)## Call.bscall_22000 Call.bscall_22050 Call.bscall_22100
## Premium 5.672404e-01 8.995214e-01 1.398441e+00
## Delta 5.344606e-03 8.115640e-03 1.206711e-02
## Gamma 4.568790e-05 6.622258e-05 9.322321e-05
## Vega 4.674630e-01 6.778329e-01 9.605509e-01
## Rho 2.244106e-02 3.414664e-02 5.087653e-02
## Theta -3.672939e-01 -5.325830e-01 -7.547162e-01
## Psi -2.254984e-02 -3.431915e-02 -5.114472e-02
## Elasticity 2.072866e+02 1.989390e+02 1.907004e+02
## Call.bscall_22150 Call.bscall_22200 Call.bscall_22250
## Premium 2.132130e+00 3.189151e+00 4.681533e+00
## Delta 1.757464e-02 2.507880e-02 3.507557e-02
## Gamma 1.284661e-04 1.733724e-04 2.307843e-04
## Vega 1.330477e+00 1.801563e+00 2.385133e+00
## Rho 7.424722e-02 1.061622e-01 1.487740e-01
## Theta -1.045369e+00 -1.415505e+00 -1.874020e+00
## Psi -7.465613e-02 -1.067739e-01 -1.496718e-01
## Elasticity 1.825772e+02 1.745761e+02 1.667043e+02
## Call.bscall_22300 Call.bscall_22350 Call.bscall_22400
## Premium 6.747131e+00 9.550829722 1.328415e+01
## Delta 4.809808e-02 0.064689060 8.536453e-02
## Gamma 2.967226e-04 0.000371756 4.558842e-04
## Vega 3.087891e+00 3.909868763 4.842585e+00
## Rho 2.044077e-01 0.275445146 3.641690e-01
## Theta -2.426184e+00 -3.072021120 -3.804869e+00
## Psi -2.057017e-01 -0.277276812 -3.667167e-01
## Elasticity 1.589694e+02 151.379569627 1.439434e+02
## Call.bscall_22450 Call.bscall_22500 Call.bscall_22550
## Premium 1.816286e+01 2.442234e+01 3.231061e+01
## Delta 1.105708e-01 1.406381e-01 1.757354e-01
## Gamma 5.434231e-04 6.525624e-04 7.366907e-04
## Vega 5.867739e+00 6.956741e+00 8.071328e+00
## Rho 4.725770e-01 6.021792e-01 7.537990e-01
## Theta -4.610348e+00 -5.465996e+00 -6.341748e+00
## Psi -4.760603e-01 -6.068629e-01 -7.599956e-01
## Elasticity 1.366698e+02 1.295681e+02 1.226481e+02
## Call.bscall_22600 Call.bscall_22650 Call.bscall_22700
## Premium 4.207933e+01 53.973045151 68.217578141
## Delta 2.158325e-01 0.260672678 0.309763823
## Gamma 8.458301e-04 0.000941327 0.001027729
## Vega 9.165375e+00 10.187863587 11.086761805
## Rho 9.274010e-01 1.121968293 1.335450611
## Theta -7.201364e+00 -8.004757062 -8.711043165
## Psi -9.354711e-01 -1.132319288 -1.348533434
## Elasticity 1.159195e+02 109.392311103 103.076640486
## Call.bscall_22750 Call.bscall_22800 Call.bscall_22850
## Premium 85.008406608 104.499982387 126.797021984
## Delta 0.362387109 0.417626998 0.474418939
## Gamma 0.001086846 0.001109584 0.001127773
## Vega 11.813417785 12.326952636 12.598092577
## Rho 1.564796932 1.806075821 2.054677500
## Theta -9.281995152 -9.685492851 -9.898534628
## Psi -1.581099914 -1.826116914 -2.078994737
## Elasticity 96.982252187 91.118633028 85.494695295
## Call.bscall_22900 Call.bscall_22950 Call.bscall_23000
## Premium 151.948560657 179.945334316 210.720716688
## Delta 0.531611422 0.588035973 0.642578107
## Gamma 0.001136868 0.001136868 0.001073204
## Vega 12.611939462 12.369313915 11.886504756
## Rho 2.305580008 2.553653709 2.793973380
## Theta -9.909414361 -9.718776835 -9.339420858
## Psi -2.334720828 -2.588163773 -2.834385573
## Elasticity 80.118571129 74.997363141 70.136893443
## Call.bscall_23050 Call.bscall_23100 Call.bscall_23150
## Premium 244.155080009 2.800831e+02 3.183034e+02
## Delta 0.694242181 7.422039e-01 7.858462e-01
## Gamma 0.001009539 9.276846e-04 8.367351e-04
## Vega 11.193483340 1.033085e+01 9.345953e+00
## Rho 3.022106544 3.234350e+00 3.427897e+00
## Theta -8.794896154 -8.117105e+00 -7.343247e+00
## Psi -3.068930806 -3.288065e+00 -3.488942e+00
## Elasticity 65.541467582 6.121365e+01 5.715409e+01
## Call.bscall_23200 Call.bscall_23250 Call.bscall_23300
## Premium 3.585891e+02 4.006995e+02 4.443904e+02
## Delta 8.247761e-01 8.588230e-01 8.880204e-01
## Gamma 7.275958e-04 6.184564e-04 4.911271e-04
## Vega 8.288653e+00 7.207309e+00 6.145351e+00
## Rho 3.600918e+00 3.752563e+00 3.882888e+00
## Theta -6.512504e+00 -5.662871e+00 -4.828472e+00
## Psi -3.669689e+00 -3.829409e+00 -3.968113e+00
## Elasticity 5.336138e+01 4.983195e+01 4.656013e+01
## Call.bscall_23350 Call.bscall_23400 Call.bscall_23450
## Premium 4.894241e+02 5.355763e+02 5.826426e+02
## Delta 9.125755e-01 9.328301e-01 9.492186e-01
## Gamma 4.547474e-04 3.637979e-04 2.728484e-04
## Vega 5.138774e+00 4.214696e+00 3.390948e+00
## Rho 3.992726e+00 4.083521e+00 4.157143e+00
## Theta -4.037588e+00 -3.311527e+00 -2.664299e+00
## Psi -4.086588e+00 -4.186234e+00 -4.268883e+00
## Elasticity 4.353819e+01 4.075652e+01 3.820382e+01
## Call.bscall_23500 Call.bscall_23550 Call.bscall_23600
## Premium 6.304418e+02 6.788174e+02 7.276380e+02
## Delta 9.622277e-01 9.723598e-01 9.801036e-01
## Gamma 2.000888e-04 2.000888e-04 1.455192e-04
## Vega 2.676565e+00 2.072954e+00 1.575468e+00
## Rho 4.215708e+00 4.261419e+00 4.296429e+00
## Theta -2.103001e+00 -1.628738e+00 -1.237860e+00
## Psi -4.336615e+00 -4.391603e+00 -4.435976e+00
## Elasticity 3.586747e+01 3.373378e+01 3.178840e+01
## Call.bscall_23650 Call.bscall_23700 Call.bscall_23750
## Premium 7.767956e+02 8.262037e+02 8.757946e+02
## Delta 9.859120e-01 9.901881e-01 9.932785e-01
## Gamma 1.273293e-04 7.275958e-05 3.637979e-05
## Vega 1.175141e+00 8.603657e-01 6.183588e-01
## Rho 4.322744e+00 4.342158e+00 4.356219e+00
## Theta -9.233210e-01 -6.760003e-01 -4.858540e-01
## Psi -4.471718e+00 -4.500608e+00 -4.524179e+00
## Elasticity 3.001667e+01 2.840396e+01 2.693595e+01
## Call.bscall_23800 Call.bscall_23850 Call.bscall_23900
## Premium 9.255166e+02 9.753307e+02 1.025208e+03
## Delta 9.954711e-01 9.969987e-01 9.980436e-01
## Gamma 5.456968e-05 1.818989e-05 3.637979e-05
## Vega 4.363286e-01 3.023106e-01 2.056885e-01
## Rho 4.366216e+00 4.373195e+00 4.377979e+00
## Theta -3.428316e-01 -2.375325e-01 -1.616154e-01
## Psi -4.543712e+00 -4.560244e+00 -4.574594e+00
## Elasticity 2.559891e+01 2.437985e+01 2.326673e+01
## Call.bscall_23950 Call.bscall_24000 Put.bsput_22000
## Premium 1.075129e+03 1125.07904206 8.755672e+02
## Delta 9.987457e-01 0.99920901 -9.946554e-01
## Gamma 1.818989e-05 0.00000000 5.456968e-05
## Vega 1.374466e-01 0.09021413 4.674630e-01
## Rho 4.381200e+00 