Behaviour of GAMMA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

As discussed previously in the earlier post, here is the behavior of Gamma in relation to
Time to Expiration:

Assume all other factors unchanged:
For ATM options, Gamma increases (is higher) as time to expiration is nearing.
In contrast, for both deep ITM and deep OTM options, Gamma normally decreases (is lower) as time to expiration is nearing.

We will use the same past actual data as shown in the previous post on the behavior of Delta, namely:
Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

Similarly, here is the summary of Gamma values for different Time to Expiration:



As can be seen from the table, for both deep ITM (strike price $35.00 & $37.50) and deep OTM options (strike price $52.50 & $55.00), the Gamma values are the lowest for the options with expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).

On the other hand, for near ATM options (i.e. strike price $45.00, because the stock price is $44.78), the Gammas are the highest for the options with expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).

These prove the statement above.

Now, let’s compare Gamma of different time to expiration at various strike prices, as shown in the chart below.



As can be seen in the chart:

For all the three options with different time to expiration, Gamma always behaves the same way, i.e. Gamma of ATM options is always higher, and it gets lower as it moves towards deep ITM and deep OTM options.

That means:
Given the same time to expiration, the Delta of ATM options changes the most when the stock price moves up or down, as compared to deeper ITM and OTM options.

However, the blue line (i.e. options with expiration month “Sep-10”) is much steeper than the red line (i.e. options with expiration month “Oct-10”) and green line (i.e. options with expiration month “Dec-10”).
This shows that:

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 the Gamma values across different strike prices will be.

Conclusion:
Given the same time to expiration, Gamma of ATM option will always be higher than Gamma of deeper ITM and OTM options.

Given an ATM option, the option with nearer time to expiration will have the highest Gamma, as compared to the option with longer time to expiration.

Given a deeper ITM or OTM option, the option with nearer time to expiration will have the lowest Gamma, as compared to the option with longer time to expiration.

To view the list of all the series on the this topic, please refer to:
“Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.”

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
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Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2