12-Oct-2022 08:16:15

black_scholes_test():
  MATLAB/Octave version 4.2.2
  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

  Partial results:
   2.0000
   2.0019
   2.0598
   2.1292
   2.1322
   2.2470
   2.0935
   2.0361
   2.1242
   2.1381
...
 1.2783
  Data saved as "asset_path.txt".

binomial_test():
  binomial() applies 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() applies 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 = 1.144742

forward_test():
  forward() applies 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

  1.000000  0.001394
  2.000000  0.037337
  3.000000  0.223638
  4.000000  0.627210
  5.000000  1.209924
  6.000000  1.914388
  7.000000  2.695426
  8.000000  3.522607
  9.000000  4.376385
  10.000000  5.244276

mc_test():
  mc() applies 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 [ 1.142991, 1.146526 ]

black_scholes_test():
  Normal end of execution.

12-Oct-2022 08:16:25