Calculate theoretical option prices and Greeks using the Black-Scholes model. Enter your parameters below to get started.
The Greeks measure how an option's price responds to changes in market conditions. They are essential tools for managing risk and building hedging strategies.
Measures how much the option price changes for a $1 move in the underlying stock.
Call range: 0 to 1 ·
Put range: -1 to 0
A delta of 0.60 means the option gains ~$0.60 for every $1 the
stock rises. Often interpreted as the approximate probability
the option expires in-the-money.
Measures the rate of change of delta for a $1 move in the underlying stock.
Same for calls and puts.
High gamma means delta is shifting quickly — common for
at-the-money options near expiration. Important for
understanding how stable your hedge is.
Measures how much value the option loses per day due to the passage of time.
Usually negative for long options.
A theta of -0.05 means the option loses ~$0.05 per day, all else
equal. Time decay accelerates as expiration approaches —
sometimes called "the silent killer" of option value.
Measures how much the option price changes for a 1% change in implied volatility.
Same for calls and puts.
A vega of 0.15 means the option gains ~$0.15 if implied
volatility rises by 1%. Vega is highest for at-the-money options
with longer time to expiration.
Measures how much the option price changes for a 1% change in the risk-free interest rate.
Calls: positive rho ·
Puts: negative rho
Generally the least impactful Greek for short-dated options, but
becomes meaningful for LEAPS and other long-dated contracts.
The Greeks work together. For example, a high-gamma position near expiration will also have high theta — the rapid delta shifts come at the cost of accelerated time decay. Understanding these tradeoffs is key to effective options trading.
The Black-Scholes model, developed by Fischer Black, Myron Scholes, and Robert Merton in 1973, is the foundational framework for pricing European-style options. It calculates the theoretical fair value of calls and puts based on five key inputs:
The model assumes log-normal price distributions, constant volatility, no dividends (though this calculator supports a continuous dividend yield adjustment), and frictionless markets.
Note: This calculator uses the generalized Black-Scholes formula (also called Black-Scholes-Merton) which accounts for continuous dividend yields. Results are theoretical and should not be used as the sole basis for trading decisions.
This calculator is provided for educational and entertainment purposes only and does not constitute financial, investment, or trading advice. The results are based on a theoretical pricing model that relies on simplifying assumptions and may not reflect actual market conditions. I am not a licensed financial advisor, broker, or dealer. You should consult a qualified financial professional before making any investment decisions. Use this tool at your own risk. See the site disclosures for more information.