Black-Scholes Option Pricing

This module contains functions for calculating the Black-Scholes price for European call and put options, as well as a function for calibrating implied volatility by minimizing the sum of squared differences between Black-Scholes prices and market prices.

Functions

black_scholes_price(S, K, T, r, q, sigma, option_type)

Computes the Black-Scholes price for European call and put options with dividends.

Parameters:

• S (float): Current stock price.

• K (float): Strike price.

• T (float): Time to maturity (years).

• r (float): Risk-free interest rate.

• sigma (float): Volatility of the underlying asset.

• option_type (int): 0 for call option, 1 for put option.

• q (float): Dividend yield (default is 0, no dividend).

Returns:

• (float): Option price.

Example:

price = black_scholes_price(S=100, K=95, T=1, r=0.05, q=0, sigma=0.2, option_type=0)