nag_pde_dim1_blackscholes_closed (d03ndc) Example Program Results
Option Values
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Stock Price | Time to Maturity (months)
| 5.0000e+00 4.5000e+00 4.0000e+00 3.5000e+00
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0.0000e+00 | 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
5.0000e+00 | 4.4491e-19 4.5989e-21 1.5461e-23 1.0478e-26
1.0000e+01 | 5.5566e-10 5.5129e-11 3.1298e-12 8.0281e-14
1.5000e+01 | 4.7337e-06 1.2187e-06 2.2774e-07 2.7003e-08
2.0000e+01 | 7.2236e-04 3.1054e-04 1.1005e-04 2.9678e-05
2.5000e+01 | 1.6557e-02 9.6610e-03 5.0099e-03 2.2012e-03
3.0000e+01 | 1.3307e-01 9.4037e-02 6.1869e-02 3.6848e-02
3.5000e+01 | 5.6631e-01 4.5257e-01 3.4667e-01 2.5053e-01
4.0000e+01 | 1.6004e+00 1.3850e+00 1.1699e+00 9.5640e-01
4.5000e+01 | 3.4384e+00 3.1328e+00 2.8168e+00 2.4891e+00
5.0000e+01 | 6.1165e+00 5.7600e+00 5.3874e+00 4.9960e+00
5.5000e+01 | 9.5300e+00 9.1645e+00 8.7846e+00 8.3882e+00
6.0000e+01 | 1.3509e+01 1.3163e+01 1.2808e+01 1.2445e+01
6.5000e+01 | 1.7883e+01 1.7568e+01 1.7251e+01 1.6932e+01
7.0000e+01 | 2.2513e+01 2.2230e+01 2.1949e+01 2.1671e+01
7.5000e+01 | 2.7301e+01 2.7045e+01 2.6792e+01 2.6544e+01
8.0000e+01 | 3.2182e+01 3.1946e+01 3.1713e+01 3.1485e+01
8.5000e+01 | 3.7117e+01 3.6894e+01 3.6674e+01 3.6458e+01
9.0000e+01 | 4.2081e+01 4.1868e+01 4.1656e+01 4.1446e+01
9.5000e+01 | 4.7062e+01 4.6854e+01 4.6647e+01 4.6441e+01
1.0000e+02 | 5.2052e+01 5.1847e+01 5.1643e+01 5.1439e+01
Theta
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Stock Price | Time to Maturity (months)
| 5.0000e+00 4.5000e+00 4.0000e+00 3.5000e+00
--------------------------------------------------------------------------
0.0000e+00 | 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
5.0000e+00 | -4.4017e-17 -5.5977e-19 -2.3735e-21 -2.0936e-24
1.0000e+01 | -2.7827e-08 -3.3857e-09 -2.4163e-10 -8.0398e-12
1.5000e+01 | -1.3953e-04 -4.3864e-05 -1.0258e-05 -1.5706e-06
2.0000e+01 | -1.3287e-02 -6.9342e-03 -3.0567e-03 -1.0576e-03
2.5000e+01 | -1.9512e-01 -1.3714e-01 -8.7730e-02 -4.9018e-02
3.0000e+01 | -1.0161e+00 -8.5596e-01 -6.8695e-01 -5.1395e-01
3.5000e+01 | -2.8112e+00 -2.6426e+00 -2.4328e+00 -2.1723e+00
4.0000e+01 | -5.1662e+00 -5.1709e+00 -5.1500e+00 -5.0892e+00
4.5000e+01 | -7.2196e+00 -7.4540e+00 -7.7180e+00 -8.0183e+00
5.0000e+01 | -8.3848e+00 -8.7388e+00 -9.1543e+00 -9.6525e+00
5.5000e+01 | -8.6152e+00 -8.9372e+00 -9.3056e+00 -9.7329e+00
6.0000e+01 | -8.2058e+00 -8.4077e+00 -8.6186e+00 -8.8343e+00
6.5000e+01 | -7.5116e+00 -7.5845e+00 -7.6368e+00 -7.6553e+00
7.0000e+01 | -6.7905e+00 -6.7711e+00 -6.7202e+00 -6.6262e+00
7.5000e+01 | -6.1758e+00 -6.1099e+00 -6.0160e+00 -5.8893e+00
8.0000e+01 | -5.7084e+00 -5.6310e+00 -5.5359e+00 -5.4234e+00
8.5000e+01 | -5.3786e+00 -5.3103e+00 -5.2340e+00 -5.1533e+00
9.0000e+01 | -5.1582e+00 -5.1071e+00 -5.0551e+00 -5.0062e+00
