Python for Finance Cookbook

How to do it...

Execute the following steps to price American options using the Least Squares Monte Carlo method.

1. Import the libraries:

import numpy as npfrom chapter_6_utils import (simulate_gbm,                              black_scholes_analytical,                              lsmc_american_option)

2. Define the parameters:

S_0 = 36K = 40r = 0.06sigma = 0.2T = 1 # 1 yearN = 50 dt = T / N N_SIMS = 10 ** 5 discount_factor = np.exp(-r * dt)OPTION_TYPE = 'put'POLY_DEGREE = 5 

3. Simulate the stock prices using GBM:

gbm_sims = simulate_gbm(s_0=S_0, mu=r, sigma=sigma, n_sims=N_SIMS,                        T=T, N=N)

4. Calculate the payoff matrix:

payoff_matrix = np.maximum(K - gbm_sims, np.zeros_like(gbm_sims))

5. Define the value matrix and fill in the last column (time T):

value_matrix = np.zeros_like(payoff_matrix)value_matrix[:, ...