BSM

##Monte Carlo valuation of European call option
# in Black-Scholes-Merton model
# bsm_mcs_euro.py
import numpy as np

# Parameter Values
S0 = 100. # initial index level
K = 105. # strike price
T = 1.0 # time-to-maturity
r = 0.05 # riskless short rate
sigma = 0.2 # volatility
I = 100000 # number of simulations

# Valuation Algorithm
z = np.random.standard_normal(I) # pseudorandom numbers
ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T + sigma * np.sqrt(T) * z)

# index values at maturity
hT = np.maximum(ST - K, 0) # inner values at maturity
C0 = np.exp(-r * T) * np.sum(hT) / I # Monte Carlo estimator

# Result Output
print “Value of the European Call Option %5.3f” % C0