Definition
Gamma is the option Greek that measures how much an option's delta changes for a one-unit move in the underlying price. It is the rate of change of delta, and it describes how quickly an option's exposure to the underlying shifts.
How it works
Long calls and long puts have positive gamma, while sold options have negative gamma. Gamma is highest for at-the-money options close to expiry and smaller for deep in-the-money or far out-of-the-money options. High gamma means delta changes quickly, so exposure accelerates in favor of a long holder and against a short one.
Gamma trades off against theta: a long-gamma position pays time decay for that convexity, while a short-gamma position collects decay but can lose quickly after sharp moves. Hedgers need to rebalance delta more often when gamma is high.
Formula / convention
Gamma ≈ Change in delta ÷ Change in underlying price; Option price change ≈ Delta × ΔS + ½ × Gamma × (ΔS)²
Illustrative example
A fictional call on Sample Co has a delta of 0.50 and a gamma of 0.04 per HK$1 move in the share price. After a HK$1 rise, delta is about 0.54; after a HK$2 fall it is about 0.42. For a HK$1 rise, the estimated option gain is 0.50 × 1 + ½ × 0.04 × 1² = HK$0.52 per share, slightly more than delta alone suggests.
What to watch for
Gamma itself changes quickly near the strike and close to expiry, so short-gamma positions such as sold options can lose far faster than a static delta view suggests; check whether a platform quotes gamma per one unit of the underlying or per 1% move.