9.5000e+01 | -5.0165e+00 -4.9835e+00 -4.9536e+00 -4.9298e+00
1.0000e+02 | -4.9281e+00 -4.9107e+00 -4.8979e+00 -4.8916e+00
Delta
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Stock Price | Time to Maturity (months)
| 5.0000e+00 4.5000e+00 4.0000e+00 3.5000e+00
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0.0000e+00 | 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
5.0000e+00 | 3.1381e-18 3.5969e-20 1.3576e-22 1.0494e-25
1.0000e+01 | 1.4005e-09 1.5376e-10 9.7805e-12 2.8553e-13
1.5000e+01 | 6.1418e-06 1.7452e-06 3.6436e-07 4.9030e-08
2.0000e+01 | 5.6040e-04 2.6494e-04 1.0451e-04 3.1863e-05
2.5000e+01 | 8.3312e-03 5.3217e-03 3.0570e-03 1.5104e-03
3.0000e+01 | 4.5711e-02 3.5158e-02 2.5461e-02 1.6934e-02
3.5000e+01 | 1.3765e-01 1.1889e-01 9.9459e-02 7.9557e-02
4.0000e+01 | 2.8307e-01 2.6258e-01 2.3996e-01 2.1479e-01
4.5000e+01 | 4.5320e-01 4.3858e-01 4.2214e-01 4.0335e-01
5.0000e+01 | 6.1427e-01 6.0856e-01 6.0249e-01 5.9601e-01
5.5000e+01 | 7.4525e-01 7.4687e-01 7.4937e-01 7.5308e-01
6.0000e+01 | 8.4052e-01 8.4611e-01 8.5298e-01 8.6148e-01
6.5000e+01 | 9.0433e-01 9.1096e-01 9.1862e-01 9.2752e-01
7.0000e+01 | 9.4449e-01 9.5045e-01 9.5699e-01 9.6412e-01
7.5000e+01 | 9.6862e-01 9.7325e-01 9.7808e-01 9.8300e-01
8.0000e+01 | 9.8260e-01 9.8589e-01 9.8913e-01 9.9221e-01
8.5000e+01 | 9.9050e-01 9.9269e-01 9.9473e-01 9.9653e-01
9.0000e+01 | 9.9487e-01 9.9627e-01 9.9748e-01 9.9848e-01
9.5000e+01 | 9.9725e-01 9.9811e-01 9.9881e-01 9.9935e-01
1.0000e+02 | 9.9854e-01 9.9905e-01 9.9945e-01 9.9972e-01
Gamma
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Stock Price | Time to Maturity (months)
| 5.0000e+00 4.5000e+00 4.0000e+00 3.5000e+00
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0.0000e+00 | 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
5.0000e+00 | 2.1246e-17 2.7112e-19 1.1536e-21 1.0211e-24
1.0000e+01 | 3.3102e-09 4.0468e-10 2.9020e-11 9.7029e-13
1.5000e+01 | 7.2660e-06 2.2982e-06 5.4080e-07 8.3319e-08
2.0000e+01 | 3.8245e-04 2.0111e-04 8.9333e-05 3.1153e-05
2.5000e+01 | 3.5190e-03 2.4960e-03 1.6118e-03 9.0924e-04
3.0000e+01 | 1.2392e-02 1.0554e-02 8.5660e-03 6.4838e-03
3.5000e+01 | 2.4348e-02 2.3181e-02 2.1626e-02 1.9580e-02
4.0000e+01 | 3.2765e-02 3.3274e-02 3.3650e-02 3.3795e-02
4.5000e+01 | 3.4099e-02 3.5763e-02 3.7655e-02 3.9828e-02
5.0000e+01 | 2.9625e-02 3.1360e-02 3.3403e-02 3.5860e-02
5.5000e+01 | 2.2600e-02 2.3743e-02 2.5052e-02 2.6569e-02
6.0000e+01 | 1.5672e-02 1.6137e-02 1.6603e-02 1.7048e-02
6.5000e+01 | 1.0123e-02 1.0119e-02 1.0032e-02 9.8216e-03
7.0000e+01 | 6.1999e-03 5.9720e-03 5.6534e-03 5.2154e-03
7.5000e+01 | 3.6474e-03 3.3666e-03 3.0215e-03 2.6027e-03
8.0000e+01 | 2.0815e-03 1.8329e-03 1.5510e-03 1.2387e-03
8.5000e+01 | 1.1610e-03 9.7196e-04 7.7211e-04 5.6851e-04
9.0000e+01 | 6.3660e-04 5.0529e-04 3.7553e-04 2.5382e-04
9.5000e+01 | 3.4468e-04 2.5884e-04 1.7950e-04 1.1099e-04
