## Definition

The term gamma refers to the rate of change in delta for a one point change in the price of an underlying asset. An option's gamma is typically expressed in terms of a percentage change in delta for a one-point change in the underlying asset's price.

### Explanation

An option's gamma tells the investor how fast delta will change if the price of the underlying asset changes by one point. While delta helps the investor to understand how much the value of an option will change for every one dollar change in the value of the underlying asset, gamma tells the investor the impact the change in the underlying asset's value has on delta.

Four generalizations can be made concerning gamma for a given option:

- When an option is at-the-money, delta approaches 0.5 and gamma is maximized.
- When an option is deep in-the-money or deep out-of-the-money, its delta approaches one and gamma approaches zero.
- Gamma is positive for individuals that take a long position (holders of a call option) in the underlying asset.
- Gamma is negative for individuals that take a short position (holders of a put option) in the underlying asset.

As is the case with delta, gamma is also a function of time to expiration and volatility. As an option approaches its expiration date, the gamma of an at-the-money option will increase and the gamma of an out-of-the money option approaches zero. If the price of the underlying asset is volatile, then gamma tends to remain constant, since the time value of an in-the-money or out -of the money option is relatively high. If the underlying asset price is relatively stable, the time value of the option approaches zero; therefore, gamma is relatively high.

### Related Terms

hedge, hedge ratio, fungibility, expiration Friday, expiration date, exercise by exception, European option, American option