Calcular o valor de uma Opção Europeia Call

import math
import numpy as np

# Valor dos parametros
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) # pseudo-random numbers
# index values at maturity
ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T + sigma * math.sqrt(T) * z)
hT = np.maximum(ST - K, 0) # payoff at maturity
C0 = math.exp(-r * T) * np.mean(hT) # Monte Carlo estimator

# Result Output
print('Value of the European call option {:5.3f}.'.format(C0))

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