Gamma’s Relationship With Spot And Strike Price

Gamma with respect to change in spot price:

The table below shows how Gamma changes with respect to change in SPOT PRICE, given the other factors are constant. Let’s find out the same for a 16500 strike Call and Put option, assuming the volatility to be 17% and days to expiry 17 days.

Observations: 

We can clearly observe that as spot price increases from 16100 to 16900, call premium increases and put premium decreases. Gamma is highest at ATM (here 0.0008) and decreases as spot price moves away in either direction. When Nifty slides down to 16100, gamma too goes down to 0.0007. When Nifty goes up to 16900, gamma still goes down to 0.0005.

The Gamma peaks when the option hits ATM status. This implies that the rate of change of Delta is highest when the option is ATM. In other words, ATM options are most sensitive to the changes in the underlying. Also, since ATM options have the highest Gamma – avoid shorting ATM options.

Let us now evaluate how Gamma changes with respect to change in other variables.

Gamma with respect to change in Strike Price:

Given the spot 16500, volatility at 17% and days to expiry 17 days.

We can see that the Gamma is highest (0.0008) at the ATM(13500)  and decreases as Nifty moves away on either side. When Nifty comes down to 15500, gamma too slides down to 0.0001 and when Nifty moves up to 17500, gamma still reduces to 0.0002. This explains why gamma has a bell curve.