Option Pricing Functions

This module provides various functions for pricing options using different models for stock paths. The functions use Monte Carlo simulations to estimate the option prices.

Functions

price_european_call(S0, K, r, q, sigma, T, N, M)

Prices a European call option using Monte Carlo simulation based on the Geometric Brownian Motion model.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - sigma (float): Volatility. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the European call option.

price_european_put(S0, K, r, q, sigma, T, N, M)

Prices a European put option using Monte Carlo simulation based on the Geometric Brownian Motion model.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - sigma (float): Volatility. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the European put option.

price_heston_euler_call(S0, K, r, q, v0, kappa, eta, theta, rho, T, N, M)

Prices a European call option using Monte Carlo simulation based on the Heston model with Euler discretization.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - v0 (float): Initial variance. - kappa (float): Rate of mean reversion. - eta (float): Volatility of volatility. - theta (float): Long-term variance. - rho (float): Correlation between stock and variance. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the European call option under the Heston model.

price_heston_euler_put(S0, K, r, q, v0, kappa, eta, theta, rho, T, N, M)

Prices a European put option using Monte Carlo simulation based on the Heston model with Euler discretization.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - v0 (float): Initial variance. - kappa (float): Rate of mean reversion. - eta (float): Volatility of volatility. - theta (float): Long-term variance. - rho (float): Correlation between stock and variance. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the European put option under the Heston model.

price_heston_milstein_call(S0, K, r, q, v0, kappa, eta, theta, rho, T, N, M)

Prices a European call option using Monte Carlo simulation based on the Heston model with Milstein discretization.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - v0 (float): Initial variance. - kappa (float): Rate of mean reversion. - eta (float): Volatility of volatility. - theta (float): Long-term variance. - rho (float): Correlation between stock and variance. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the European call option under the Heston model with Milstein discretization.

price_heston_milstein_put(S0, K, r, q, v0, kappa, eta, theta, rho, T, N, M)

Prices a European put option using Monte Carlo simulation based on the Heston model with Milstein discretization.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - v0 (float): Initial variance. - kappa (float): Rate of mean reversion. - eta (float): Volatility of volatility. - theta (float): Long-term variance. - rho (float): Correlation between stock and variance. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the European put option under the Heston model with Milstein discretization.

price_asian_call(S0, K, r, q, sigma, T, N, M)

Prices an Asian call option using Monte Carlo simulation based on the Geometric Brownian Motion model.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - r (float): Risk-free rate. - q (float): Dividend yield. - sigma (float): Volatility. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the Asian call option.

price_up_and_in_put(S0, K, H, r, q, sigma, T, N, M)

Prices an up-and-in put option using Monte Carlo simulation based on the Geometric Brownian Motion model. The option becomes active when the stock price hits the barrier.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - H (float): Barrier level. - r (float): Risk-free rate. - q (float): Dividend yield. - sigma (float): Volatility. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the up-and-in put option.

price_up_and_out_put(S0, K, H, r, q, sigma, T, N, M)

Prices an up-and-out put option using Monte Carlo simulation based on the Geometric Brownian Motion model. The option becomes inactive if the stock price hits the barrier.

Parameters: - S0 (float): Initial stock price. - K (float): Strike price. - H (float): Barrier level. - r (float): Risk-free rate. - q (float): Dividend yield. - sigma (float): Volatility. - T (float): Time to maturity. - N (int): Number of time steps. - M (int): Number of simulations.

Returns: - (float): The price of the up-and-out put option.