The Gamma of an option measures the rate of change/responsiveness of its delta with respect to a change in the underlying's price.
- It is the first derivative of the delta of an options contract. It is used to determine price movement relative to the amount the contract is in/out of the money. For example, a call option has a delta of 0.30. If its underlying increases by Re.1, its delta will change. Assuming delta to now be 0.50, its gamma is 0.20 (the change in delta)
- It is the second derivative of an option contract's price (premium) in relation to the price of the underlying.
- It is at its largest value when the option is near/at the money and is small when the option is deep/out of the money.
- Short positions have a negative gamma and long positions have a positive gamma value.
- The price of near at the money options is more responsive to price changes in the underlying:
If you’re an option buyer, a high gamma is good as long as your forecast is correct. As your option moves in the money, delta will approach 1 more rapidly.
However, if your forecast is wrong, it can result in delta rapidly falling.
If you’re an option seller, a high gamma is good as long as your forecast is correct. This is because the value of the sold option will lose value rapidly.
However, if your forecast is wrong, it can result in your position working against you faster if the sold option moves in the money.
Let’s look at the change in delta due to the effect of higher gamma for different strikes closer to expiry.