Black-Scholes Options Pricing Calculator
Price European call and put options and compute option Greeks using the Black-Scholes model. Enter annualized volatility as a percentage.
Black-Scholes Model Overview
The Black-Scholes model prices European-style options using five inputs: current stock price, strike price, time to expiration (in years), risk-free rate, and annualized volatility (sigma). Results include theoretical call and put prices plus all five option Greeks.
All results update automatically as you type. Annualized volatility should be entered as a percentage (for example, enter 25 for 25% annual volatility).
Option Pricing Inputs
Black-Scholes (European)Results update automatically as you enter values.
Black-Scholes FAQ
What is the Black-Scholes model?
The Black-Scholes model is a mathematical framework for pricing European-style call and put options. It assumes constant volatility and a log-normal distribution of stock returns. Inputs are the current stock price, strike price, time to expiration, risk-free rate, and annualized volatility.
What are option Greeks and how do I read them?
Delta — price change of the option per $1 move in the stock. Gamma — rate of change of Delta per $1 stock move (same for calls and puts). Theta — option value lost per calendar day due to time decay. Vega — price change per 1% increase in annualized volatility (same for calls and puts). Rho — price change per 1% increase in the risk-free rate.
What volatility should I enter?
Enter annualized volatility as a percentage. You can use historical (realized) volatility from a stock's past returns or implied volatility backed out from current market option prices. For reference, large-cap US stocks often carry 20–40% annualized volatility; the VIX index tracks the implied volatility of S&P 500 options.
What are the limitations of the Black-Scholes model?
Black-Scholes assumes constant volatility, continuous trading, no dividends, and European-style exercise only (no early exercise). It does not account for volatility skew, dividends, or liquidity constraints. For American-style options or dividend-paying stocks, more advanced models such as binomial trees or the Black-Scholes-Merton extension are commonly used.