Gamma is derived from delta. The gamma of a position is the rate of change of the delta relative to the rate of change of the price of the underlying security. Mathematically, the formula can be expressed as :
Gamma = rate of change of delta rate of change of underlying security price
By observing the gamma of a position , traders will be able to tell how quickly a delta changes. It informs the trader of the probability of an option expiring in the money. When the gamma of a position is high, it means that the delta is sensitive to changes in the underlying asset price. When the above is observed, it means that there is a high probability of the option moving from out of the money status to in the money. In general, ATM options have high gammas.Also, the gamma for a call and a put is always identical and can be positive or negative.
Summary on gamma
| Position | Delta | Gamma |
| At-The-Money option | Delta of approximately 0.5 for calls and -0.5 for puts | High gamma |
| Near-The-Money option | Delta of approximately 0.5 for calls and -0.5 for puts | High gamma |
| Deep In-The-Money option | Delta of approximately 1 for calls and -1 for puts | Low gamma |
| Deep Out-Of-The-Money option | Low delta | Low gamma |
Read : Delta
How To Mitigate The Effects Of Time Value Decay