Black-Scholes Calculator

Calculate theoretical option prices using the Black-Scholes-Merton pricing model.

Understanding Black-Scholes

The Black-Scholes model, published by Fischer Black, Myron Scholes, and Robert Merton in 1973, revolutionized options pricing. The model provides a closed-form solution for pricing European call and put options based on five observable inputs.

The Formula

For a call option: C = S·N(d1) - K·e^(-rT)·N(d2), where d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d2 = d1 - σ√T. N() is the cumulative standard normal distribution.

For a put option: P = K·e^(-rT)·N(-d2) - S·N(-d1). The put-call parity relationship ensures: C - P = S - K·e^(-rT).

Input Parameters

Stock Price (S): Current market price of the underlying stock.
Strike Price (K): The price at which the option can be exercised.
Time to Expiration (T): Time remaining until the option expires, expressed in years.
Risk-Free Rate (r): The annualized risk-free interest rate, typically the Treasury bill rate.
Volatility (σ): The annualized standard deviation of the stock's log returns (implied volatility).