Options Pricing Calculator

About the Black-Scholes Model

The Black-Scholes model was developed in 1973 by Fischer Black, Myron Scholes, and Robert Merton. It provides a formula for calculating the fair price of European-style options based on factors like stock price, strike price, time to expiration, volatility, and interest rates.

Key Inputs

• Stock Price (S): the current market price of the underlying asset
• Strike Price (K): the price at which the option holder can buy or sell the asset
• Time to Expiration (T): the remaining time until the option contract expires, measured in years
• Volatility (σ): the expected price fluctuation of the underlying asset, typically expressed as annualized standard deviation
• Risk-Free Rate (r): the theoretical return on a zero-risk investment, often based on government bond yields
• Dividend Yield (q): the expected annual dividend payments as a percentage of the stock price

The Greeks

Beyond the option price itself, our calculator computes the Greeks—a set of risk measures that show how sensitive an option's value is to changes in market conditions:

• Delta (Δ) measures how much the option price moves for each $1 change in the underlying stock
• Gamma (Γ) tracks how quickly Delta itself changes as the stock price moves
• Theta (Θ) represents time decay, showing how much value the option loses each day
• Vega (ν) indicates how the option price responds to a 1% shift in implied volatility
• Rho (ρ) captures sensitivity to a 1% change in interest rates