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Options glossary · how fast delta itself changes as the stock moves
Gamma measures how much delta changes for each $1 move in the stock. If delta is speed, gamma is acceleration. A gamma of 0.03 means that after a $1 rise, delta increases by about 0.03.
Gamma is highest for at-the-money options near expiry, where a small stock move can flip an option from nearly worthless to deep in the money. That is why short-dated options feel so twitchy. High gamma cuts both ways: it makes a long option gain faster on a favorable move and lose slower on an adverse one, and it is the reason estimates built on today's delta go wrong for big moves.
For option sellers, gamma is the risk that pairs with the fat theta they collect near expiry.
Close to expiry, a small stock move can decide whether an at-the-money option finishes in or out of the money, so delta swings sharply from near 0 to near 1 over a small price range. That sharp swing is high gamma.