4.38333036 -4.364545e+00
## Theta -1.079967e-01 -0.07088523 -3.672939e-01
## Psi -4.587389e+00 -4.59909894 4.196628e+00
## Elasticity 2.224845e+01 21.31496120 -2.499228e+01
## Put.bsput_22050 Put.bsput_22100 Put.bsput_22150 Put.bsput_22200
## Premium 8.258995e+02 7.763984e+02 7.271321e+02 6.781892e+02
## Delta -9.918844e-01 -9.879329e-01 -9.824254e-01 -9.749212e-01
## Gamma 7.275958e-05 9.094947e-05 1.273293e-04 1.818989e-04
## Vega 6.778329e-01 9.605509e-01 1.330477e+00 1.801563e+00
## Rho -4.352840e+00 -4.336110e+00 -4.312739e+00 -4.280824e+00
## Theta -5.325830e-01 -7.547162e-01 -1.045369e+00 -1.415505e+00
## Psi 4.194448e+00 4.187211e+00 4.173289e+00 4.150760e+00
## Elasticity -2.648149e+01 -2.812128e+01 -2.992678e+01 -3.191330e+01
## Put.bsput_22250 Put.bsput_22300 Put.bsput_22350 Put.bsput_22400
## Premium 6.296815e+02 5.817471e+02 5.345508e+02 4.882842e+02
## Delta -9.649244e-01 -9.519019e-01 -9.353109e-01 -9.146355e-01
## Gamma 2.182787e-04 2.910383e-04 3.637979e-04 4.729372e-04
## Vega 2.385133e+00 3.087891e+00 3.909869e+00 4.842585e+00
## Rho -4.238212e+00 -4.182579e+00 -4.111541e+00 -4.022817e+00
## Theta -1.874020e+00 -2.426184e+00 -3.072021e+00 -3.804869e+00
## Psi 4.117452e+00 4.071011e+00 4.009025e+00 3.929174e+00
## Elasticity -3.409592e+01 -3.648907e+01 -3.910610e+01 -4.195884e+01
## Put.bsput_22450 Put.bsput_22500 Put.bsput_22550 Put.bsput_22600
## Premium 4.431629e+02 3.994223e+02 3.573106e+02 317.079334375
## Delta -8.894292e-01 -8.593619e-01 -8.242646e-01 -0.784167551
## Gamma 5.275069e-04 6.548362e-04 7.275958e-04 0.000854925
## Vega 5.867739e+00 6.956741e+00 8.071328e+00 9.165374661
## Rho -3.914409e+00 -3.784807e+00 -3.633187e+00 -3.459585255
## Theta -4.610348e+00 -5.465996e+00 -6.341748e+00 -7.201364147
## Psi 3.829419e+00 3.708206e+00 3.564662e+00 3.398775520
## Elasticity -4.505722e+01 -4.840902e+01 -5.201963e+01 -55.891963689
## Put.bsput_22650 Put.bsput_22700 Put.bsput_22750 Put.bsput_22800
## Premium 2.789730e+02 243.217578141 210.008406608 179.499982387
## Delta -7.393273e-01 -0.690236193 -0.637612902 -0.582373032
## Gamma 9.458745e-04 0.001055014 0.001091394 0.001109584
## Vega 1.018786e+01 11.086761805 11.813417785 12.326952636
## Rho -3.265018e+00 -3.051535690 -2.822189369 -2.580910480
## Theta -8.004757e+00 -8.711043165 -9.281995152 -9.685492851
## Psi 3.211516e+00 3.004891223 2.781913784 2.546485826
## Elasticity -6.002646e+01 -64.421172592 -69.071966021 -73.972737741
## Put.bsput_22850 Put.bsput_22900 Put.bsput_22950 Put.bsput_23000
## Premium 151.797021984 126.948560657 104.945334316 85.720716688
## Delta -0.525581054 -0.468388571 -0.411964029 -0.357421904
## Gamma 0.001127773 0.001127773 0.001127773 0.001073204
## Vega 12.598092577 12.611939462 12.369313915 11.886504756
## Rho -2.332308802 -2.081406293 -1.833332592 -1.593012921
## Theta -9.898534628 -9.909414361 -9.718776835 -9.339420858
## Psi 2.303197044 2.057059994 1.813206090 1.576573331
## Elasticity -79.115696227 -84.491688741 -90.090469718 -95.901015772
## Put.bsput_23050 