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Tuesday, March 19, 2013

Effects of IMPLIED VOLATILITY (IV) on Option Greek GAMMA – With Past DATA and CHARTS

Impact of Implied Volatility (IV) on Gamma
When the Implied Volatility increases, the Gamma of ATM options decreases, whereas the Gamma for deep ITM or OTM options increases.

When the Implied Volatility is very low, the Gamma of ATM options is relatively high, while the Gamma for deep ITM / OTM options is relatively low (close to 0).
This is because when the volatility is low, the time value portion of an option is low. However, time value of ATM option is still higher relative to ITM & OTM options, hence the Gamma of ATM option is higher as compared to ITM & OTM options.

On the other hand, when IV is high, Gamma tends to be stable for ATM option as well as ITM and OTM options. This is because when volatility is high, the time value of deep ITM / OTM options are already quite substantial. As a result, the increase in the time value of deep ITM / OTM options as they go nearer the money will be less dramatic. Therefore, Gamma tends to be more stable across all strike prices in this case.


We’ll 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).

Here is the summary of Gamma values for different IV:


From the table, we can observe that for near ATM options (i.e. the option’s strike price $45.00, because the stock price is $44.78), Gamma decreases as IV increases, i.e. as it moves from the left (IV = 25, the lowest IV in this example) to the right (IV = 85, the highest IV in this example).

Whereas for deep ITM options (e.g. option’s strike price $35 and $37.5) and deep OTM options (e.g. option’s strike price $55 and $52.5), Gamma increase when IV increases.

Hence, these observations show evidence to the first statement above.

Now, let’s observe the behavior of Gamma of different IV at various strike prices (as shown in the chart below) to verify the next statements.


As can be seen in the chart:
For all the three options with different IV, 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:
Regardless of IV levels, the delta of ATM option is most sensitive to changes in stock price (i.e. gamma is the highest for ATM option), as compared to ITM and OTM options.

The chart also shows that when the IV is very low (i.e. IV = 25 in this example), the Gamma of ATM options is relatively high, while the Gamma for deep ITM / OTM options is relatively low (close to 0).
When IV is high (i.e. IV = 85 in this example), Gamma values do not change so drastically (i.e. tend to be more stable) as the price moves across different level of option moneyness / strike prices.

Conclusion:
Given the same IV, Gamma of ATM option will always be higher than that of deeper ITM and OTM options.
However, when IV is very low, Gamma of ATM options is relatively high, while the Gamma for deep ITM / OTM options is relatively low (close to 0).
And when IV is very high, Gamma values do not change so drastically (i.e. tend to be more stable) as the price moves from deeper ITM/OTM towards ATM.

Given an ATM option, the option with higher IV will have lower Gamma.

Given a deeper ITM or OTM option, the option with higher IV will have higher Gamma.



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