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Tools — Black-Scholes & Greeks Calculator

Black-Scholes & Greeks Calculator

Price European call and put options with the Black-Scholes model and see all five Greeks — Delta, Gamma, Theta, Vega, Rho. Switch to Implied Volatility mode to reverse-solve volatility from a market price.

Trade Setup

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Results

Option Price —
Delta —
Gamma —
Theta (per day) —
Vega (per 1% vol) —
Rho (per 1% rate) —

European-style options priced with the Black-Scholes-Merton model (no dividend yield). Time to expiry is entered in calendar days.

How to use this calculator

Black-Scholes prices a European option from five inputs: the current spot price, the strike, the option's implied volatility, the risk-free interest rate, and the time remaining to expiry. Switch to "Implied Volatility" mode to work backwards: enter the option's actual market price instead of a volatility guess, and the calculator solves for the volatility the market is pricing in, then shows the Greeks evaluated at that solved volatility. Delta measures how much the option's price moves per $1 move in the underlying; Gamma is how fast Delta itself changes; Theta is the dollar value lost per calendar day as time passes; Vega is the price change per 1 percentage point of volatility; Rho is the price change per 1 percentage point of interest rates. This model assumes European-style exercise (at expiry only) and no dividends — American options and dividend-paying underlyings will price slightly differently.

Frequently Asked Questions

What is the Black-Scholes model?
It's a mathematical model for pricing European-style options (exercisable only at expiry) based on the underlying's spot price, the strike, volatility, the risk-free rate, and time to expiry. It assumes the underlying follows a lognormal random walk with constant volatility and no dividends.
What do the Greeks (Delta, Gamma, Theta, Vega, Rho) mean?
They measure how the option's price reacts to changes in different inputs: Delta to a $1 move in the underlying, Gamma to how fast Delta itself changes, Theta to one calendar day passing, Vega to a 1 percentage point change in volatility, and Rho to a 1 percentage point change in interest rates. Traders use them to understand and hedge an option position's risk.
How does Implied Volatility mode work?
Enter the option's actual traded market price instead of guessing a volatility, and the calculator searches for the volatility that makes the Black-Scholes price match that market price exactly. This "implied" volatility reflects what the market is currently pricing in for future price swings, and is the basis for metrics like a volatility index.

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