mcs_pure_python.py

#
# Monte Carlo valuation of European call options with pure Python
# mcs_pure_python.py
#

from time import time
from math import exp, sqrt, log
from random import gauss, seed

seed(20000)
t0 = time()

# Parameters
S0 = 100.  # initial value
K = 105.  # strike price
T = 1.0  # maturity
r = 0.05  # riskless short rate
sigma = 0.2  # volatility
M = 50  # number of time steps
dt = T / M  # length of time interval
I = 250000  # number of paths

# Simulating I paths with M time steps
S = []
for i in range(I):
    path = []
    for t in range(M + 1):
        if t == 0:
            path.append(S0)
        else:
            z = gauss(0.0, 1.0)
            St = path[t - 1] * exp((r - 0.5 * sigma ** 2) * dt
                                  + sigma * sqrt(dt) * z)
            path.append(St)
    S.append(path)
    
# Calculating the Monte Carlo estimator
C0 = exp(-r * T) * sum([max(path[-1] - K, 0) for path in S]) / I

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