Python for Finance Cookbook

How to do it...

Execute the following steps to price European options using Monte Carlo simulations.

1. Import the libraries:

import numpy as npfrom scipy.stats import normfrom chapter_6_utils import simulate_gbm

2. Define the parameters for the valuation:

S_0 = 100K = 100r = 0.05sigma = 0.50T = 1 # 1 yearN = 252 # 252 days in a yeardt = T / N # time stepn_sims = 10 ** 6 discount_factor = np.exp(-r * T)

3. Define the function using the analytical solution:

def black_scholes_analytical(S_0, K, T, r, sigma, type='call'):         d1 = (np.log(S_0/K) + (r + 0.5 * sigma**2) * T)                           /(sigma * np.sqrt(T))    d2 = (np.log(S_0/K) + (r - 0.5 * sigma**2) * T)                           /(sigma * np.sqrt(T))        if type == 'call':        val = (S_0*norm.cdf(d1, 0, 1)-K*np.exp(-r*T) *norm.cdf(d2, 0, ...