What is Gamma in Options Trading?
Gamma measures how fast an option's delta changes when the underlying moves one point. It is the second-order Greek and the engine behind almost every modern intraday flow story.
Definition
Gamma (Γ) is the second derivative of an option's price with respect to the underlying — equivalently, the rate of change of its delta. If delta tells you how exposed you are to the next one-point move, gamma tells you how fast that exposure shifts. Long-gamma positions get longer as the market rallies and shorter as it falls, which means they automatically buy weakness and sell strength when you delta-hedge. Short-gamma positions do the opposite: they accumulate exposure into the move and force you to chase. Gamma is highest at-the-money and on short-dated options, which is why 0DTE flow dominates U.S. equity intraday action.
Why it matters & how it's calculated
Mathematically, gamma is ∂²V/∂S² where V is option value and S is spot. Under standard pricing models it peaks at the strike, decays toward zero for deeply in- or out-of-the-money strikes, and increases as time to expiry shrinks (it actually goes to infinity at the strike at expiry). For a market maker delta-hedging a book, gamma is the cost of doing business: positive gamma generates a positive hedging P&L when realised volatility exceeds the implied vol they paid, and negative gamma bleeds when realised exceeds implied. This is the whole basis of variance trading. On the dealer side, when you aggregate gamma across all strikes weighted by open interest and a positioning assumption, you get gamma exposure (GEX). Above the "gamma flip" level, dealers are net long gamma and supply liquidity into both sides; below it, they are short gamma and amplify moves. Reading gamma properly — by strike, by expiry, by underlying — is the difference between a desk that survives a 0DTE squeeze and one that gets carried out.
Formula
Γ = ∂²V/∂S² | Hedging P&L ≈ ½ × Γ × (ΔS)² − θ × Δt
Worked example
Suppose SPX trades at 5,000, an ATM call has delta 0.50 and gamma 0.02 per point. If SPX rallies to 5,010, the call's delta rises to roughly 0.50 + 0.02×10 = 0.70. A market maker short 1,000 of these calls would have to buy an extra 200 ES futures-equivalent into the rally just to stay flat — and another 200 if it rips another 10. That mechanical buying IS the squeeze you see on the tape near big strikes.
Related concepts
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