Gamma is a metric that measures the rate of change in an option’s delta for every one-point move in the price of the underlying asset.
Understanding gamma in options trading
Delta measures how much an option’s price is expected to move when the underlying asset changes in value. Gamma is the second derivative of the option’s price. It tells traders how fast the delta itself is changing. For Elephants trading the options markets, gamma is a gauge of delta’s stability. A high gamma indicates that the delta will fluctuate rapidly with minor movements in the underlying asset. A low gamma means the delta remains relatively stable.
The value of gamma is highest for at-the-money options. As an option moves further in-the-money or further out-of-the-money, its gamma decreases. This happens because the delta of a deep in-the-money option approaches 1.0 (or -1.0 for puts) and stops changing significantly, while the delta of a deep out-of-the-money option approaches zero. Gamma is always a positive number for long options positions, whether they are calls or puts, and it is negative for short options positions.
Time to expiration also impacts gamma. As an option contract approaches its expiration date, the gamma of at-the-money options increases sharply. The delta of these options can shift rapidly between zero and one depending on slight price movements in the underlying asset. Traders monitor gamma to manage their exposure, as high gamma positions carry higher risk of sudden price swings.
Example
Imagine an Elephant holding a call option on a peanut farming exchange-traded fund. The peanut fund is currently trading at 50 units per share. The call option has a strike price of 50, making it exactly at-the-money. At this point, the option has a delta of 0.50 and a gamma of 0.05.
If the price of the peanut fund increases by 1 to reach 51, the delta of the option will increase by the gamma amount. The new delta is 0.55. This means that for the next 1 point increase in the underlying fund price, the option price will increase by 0.55 instead of 0.50.
Because the option is now slightly in-the-money, the gamma will decrease. If the new gamma is 0.04 and the fund price rises again to 52, the delta will increase by 0.04 to reach a new delta of 0.59. The Elephant can use these gamma figures to calculate exactly how their position’s sensitivity to market movements will change as the underlying asset price shifts.