Gamma tells us how quickly delta changes when the underlying asset moves.

Options with a high gamma have deltas that shift rapidly, which means traders need to rebalance hedges more frequently in a moving market.

So which options tend to have the highest gamma value? The answer is that gamma is concentrated around at the money strikes, and it is most pronounced when time to expiry is short.

Here's the intuition at the money options are finely balanced.

A small move in the underlying asset can swing the probability of finishing in the money quite dramatically, especially when time to expiry is short.

That sharp change in probability translates into a sharp change in delta, which is exactly what gamma measures deep in the money or deep outta the money. Options don't behave this way.

Their outcomes are already almost certain.

Either exercise is virtually guaranteed or virtually impossible.

So Delta doesn't react much to small price moves, and so gamma is low time to expiry also matters.

With only a day left, a $1 move in the underlying can materially change the likelihood of exercise.

With so little time left to expiry gamma, the rate of change in Delta is higher for options with a long time potentially years left to expiry the same.

$1 move is far less influential in changing the option price because there's still plenty of time for the market to move around, meaning today's $1 move is unlikely to have a significant impact on the likelihood of exercise a long way into the future.

So gamma is low.

That's exactly what the charts show on the left.

The one day option has a very sharp gamma peak at the strike price of 100, while longer dated options have much flatter curves on the right, you see the same effect in three dimensions.

Gamma is highest for at the money options and rises dramatically as expiry approaches.