Options Greeks explained: delta, gamma, theta, vega, and rho
Options Greeks describe how an option's modeled value may respond to changes in inputs such as the underlying price, time, volatility, and interest rates. Delta, gamma, theta, vega, and rho are sensitivities, not forecasts. They change with the contract and market conditions, so they should be read with the pricing assumptions and quote quality. Last updated 2026-09-01.
Delta is a local sensitivity of modeled option value to a small change in the underlying price. Gamma describes the rate at which delta changes. Theta is a modeled sensitivity to the passage of time, while vega describes sensitivity to implied volatility. Rho describes modeled sensitivity to interest rates. Each is conditional on the current inputs.
A Greek is not a statement about what the market will do next. The value can change when the underlying, implied volatility, time, rates, dividends, or liquidity changes. Greeks can differ between models and from the price at which a contract can actually be traded. Multi-leg positions require the sensitivities of their legs to be considered together.
Fincai's broker-independent options engine models prices and Greeks, and its visualizer and P&L simulator help users inspect scenarios. Model values can differ from executable market prices. Important inputs include strike, expiration, contract type, implied volatility, rates, dividends, bid-ask spread, open interest, and the possibility of stale quotes.
Options involve substantial risk and are not suitable for every investor. Review the options disclosure, understand early exercise or assignment considerations for American-style contracts, and verify the inputs before acting. A calculated Greek is a research aid, not a promise, recommendation, or guarantee.
Fincai is for informational purposes only and is not a registered investment adviser. It does not provide personalized financial advice. Trading stocks and options involves risk, including the possible loss of principal.
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- Delta: underlying-price sensitivity
- Gamma: change in delta
- Theta: time sensitivity
- Vega: implied-volatility sensitivity
- Rho: interest-rate sensitivity