Wed Sep 12 15:53:07 2018

BLACK_SCHOLES_TEST
  Python version: 3.6.5
  Test the BLACK_SCHOLES library.

ASSET_PATH_TEST:
  Demonstrate the simulation of 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
  Figure saved as "asset_path.png"

  Partial results:

       0               2
       1          2.0437
       2          2.0942
       3         2.00094
       4         2.05278
       5         2.08961
       6          2.1547
       7         2.21593
  ......  ..............
     100         1.55942

  Full results written to "asset_path.txt".

BINOMIAL_TEST:
  A demonstration of 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:
  A demonstration of 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:
  A demonstration of 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:
  A demonstration of 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 [ 1.141206, 1.144734 ]

BLACK_SCHOLES_TEST
  Normal end of execution.
Wed Sep 12 15:53:12 2018