What is gamma? How fast delta changes

Delta tells you how much an option's price moves per $1 in the stock. Gamma tells you how much that delta itself changes per $1 in the stock. If delta is speed, gamma is acceleration.

A gamma of 0.05 means that for every $1 the stock rises, the option's delta increases by about 0.05. So a 0.30-delta call could become a 0.35-delta call after a $1 move — and keep steepening as the stock keeps rising.

Gamma is not constant across strikes. It peaks for at-the-money options and fades toward zero for deep in- or out-of-the-money options, whose deltas are already pinned near 1 or 0 and barely move.

That is why the at-the-money region is the most sensitive: a small move in the stock there causes the biggest swing in delta, and therefore the fastest change in your exposure.

When you sell an option you are 'short gamma.' Your position's delta moves against you as the stock moves: it gets more negative as the stock falls into your short put, and more positive as the stock rises into your short call.

Practically, that means a short option near the strike can flip from comfortable to threatening quickly. Gamma is the math behind that 'it was fine, then it wasn't' feeling.

The closer an option gets to expiration, the higher its gamma near the strike. An at-the-money option in its final days can see delta swing violently between near-0 and near-1 on small price moves.

This is 'gamma risk,' and it is why many sellers avoid holding short options into the last day near the money — the position can whipsaw between assigned and not assigned on tiny moves.

In the wheel you are almost always short gamma, collecting premium and theta in exchange for that risk. The defense is not to fear gamma but to manage it: sell out-of-the-money strikes, size positions so assignment is acceptable, and consider rolling before the final high-gamma days.

Because you actually want to own the stock, being on the wrong side of gamma near expiration usually just means assignment — the next expected step in the cycle, not a disaster.

Think of delta as your current directional exposure and gamma as how unstable that exposure is. High gamma means your delta will not stay put.

For a wheel seller the takeaway is simple: gamma is highest at the money and near expiry, so those are exactly the conditions where a short option demands the most attention.