Gamma: How Fast Delta Itself Changes

In short

Gamma measures how fast an option's delta itself changes as the stock moves, and it peaks for at-the-money options near expiration, worked out with a 0.50-delta, 0.06-gamma example.

Delta tells you your exposure right now. Gamma tells you how fast that exposure is about to change.

What gamma measures

Gamma measures how quickly delta itself changes as the stock moves. It's delta's own rate of change — not just where your directional exposure sits today, but how fast it's shifting under you.

A worked example

An XYZ call has a delta of 0.50 and a gamma of 0.06. If XYZ rises $1, the new delta becomes roughly 0.56 (0.50 + 0.06). Rise another $1, and delta climbs again, though gamma itself also shifts as delta approaches 1.0.

Why gamma matters most near the money and near expiration

Gamma peaks for at-the-money options, especially close to expiration. A deep ITM or deep OTM option's delta is already near 1.0 or 0.0 and has little room left to move. An at-the-money option's delta, though, can swing hard on small stock moves — particularly in its final days, when a small price change can flip it between "likely to finish in the money" and "likely to finish out of it." That's why short-dated, at-the-money positions carry more unpredictable, fast-changing exposure than longer-dated or further-out-of-the-money ones.

High gamma cuts both ways — it can work for or against you depending on which way the stock moves next, so it's worth knowing which of your positions carry it before a big move happens, not after.

Key takeaway: gamma tells you how fast your directional exposure is shifting, not just what it is right now — and it's highest for at-the-money options close to expiration.

Next: vega, which measures exposure to something delta and gamma don't touch at all — changing volatility.

This lesson is educational content explaining standard options mechanics, not personalized investment or trading advice.