Gamma

Gamma measures how quickly an option's delta changes as the underlying moves. If delta is like speed, gamma is acceleration. A call with a delta of 0.50 and a gamma of 0.05 will have a delta of about 0.55 after a $1 rise and about 0.45 after a $1 fall. Gamma explains why option positions can gain or lose much faster than delta alone suggests, and why options close to expiry can swing so wildly.

Gamma basics#

Calls and puts with the same strike and expiry have the same gamma.

Positive gamma: moves work for you#

With positive gamma, your delta rises as the market goes up and falls as the market goes down. You get longer as prices rise and shorter as they fall, which means gains accelerate and losses slow down.

Negative gamma: moves work against you#

Option sellers are short gamma. As the market rises, their position gets shorter; as it falls, it gets longer. Losses accelerate in big moves in either direction. That is why selling options can produce steady profits in quiet markets and sharp losses in volatile ones. See Theta Harvesting.

Gamma and time to expiry#

Gamma for at the money options rises sharply as expiration approaches. With days or hours left, a tiny move can push an option from nearly worthless to deep in the money, so delta can jump from 0.1 to 0.9 quickly. This is why 0DTE options and expiration days are so volatile for option positions. See Option Expiration Dates.

The gamma and theta trade off#

Gamma and theta are linked. In the Black Scholes framework, a delta hedged option position's profit over a short period is roughly:

daily P&L ≈ ½ × gamma × (price move)² + theta

Long gamma positions earn from the squared price move and pay theta each day; short gamma positions collect theta and lose on big moves. The break even move is where the two balance. This relationship drives Gamma Scalping.

Gamma in the wider market#

When options dealers are, in aggregate, short gamma, their hedging can amplify market moves: they must sell into falls and buy into rallies. When they are long gamma, their hedging dampens moves. Analysts estimate this dealer gamma exposure to explain why markets sometimes trend sharply or stay pinned. See Dealer Gamma Exposure.

Managing gamma risk#

• Know your position gamma, not just delta. See Managing Portfolio Greeks.
• Reduce short gamma before big events and near expiry.
• Use spreads to cap short gamma risk instead of naked short options. See Vertical Spreads.
• Rehedge delta more often when gamma is high.

Common mistakes#

• Ignoring gamma near expiration, when it is largest.
• Selling at the money options into events without considering short gamma.
• Hedging delta once and assuming it stays hedged.

Frequently asked questions#

What is gamma in options?#

The rate at which an option's delta changes for a $1 change in the underlying price.

Why is gamma highest at the money?#

Because at the money options are most uncertain about finishing in or out of the money, so their delta changes fastest as price moves.

Is high gamma good or bad?#

For option buyers, high gamma means large potential gains from big moves; for sellers, it means large potential losses. It is paid for or earned through theta.

Next, learn how time decay works in Theta.