Gamma
Gamma measures how fast delta changes — it is the acceleration behind the speedometer, and it is the short option seller’s quiet headache.
If delta tells you how much an option moves when the stock moves one dollar, gamma tells you how much that delta itself changes for the same 1-dollar move. Delta is the speed; gamma is the acceleration. A position can have a comfortable delta right now and still be dangerous, because high gamma means that comfortable delta can lurch somewhere else the moment the stock twitches. You can think of delta as where you are and gamma as how quickly that is about to change.
Where gamma is largest
Gamma is not spread evenly. It is largest for at-the-money options — those with a strike near the current stock price — because that is exactly where a small move flips an option between out-of-the-money and in-the-money, swinging its delta hard. Deep in-the-money and far out-of-the-money options have low gamma; their delta is already pinned near 1 or near 0 and barely budges. Gamma also grows as expiration approaches. With weeks left, there is time for the stock to wander back, so delta shifts gently. With a day or two left, every dollar of stock movement forces a large, immediate adjustment in delta. Near-dated, at-the-money options are the high-gamma corner of the board.
Long gamma versus short gamma
Buying options puts you long gamma: as the stock moves, your delta shifts in your favor. Rallies make a long call ever more bullish; declines make a long put ever more bearish. The position helps itself.
Selling options puts you short gamma: your delta shifts against you. This is the seller’s headache. As the stock moves toward your strike, your delta grows in the wrong direction, so each additional dollar of adverse movement hurts more than the last. You collected premium up front for accepting exactly this discomfort.
Worked example: a short put with two days left
Imagine you are short a put that is now at-the-money with two days to expiration — the high-gamma corner. The stock dips a dollar: the put’s delta lurches from around −0.50 toward −0.80, so your position suddenly behaves almost as if you are fully long the stock, just as it is falling. The stock bounces a dollar: delta falls back toward −0.30, and you are barely exposed again. Your profit and loss whips around on tiny moves, because high gamma is converting small stock wiggles into large swings in how stock-like your position is.
This is why many sellers close a position before the final week rather than squeezing out the last few dollars of premium. The remaining premium is small, but the gamma — the risk per remaining dollar of premium — climbs sharply into expiration. The last stretch offers the least reward for the most jumpiness. (Note: this is a description of why the risk profile changes, not advice about what you should do.)
Gamma and theta are the same trade-off seen from two angles. The income you collect for selling an option (positive theta — time decay working for you) is the pay you receive for bearing fast-move risk (negative gamma — delta swinging against you). You are not given the decay for free; gamma is the bill. When a seller says “theta is doing its job,” what they mean is “the stock has stayed calm enough that gamma hasn’t hurt me yet.”
Gamma is the reason a short option that looks safe on Monday can feel alarming on Friday afternoon without the stock having moved much in total. Nothing about the contract changed except the calendar — and with it, the acceleration. For how gamma combines with delta, theta, and vega across a whole position, see The Greeks Explained. The short version: gamma tells you how violently delta can change, and it is highest exactly where and when sellers feel it most — at-the-money, near expiration.
Educational only — not investment advice. Options involve a substantial risk of loss and are not suitable for every investor.