Gamma (Γ)
Rate of delta change per $1 move. The second derivative that creates Gamma Exposure (GEX).
Gamma (Γ) is the second partial derivative of option price with respect to the underlying price (∂²V/∂S²). It measures how fast delta changes for each $1 move in the underlying. Gamma is always positive for long options and is highest for at-the-money options near expiration. It is the per-contract building block of Gamma Exposure (GEX).
Where φ is the standard normal PDF, S is spot, K is strike, σ is implied vol, T is time to expiry in years, r is risk-free rate, and q is dividend yield. Gamma is identical for calls and puts at the same strike.
- High gamma (ATM, near expiry): delta changes rapidly. Small price moves cause large delta swings. 0DTE options have extreme gamma.
- Low gamma (deep ITM/OTM or long-dated): delta is stable. The option behaves more linearly.
- Long gamma: position benefits from movement. Gains accelerate as price moves favourably.
- Short gamma: position is hurt by movement. Losses accelerate as price moves against you. This is the dealer's typical exposure.
How Gamma Works
Gamma is the curvature of the option payoff. If delta is the slope, gamma is how quickly that slope changes. A high-gamma option has a rapidly curving payoff — small stock moves cause big shifts in the option's directional exposure. This is why market makers who are short ATM 0DTE options face the most intense hedging pressure: every tick changes their delta, forcing continuous rebalancing.
The gamma curve peaks sharply at the strike price and decays on both sides. As expiration approaches, this peak narrows and grows taller — a phenomenon sometimes called "gamma concentration." At expiration, gamma becomes a Dirac-like spike at ATM: the option is either worthless (delta = 0) or fully ITM (delta = 1), with the transition happening over a tiny price range.
When gamma is aggregated across all open interest weighted by dealer positioning, it becomes Gamma Exposure (GEX). This is the macro metric that tells you whether dealer hedging will dampen volatility (positive GEX, dealers long gamma) or amplify it (negative GEX, dealers short gamma). Understanding per-contract gamma is the prerequisite for understanding GEX.
Gamma also has its own derivative: speed (∂³V/∂S³), which measures how fast gamma itself changes. Speed is relevant for portfolios with extreme gamma exposure because it determines whether a large move will increase or decrease the gamma risk further.
Compute Gamma via API
spot(query, required) — underlying price, e.g.550strike(query, required) — option strike price, e.g.550dte(query, required) — days to expiration, e.g.1sigma(query, required) — implied volatility as decimal, e.g.0.20type(query, required) —callorputr(query, optional) — risk-free rate, default0.05q(query, optional) — dividend yield, default0
{
"first_order": {
"delta": ...,
"gamma": 0.0381,
"theta": ...,
"vega": ...,
"rho": ...
},
"second_order": { ... }
}curl -H "X-Api-Key: YOUR_KEY" \
"https://lab.flashalpha.com/v1/pricing/greeks?spot=550&strike=550&dte=1&sigma=0.20&type=call&r=0.05&q=0.013"Why Gamma Matters for Trading
Gamma is how fast delta changes as spot moves. Long gamma = convex wins. Short gamma = convex losses. The whole GEX story is gamma aggregated.
- What it measures
- ∂²V/∂S² — second derivative of option value with respect to spot.
- What it signals
- Convexity. How much your delta accelerates when spot moves.
- Why we measure it
- Gamma is the option trader's curvature. Everything convex comes from here: pins, walls, squeezes, blowups.
- Who uses it
- Every options trader. Vol traders especially.
How to read Gamma
- Delta grows as you win
- Big moves produce convex gains
- ATM near expiry = max gamma
- Long straddles profit
- Delta grows against you
- Big moves produce convex losses
- Uncapped downside on naked shorts
- Classic blow-up exposure
- Pure directional exposure
- Deep ITM/OTM single options
- No convexity
- Not vol-dependent
Rules of thumb
- Gamma is maximum ATM near expiry. A 0DTE ATM option has gamma an order of magnitude higher than a 30DTE ATM.
- Short gamma needs active hedging. Without continuous rebalancing, short-gamma losses run away quickly.
- Pair with theta. Gamma and theta are opposite sides of every options trade. Long one, short the other.
- Gamma peaks define pin strikes. Strikes with the highest gamma are where dealer hedging is most intense.
- Scale by spot. Dollar gamma (gamma × S² × 100) is more actionable than raw gamma for sizing.
Related Concepts
The first derivative that gamma measures the change of. Delta is the slope; gamma is the curvature.
Gamma aggregated across all open interest. Positive GEX dampens; negative GEX amplifies.
The price level where net GEX crosses zero — the boundary between dampening and amplification regimes.
The third derivative (∂³V/∂S³) — how fast gamma itself changes with the underlying.
Time decay — the cost of holding gamma. Long gamma positions pay theta; short gamma positions collect it.
How delta changes with vol — the cross-derivative complement to gamma's spot sensitivity.
Learn More
Full endpoint reference for computing all Black-Scholes Greeks.
Understand delta before gamma. Delta is the slope; gamma is how that slope changes.
How gamma aggregated across dealer positions creates market-wide support and resistance.
Complete guide to dealer gamma mechanics, from per-contract gamma to market-level GEX.