mcs_full_vector_numpy

##
#Monte Carlo valuation of European call options with NumPy (log version)
# mcs_full_vector_numpy.py
# import math
from numpy import *
from time import time
# star import for shorter code
random.seed(20000)
t0 = time()
# Parameters
S0 = 100.; K = 105.; T = 1.0; r = 0.05; sigma = 0.2
M = 50; dt = T / M; I = 250000
# Simulating I paths with M time steps
S = S0 * exp(cumsum((r - 0.5 * sigma ** 2) * dt
    + sigma * math.sqrt(dt)
            * random.standard_normal((M + 1, I)), axis=0))
# sum instead of cumsum would also do
# if only the final values are of interest
S[0] = S0
# Calculating the Monte Carlo estimator
C0 = math.exp(-r * T) * sum(maximum(S[-1] - K, 0)) / I
# Results output
tnp2 = time() - t0
print ('European Option Value %7.3f' % C0)
print ('Duration in Seconds %7.3f' % tnp2)

import matplotlib.pyplot as plt
plt.grid(True)
plt.xlabel('time step')
plt.ylabel('index level')
plt.plot(S[:, :10])