1.0000e+02 | 1.8494e-04 1.3118e-04 8.4708e-05 4.7786e-05
Lambda
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Stock Price | Time to Maturity (months)
| 5.0000e+00 4.5000e+00 4.0000e+00 3.5000e+00
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0.0000e+00 | 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
5.0000e+00 | 8.8525e-17 1.0167e-18 3.8453e-21 2.9781e-24
1.0000e+01 | 5.5171e-08 6.0702e-09 3.8694e-10 1.1320e-11
1.5000e+01 | 2.7247e-04 7.7565e-05 1.6224e-05 2.1871e-06
2.0000e+01 | 2.5496e-02 1.2066e-02 4.7644e-03 1.4538e-03
2.5000e+01 | 3.6656e-01 2.3400e-01 1.3431e-01 6.6299e-02
3.0000e+01 | 1.8588e+00 1.4248e+00 1.0279e+00 6.8080e-01
3.5000e+01 | 4.9710e+00 4.2595e+00 3.5323e+00 2.7983e+00
4.0000e+01 | 8.7374e+00 7.9857e+00 7.1787e+00 6.3084e+00
4.5000e+01 | 1.1508e+01 1.0863e+01 1.0167e+01 9.4094e+00
5.0000e+01 | 1.2344e+01 1.1760e+01 1.1134e+01 1.0459e+01
5.5000e+01 | 1.1394e+01 1.0773e+01 1.0104e+01 9.3768e+00
6.0000e+01 | 9.4033e+00 8.7137e+00 7.9693e+00 7.1602e+00
6.5000e+01 | 7.1285e+00 6.4127e+00 5.6514e+00 4.8412e+00
7.0000e+01 | 5.0632e+00 4.3894e+00 3.6936e+00 2.9815e+00
7.5000e+01 | 3.4194e+00 2.8406e+00 2.2661e+00 1.7080e+00
8.0000e+01 | 2.2203e+00 1.7596e+00 1.3235e+00 9.2488e-01
8.5000e+01 | 1.3981e+00 1.0534e+00 7.4380e-01 4.7920e-01
9.0000e+01 | 8.5941e-01 6.1393e-01 4.0558e-01 2.3986e-01
9.5000e+01 | 5.1846e-01 3.5040e-01 2.1600e-01 1.1686e-01
1.0000e+02 | 3.0824e-01 1.9677e-01 1.1294e-01 5.5750e-02
Rho
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Stock Price | Time to Maturity (months)
| 5.0000e+00 4.5000e+00 4.0000e+00 3.5000e+00
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0.0000e+00 | 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
5.0000e+00 | 6.3524e-18 6.5717e-20 2.2112e-22 1.4997e-25
1.0000e+01 | 5.6040e-09 5.5594e-10 3.1558e-11 8.0937e-13
1.5000e+01 | 3.6414e-05 9.3595e-06 1.7459e-06 2.0663e-07
2.0000e+01 | 4.3690e-03 1.8706e-03 6.6008e-04 1.7721e-04
2.5000e+01 | 7.9884e-02 4.6268e-02 2.3805e-02 1.0371e-02
3.0000e+01 | 5.1594e-01 3.6026e-01 2.3399e-01 1.3743e-01
3.5000e+01 | 1.7715e+00 1.3907e+00 1.0448e+00 7.3907e-01
4.0000e+01 | 4.0509e+00 3.4193e+00 2.8095e+00 2.2269e+00
4.5000e+01 | 7.0648e+00 6.2263e+00 5.3932e+00 4.5679e+00
5.0000e+01 | 1.0249e+01 9.2505e+00 8.2458e+00 7.2346e+00
5.5000e+01 | 1.3108e+01 1.1967e+01 1.0810e+01 9.6342e+00
6.0000e+01 | 1.5384e+01 1.4101e+01 1.2790e+01 1.1446e+01
6.5000e+01 | 1.7041e+01 1.5617e+01 1.4153e+01 1.2646e+01
7.0000e+01 | 1.8167e+01 1.6613e+01 1.5013e+01 1.3363e+01
7.5000e+01 | 1.8894e+01 1.7231e+01 1.5521e+01 1.3761e+01
8.0000e+01 | 1.9344e+01 1.7597e+01 1.5806e+01 1.3969e+01
8.5000e+01 | 1.9615e+01 1.7807e+01 1.5959e+01 1.4072e+01
9.0000e+01 | 1.9774e+01 1.7924e+01 1.6039e+01 1.4122e+01
9.5000e+01 | 1.9865e+01 1.7987e+01 1.6080e+01 1.4145e+01
1.0000e+02 | 1.9917e+01 1.8022e+01 1.6101e+01 1.4156e+01