Gamma

Gamma is the rate at which an option's delta changes for each $1 move in the underlying stock. If delta measures speed, gamma measures acceleration.

How it works

Gamma is positive for anyone who owns calls or puts and negative for anyone who has sold them. It is highest for at-the-money options and rises sharply as expiration approaches, which is why 0DTE options can swing from nearly worthless to deep in the money within minutes. Deep in-the-money and far out-of-the-money options have low gamma.

For small moves, the new delta is approximately the old delta plus gamma times the price change.

Why it matters for traders

Gamma matters most through market makers. A dealer who sells calls to customers is short gamma. To stay hedged, the dealer buys stock as the price rises and sells as it falls, which pushes in the same direction as the move.

When customers buy large amounts of short-dated calls, that hedging can feed on itself: rising prices push deltas higher, dealers buy more shares, and the stock climbs further. This is often called a gamma squeeze, and it can combine with a short squeeze in heavily shorted stocks. The reverse happens when dealers are long gamma: their hedging tends to dampen moves and can pin a stock near a large strike into expiration.

For option sellers, high gamma means a position's risk can change very quickly.

Example

Contoso Robotics (CTSO) trades at $50. The $50 call expiring in five days has a delta of 0.50 and a gamma of 0.08.

• If CTSO rises $1 to $51, delta becomes roughly 0.58.
• If it rises another $1 to $52, delta is roughly 0.66 (gamma itself shifts slightly as the stock moves).

A dealer short 1,000 of these calls would need to hold about 50,000 shares to hedge at $50, about 58,000 at $51 and about 66,000 at $52, buying into the rally each time.

FAQ

What is a gamma squeeze?

A rapid rise in a stock driven partly by option dealers buying shares to hedge calls they have sold, as rising prices increase those calls' deltas.

Why is gamma highest near expiration?

With little time left, a small move in the stock can decide whether an at-the-money option finishes worth something or nothing, so its delta swings much faster.