🧠 Black Scholes Calculator
Estimate the theoretical price of a European call or put option using the Black-Scholes option pricing model.
What is the Black-Scholes model?
The Black-Scholes model is a widely used mathematical model for estimating the theoretical fair price of European-style options (options that can only be exercised at expiration), based on the underlying stock price, strike price, time remaining, volatility, and the risk-free interest rate.
The formula
Call Price = S × N(d1) – K × e^(-rT) × N(d2), and Put Price = K × e^(-rT) × N(-d2) – S × N(-d1), where d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T), d2 = d1 – σ√T, N() is the standard normal cumulative distribution function, S is the stock price, K is the strike price, T is time to expiration in years, σ is volatility, and r is the risk-free rate.
This tool is for general educational purposes only. Black-Scholes assumes constant volatility and no dividends among other simplifications, and real option prices can differ due to market factors like dividends, early exercise, and changing volatility; this is not trading advice.