mcs_vector_numpy.py

#
# Monte Carlo valuation of European call options with NumPy
# mcs_vector_numpy.py
#

import math
import numpy as np
from time import time

np.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 = np.zeros((M+1, I))
S[0] = S0
for t in range(1, M + 1):
    z = np.random.standard_normal(I) # pseudorandom numbers
    S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt
                        + sigma * math.sqrt(dt) * z)
    # vectorized operation per time step over all paths

# Calculating the Monte Carlo estimator
C0 = math.exp(-r * T) * np.sum(np.maximum(S[-1] - K, 0)) / I

# Results output
tnp1 = time() - t0
print "European Option Value %7.3f" % C0
print "Duration in Seconds   %7.3f" % tnp1