Calculator Inputs
This page keeps a single-column flow, while the input area uses three columns on large screens, two on medium screens, and one on mobile.
Formula Used
For a European option under Black-Scholes assumptions, gamma is the same for calls and puts when the pricing inputs match.
d2 = d1 - σ√T
Gamma = e-qT × φ(d1) / [ S × σ × √T ]
- S = current underlying price
- K = strike price
- σ = annualized volatility in decimal form
- r = risk-free rate in decimal form
- q = dividend yield in decimal form
- T = time to expiry in years
- φ(d1) = standard normal probability density at d1
Position gamma equals gamma per share multiplied by contracts and contract size. The 1% convexity estimate shown here is 0.5 × position gamma × (1% spot move)².
How to Use This Calculator
- Choose call or put. Gamma stays the same for both under this model.
- Enter spot price, strike price, annualized volatility, rates, and dividend yield.
- Provide days to expiry, contracts, and contract size for position-level exposure.
- Set the graph range and point count to study sensitivity around spot.
- Press Calculate Gamma to display results above the form.
- Use the CSV and PDF buttons to export your computed metrics.
- Review the chart to see where gamma clusters around moneyness.
Example Data Table
These sample scenarios illustrate how gamma changes with moneyness, time, and volatility.
| Option | Spot | Strike | Vol % | Rate % | Yield % | Days | Contracts | Gamma | Position Gamma | 1% Convexity Estimate |
|---|---|---|---|---|---|---|---|---|---|---|
| Call | 100 | 100 | 25 | 5 | 2 | 45 | 3 | 0.04516816 | 13.550448 | $6.78 |
| Call | 120 | 115 | 18 | 4 | 1 | 30 | 5 | 0.04299865 | 21.499327 | $15.48 |
| Put | 80 | 90 | 35 | 3 | 0 | 75 | 2 | 0.02586784 | 5.173567 | $1.66 |
Frequently Asked Questions
1) What does option gamma measure?
Gamma measures how fast delta changes when the underlying price moves. A higher gamma means delta reacts more aggressively to small price changes.
2) Why are call and put gamma equal here?
Under Black-Scholes, calls and puts with the same strike, expiry, volatility, rates, and dividend yield share the same gamma. Their deltas differ, but curvature is identical.
3) When is gamma usually highest?
Gamma is often highest for near-the-money options close to expiry. Far in-the-money or far out-of-the-money contracts usually carry lower gamma.
4) Why does time to expiry matter so much?
As expiry approaches, delta can change more sharply around the strike. That sharpness often increases gamma, especially when the option is near the money.
5) How does volatility affect gamma?
Higher volatility spreads probability over a wider price range. That often lowers peak gamma near the strike, although the exact effect depends on time and moneyness.
6) What is position gamma?
Position gamma scales per-share gamma by the number of contracts and each contract’s share count. It helps estimate how portfolio delta changes for a one-unit move.
7) What does the 1% convexity estimate show?
It provides a simple curvature-based approximation for the gamma contribution to profit or loss from a 1% move in the underlying, holding other factors constant.
8) Are these results exact market values?
No. They are model-based estimates using Black-Scholes assumptions, constant volatility, continuous rates, and European exercise. Real markets can behave differently.