Put.bsput_23100 Put.bsput_23150 Put.bsput_23200
## Premium 6.915508e+01 5.508311e+01 4.330336e+01 3.358907e+01
## Delta -3.057578e-01 -2.577961e-01 -2.141538e-01 -1.752239e-01
## Gamma 1.018634e-03 9.276846e-04 8.367351e-04 7.275958e-04
## Vega 1.119348e+01 1.033085e+01 9.345953e+00 8.288653e+00
## Rho -1.364880e+00 -1.152636e+00 -9.590889e-01 -7.860681e-01
## Theta -8.794896e+00 -8.117105e+00 -7.343247e+00 -6.512504e+00
## Psi 1.351617e+00 1.142072e+00 9.507841e-01 7.796263e-01
## Elasticity -1.019118e+02 -1.081110e+02 -1.144867e+02 -1.210273e+02
## Put.bsput_23250 Put.bsput_23300 Put.bsput_23350 Put.bsput_23400
## Premium 2.569947e+01 1.939044e+01 1.442406e+01 1.057627e+01
## Delta -1.411770e-01 -1.119796e-01 -8.742451e-02 -6.716995e-02
## Gamma 6.184564e-04 4.911271e-04 4.547474e-04 3.637979e-04
## Vega 7.207309e+00 6.145351e+00 5.138774e+00 4.214696e+00
## Rho -6.344236e-01 -5.040987e-01 -3.942603e-01 -3.034651e-01
## Theta -5.662871e+00 -4.828472e+00 -4.037588e+00 -3.311527e+00
## Psi 6.294949e-01 5.003800e-01 3.914941e-01 3.014368e-01
## Elasticity -1.277212e+02 -1.345572e+02 -1.415248e+02 -1.486136e+02
## Put.bsput_23450 Put.bsput_23500 Put.bsput_23550 Put.bsput_23600
## Premium 7.642601e+00 5.441790e+00 3.817427e+00 2.637986e+00
## Delta -5.078145e-02 -3.777233e-02 -2.764016e-02 -1.989642e-02
## Gamma 2.728484e-04 2.000888e-04 2.000888e-04 1.455192e-04
## Vega 3.390948e+00 2.676565e+00 2.072954e+00 1.575468e+00
## Rho -2.298432e-01 -1.712778e-01 -1.255673e-01 -9.055762e-02
## Theta -2.664299e+00 -2.103001e+00 -1.628738e+00 -1.237860e+00
## Psi 2.283775e-01 1.702342e-01 1.248352e-01 9.005170e-02
## Elasticity -1.558141e+02 -1.631173e+02 -1.705143e+02 -1.779977e+02
## Put.bsput_23650 Put.bsput_23700 Put.bsput_23750 Put.bsput_23800
## Premium 1.795557e+00 1.203675e+00 7.946363e-01 5.165914e-01
## Delta -1.408805e-02 -9.811902e-03 -6.721530e-03 -4.528883e-03
## Gamma 1.273293e-04 7.275958e-05 3.637979e-05 5.456968e-05
## Vega 1.175141e+00 8.603657e-01 6.183588e-01 4.363286e-01
## Rho -6.424241e-02 -4.482794e-02 -3.076759e-02 -2.077061e-02
## Theta -9.233210e-01 -6.760003e-01 -4.858540e-01 -3.428316e-01
## Psi 6.389806e-02 4.459709e-02 3.061520e-02 2.067154e-02
## Elasticity -1.855594e+02 -1.931933e+02 -2.008923e+02 -2.086512e+02
## Put.bsput_23850 Put.bsput_23900 Put.bsput_23950 Put.bsput_24000
## Premium 3.306907e-01 2.084367e-01 1.293569e-01 7.904206e-02
## Delta -3.001351e-03 -1.956378e-03 -1.254302e-03 -7.910057e-04
## Gamma 1.818989e-05 3.637979e-05 1.818989e-05 0.000000e+00
## Vega 3.023106e-01 2.056885e-01 1.374466e-01 9.021413e-02
## Rho -1.379157e-02 -9.007185e-03 -5.786036e-03 -3.655940e-03
## Theta -2.375325e-01 -1.616154e-01 -1.079967e-01 -7.088523e-02
## Psi 1.372815e-02 8.967210e-03 5.761228e-03 3.640782e-03
## Elasticity -2.164627e+02 -2.243243e+02 -2.322299e+02 -2.401777e+02
# やはり同様の条件でインプライドボラティリティを計算する.
s=22920; k=22875
# コールの価格が１６５の場合のIV
bscallimpvol(s, k, r, tt, d, 165)
## [1] 0.1117468# プットの価格が１２５の場合のIV
bsputimpvol(s, k, r, tt, d, 125)
## [1] 0.1157303