Tue Oct 19 11:24:30 2021

black_scholes_test():
  Python version: 3.6.9
  Test black_scholes().

asset_path_test():
  asset_path() simulates an asset price path.

  The asset price at time 0,     S0    = 2.000000
  The asset expected growth rate MU    = 0.100000
  The asset volatility           SIGMA = 0.300000
  The expiry date                T1    = 1.000000
  The number of time steps       N     = 100
  Graphics saved as "asset_path.png"

  Partial results:

       0               2
       1         1.89374
       2         1.91779
       3         1.98392
       4         2.03887
       5         2.00293
       6         1.94134
       7         1.85253
  ......  ..............
     100         2.79191

  Full results written to "asset_path.txt".

binomial_test():
  binomial() uses the binomial method for option valuation.

  The asset price at time 0, S0    = 2.000000
  The exercise price         E     = 1.000000
  The interest rate          R     = 0.050000
  The asset volatility       SIGMA = 0.250000
  The expiry date            T1    = 3.000000
  The number of intervals    M     = 256

  The option value is 1.144756

bsf_test():
  bsf() uses the Black-Scholes formula for option valuation.

  The asset price at time T0, S0    = 2.000000
  The time                    T0    = 0.000000
  The exercise price          E     = 1.000000
  The interest rate           R     = 0.050000
  The asset volatility        SIGMA = 0.250000
  The expiry date             T1    = 3.000000

  The option value C = 1.144743

forward_test():
  forward() uses the forward difference method for option valuation.

  The exercise price        E =     4
  The interest rate         R =     0.03
  The asset volatility      SIGMA = 0.5
  The expiry date           T1 =    1
  The number of space steps NX =    11
  The number of time steps  NT =    29
  The value of              SMAX =  10

       Initial          Option
       Value            Value

               1      0.00139363
               2       0.0373367
               3        0.223638
               4         0.62721
               5         1.20992
               6         1.91439
               7         2.69543
               8         3.52261
               9         4.37638
              10         5.24428

mc_test():
  mc() uses the Monte Carlo method for option valuation.

  The asset price at time 0, S0    = 2.000000
  The exercise price         E     = 1.000000
  The interest rate          R     = 0.050000
  The asset volatility       SIGMA = 0.250000
  The expiry date            T1    = 3.000000
  The number of simulations  M     = 1000000

  The confidence interval is [ 1.143583, 1.147116 ]

black_scholes_test():
  Normal end of execution.
Tue Oct 19 11:24:34 2021