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

The following is the behavior of Theta in relation to Time to Expiration:

For ATM option, Theta increases as an option gets closer to the expiration date.
On the other hand, for ITM & OTM options, Theta decreases as an option is approaching expiration.
The above effects are particularly observed in the last few weeks (about 30 days) before expiration.

Using 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).

The following is the summary of Theta values for different Time to Expiration:



For easier analysis, we can plot the Theta values of different Degree of Moneyness across various Time to Expiration, as follows:




As can be seen from the table and the chart above:
For (near) ATM options (i.e. strike price $45.00, because the stock price is $44.78), Theta (in absolute value) is the higher for the options with expiration month “Sep-10” (nearer to expiration), as compared to “Oct-10” and “Dec-10”.
In other words, Theta (in absolute value) increases as time to expiration gets nearer.

Whereas for both deep ITM (strike price $35.00 & $37.50) and deep OTM options (strike price $52.50 & $55.00), Theta (in absolute value) is the lower for the options with expiration month “Sep-10” (nearer to expiration), as compared to “Oct-10” and “Dec-10”.
In other words, Theta (in absolute value) decreases as time to expiration gets nearer.

Note:
For Theta, we’re always comparing Theta here (whether it’s high or low) in terms of the absolute value, because the negative sign only represents the decaying effect.

Likewise, we’ll also compare Theta 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, Theta always behaves the same way, i.e. given the same time to expiration, Theta of ATM options is higher, and it gets lower as it moves towards deep ITM and deep OTM options.

That means:
Given the same time to expiration, ATM options will always decay faster as time goes by, as compared to deeper ITM and OTM options would.

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 means:

Theta 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 Theta values across different strike prices will be.

Conclusion:
Given the same time to expiration, ATM options will always decay faster as time goes by (i.e. have higher Theta) than the deeper ITM and OTM options would.

Given an ATM option, the option with nearer time to expiration will have the highest Theta (will decay the fastest), as compared to that with longer time to expiration.

Given a deeper ITM / OTM option, the option with nearer time to expiration will have the lowest Theta (will decay the slowest), as compared to that 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