Glossary
Gamma
The rate at which an option's delta changes for a $1 move in the underlying, highest for at-the-money options near expiry.
Gamma measures how fast an option's delta changes as the price of the underlying moves. If delta is an option's speed relative to the stock, gamma is its acceleration. It matters because it tells you how quickly a position's directional exposure will shift: a high-gamma position can go from modest to large exposure in a single day's move.
How it works
Gamma is quoted as the change in delta for a $1 move in the underlying. Bought calls and bought puts both have positive gamma; sold options have negative gamma.
The approximation is linear; for large moves gamma itself changes, so recompute rather than extrapolate.
Where gamma is largest
Gamma peaks for at-the-money options and rises sharply as expiration nears. A deep in-the-money or far out-of-the-money option has little gamma because its delta is already near 1 or 0. That is why short-dated, at-the-money options can swing between near-worthless and valuable within hours.
The trade-off with theta
Positive gamma is paid for with time decay. A long-option holder benefits from big moves in either direction but loses theta every day the stock sits still. A seller collects theta but is exposed to sharp moves, the classic "short gamma" risk. Market commentary about "dealer gamma" refers to how options market makers hedge: when they are net short gamma they must buy into rallies and sell into declines, which can amplify moves.