Gamma

Gamma measures how fast an option’s delta changes when the underlying moves. It is the curvature of the option’s value. A long option position is long gamma, so its delta grows in the direction of the move. A short option position is short gamma, so the opposite happens.

How it works

gamma = change in delta for a 1-point move in the underlying. Gamma peaks for at-the-money options and rises sharply as expiry approaches. A long gamma trader who re-hedges delta sells after rallies and buys after dips, which locks in gains when the underlying moves. That is the source of gamma P&L, roughly 0.5 × gamma × (move)² per unit. The cost is theta: holding gamma means paying time decay every day. A short gamma trader collects that decay but has to buy high and sell low when re-hedging.

Example

Hypothetical: a trader is long 100 call contracts on a stock at 100, multiplier 100, each with a delta of 0.50 and a gamma of 0.05. The position delta is 5,000 shares, hedged by selling 5,000 shares. If the stock rises by 2 points, each call’s delta moves to about 0.60, so the trader sells 1,000 more shares at the higher price. The gamma P&L on the move is about 0.5 × 0.05 × 2² × 10,000 = $1,000.

On the desk

Traders watch gamma by strike and by expiry, not only in aggregate. Short gamma concentrated on a strike near expiry can turn a quiet day into a large loss in a few minutes.