Option Greeks Calculator (Black-Scholes: Delta, Gamma, Theta, Vega, Rho)
Compute Black-Scholes option Greeks — delta, gamma, theta, vega, and rho — plus call and put prices from spot, strike, time, volatility, and rate. Educational, not investment advice.
Greeks from the Black-Scholes-Merton model (no dividends). Delta = ∂price/∂spot; Gamma = ∂delta/∂spot (same for call & put); Vega = ∂price/∂vol, shown per 1% change; Theta = ∂price/∂time, shown per calendar day; Rho = ∂price/∂rate, per 1%. The model assumes constant volatility and lognormal prices — real markets deviate, and these are sensitivities at a point, not predictions. Educational, not investment advice. Everything runs in your browser.
About this tool
The Greeks are the sensitivities of an option's theoretical price to the variables that drive it, and they are the core risk-management vocabulary of options trading. This calculator computes them with the Black-Scholes-Merton (BSM) model — the foundational closed-form pricing model for European options — for both calls and puts, along with the option prices themselves. Delta is the rate of change of the option price with respect to the underlying's price: roughly how many dollars the option moves per one-dollar move in the stock, and loosely the probability of finishing in the money. Gamma is the rate of change of delta itself, highest near the money and near expiry, telling you how quickly your directional exposure shifts; it is identical for the call and the put at the same strike. Vega measures sensitivity to implied volatility, shown here per one-percentage-point change — long options gain value when volatility rises. Theta is time decay, the value the option loses each calendar day as expiry approaches, shown per day; it is usually negative for long option holders. Rho captures sensitivity to interest rates, per one-percentage-point change, and matters most for long-dated options. The model makes simplifying assumptions — constant volatility, lognormally distributed returns, no dividends, frictionless markets — that real markets violate, which is why traders treat BSM Greeks as a useful framework rather than gospel and watch implied volatility skew in practice. The normal distribution function is computed with a high-accuracy numerical approximation. This is educational and explicitly not investment or trading advice. Everything runs in your browser; nothing is uploaded.
How to use it
- Enter the underlying spot price and the option strike price.
- Enter days to expiry (converted to years internally).
- Enter the annualized implied volatility and the risk-free interest rate, both as percentages.
- Read delta, gamma, vega, theta, and rho for both the call and the put, plus their prices.
Frequently asked questions
- What are option Greeks?
- They are sensitivities of an option's price to its inputs. Delta (to underlying price), Gamma (to delta), Vega (to volatility), Theta (to time), and Rho (to interest rates). Together they describe how an option's value changes as conditions move.
- What model does this use?
- The Black-Scholes-Merton model for European options on a non-dividend-paying underlying. It is the standard closed-form pricing model and the basis for the Greeks shown here.
- What units are the Greeks in?
- Delta and gamma are per $1 move in the underlying. Vega is per 1 percentage point of volatility. Theta is per calendar day. Rho is per 1 percentage point of interest rate. These conventions make the numbers easy to read against typical input changes.
- Why are call and put gamma the same?
- Because gamma is the second derivative of price with respect to the underlying, and the call and put at the same strike and expiry share the same curvature (put-call parity makes their prices differ by a linear term, which has zero second derivative).
- What are the model's limitations?
- Black-Scholes assumes constant volatility, lognormal returns, no dividends, and frictionless trading. Real markets show volatility skew, jumps, and dividends, so traders use the Greeks as a framework and adjust with market-implied volatilities.
- Is this trading advice?
- No. It is an educational pricing tool. Options carry substantial risk. Nothing is uploaded; all math runs in your browser.