Gamma And Time To Expiry

Gamma with respect to change in Days To Expiry.

Assuming Spot to be 16500, volatility 17%, let us find out how gamma changes for ATM option 16500,

As days to expiry decrease, call Delta decreases and put Delta increases. They both tend to move towards 0.5 and -0.5 respectively. However Gamma increases, showing the high sensitivity of ATM options. 

Gamma values for options with nearer time to expiration differ more significantly along various strike prices, as compared to those with further time to expiration. The further the time to expiration is, the smaller the difference in gamma values across different strike prices will be.

Now let us check the same for strike 16000 where call is ITM and put is OTM

For, 16000 strike, or ITM call Delta moves towards 1 and OTM put Delta towards 0. The Delta being less sensitive on either side, Gamma tends to move towards zero.  

Now for strike 17000 where call is OTM and put is ITM

Similarly, for ITM Put, the Delta moves towards 1, while for OTM call Delta is 0. Gamma still moves towards Zero, showing no sensitivity in either direction. 

The Gamma value is also low for ITM options. Hence for a certain change in the underlying, the rate of change of Delta for an ITM option is much lesser compared to ATM option. However, do remember the ITM option inherently has a high Delta. So while ITM Delta reacts slowly to the change in underlying (due to low Gamma) the change in premium is big (due to high base value of Delta).

Learnings!

• Delta changes rapidly for ATM options.
• Delta changes slowly for OTM and ITM options.
• Never short ATM or ITM option with a hope that they will expire worthless upon expiry
• OTM options are great choices for short trades assuming you intend to hold these short trades up to expiry wherein you expect the option to expire worthlessly.