Options Greeks Calculator
Calculate option pricing and Greeks using the Black-Scholes model. Understand how Delta, Gamma, Theta, and Vega affect your position.
Sensitivity Analysis
Understanding the Greeks
Delta
Measures how much an option price moves for a $1 change in the underlying stock. Calls have positive delta (0 to 1), puts have negative delta (-1 to 0). A delta of 0.50 means the option acts like half a share.
Gamma
The rate at which delta changes. High gamma means delta shifts quickly with stock movement. At-the-money options near expiration have the highest gamma.
Theta
Time decay — how much value the option loses each day. Theta accelerates as expiration approaches. Option sellers benefit from theta; buyers lose from it.
Vega
Sensitivity to implied volatility changes. A vega of 0.15 means the option price moves $0.15 for every 1% change in IV. Longer-dated options have higher vega.
Rho
Sensitivity to interest rate changes. Rho is usually small for short-dated options but becomes more significant for LEAPS. Calls gain value when rates rise; puts lose value.
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Frequently Asked Questions
What are options Greeks?
Options Greeks measure how an option's price changes in response to different factors. Delta measures price sensitivity, Gamma measures delta's rate of change, Theta measures time decay, and Vega measures volatility sensitivity.
What does delta mean in options trading?
Delta ranges from 0 to 1 for calls and -1 to 0 for puts. A 0.30 delta call means the option price increases roughly $0.30 for every $1 increase in the stock price. Delta also approximates the probability of expiring in the money.
How does theta decay work?
Theta represents the daily time decay of an option. A theta of -0.05 means the option loses $5 per day (per contract). Decay accelerates in the final 30 days before expiration, making short-dated options decay fastest.
What is the Black-Scholes model?
Black-Scholes is the standard mathematical model for pricing European-style options. It uses stock price, strike price, time to expiration, risk-free rate, and implied volatility to calculate theoretical option prices and Greeks.
Why is Vega important for options traders?
Vega measures how much an option's price changes when implied volatility moves 1%. High Vega means the option is more sensitive to volatility changes. This matters because IV can move significantly around earnings and market events.
How do you use Greeks to manage risk?
Monitor delta for directional exposure, theta for time decay impact, and Vega for volatility risk. Many traders aim for delta-neutral positions and use Gamma to understand how quickly delta changes as the stock moves.