NAG Library Manual, Mark 30.1
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NAG CL Interface Introduction
Example description

nag_pde_dim1_blackscholes_closed (d03ndc) Example Program Results


Option Values
-------------
   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  |     4.4491e-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
-----
   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
-----
   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  |     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
-----
   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  |     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
------
   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  |     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
---
   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  |     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