Theta And Volatility

Theta with respect to changes in volatility:

In general, options of highly volatile stocks have higher Theta than those which are less volatile. This is because the time value premium on these options is higher, and so they have more to lose each day.

Let us consider Spot at 16500, days to expiry 17

From the table we can see that regardless of the option’s strike price (ATM/ITM/OTM), Theta always increases as Volatility increases. Like for strike 16500, Theta increases from 0.3 to 33 as volatility increases from 1 % to 100%. 

Please note that negative sign, which means losing the time value, is ignored when doing the comparison.

As can be seen, for all the three options with different volatility, 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 or OTM.

However, a decrease in Theta as the option moves from ATM towards deep OTM/ITM will be much bigger for options with higher volatility as compared to options with lower volatility.

This is understandable because options with higher volatility will contain more time value than options with lower volatility. Since Theta decreases due to the passage of time, it will naturally be higher for options with higher volatility as it has more time value to lose compared to options with lower volatility.