I’ve read a few option books.
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Friday, March 29, 2013

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

The following is the behavior of Theta in relation to Implied Volatility (IV) changes:

When Implied Volatility (IV) increases, Theta would be higher.
When IV decreases, Theta will be lower, especially when it is approaching expiration.

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 Theta values for different IV:

From the table, we can observe that:
Regardless of option’s strike prices (ATM/ITM/OTM), Theta always increases 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).

Negative sign (which indicate the losing of time value) is ignored when doing the comparison.

So, these observations verify the statements above.

Now, let’s study the behavior of Theta of different IV at various strike prices (as shown in the chart below).

As can be seen in the chart:
For all the three options with different IV, Theta always behaves the same way, i.e. Theta of ATM options is always higher, and it gets lower as it moves towards deep ITM and deep OTM options.
However, the decrease in Theta as the option moves from ATM towards deep ITM/OTM will be bigger for options with higher IV as compared to options with lower IV.

This is understandable because options with higher IV will contain more time value than options with lower IV (Remember about Options Pricing).
Since Theta is the decrease of time value due to the passage of time, Theta will naturally be higher for options with higher IV as it has more time value to lose, as compared to options with lower IV.

To view the list of all the series on this topic, please refer to:

Other Learning Resources:

Related Topics:
* Options Trading Basic – Part 2