About Theta

It's Time for Theta

Theta means Time Decay.

All options will expire one day, sooner or later. As time passes, each option will lose a little of its value due to the theta value that is attached to it. Particularly, all Long option positions value will suffer from such time decay, including weekends and public holidays, with no exception. Long options value decrease over time, because of Theta, even when the underlying stays absolutely still.

Let's review Google(GOOG), which is trading at $437.60. Its option chain is shown below.



Let me just digress a little and highlight a key ingredient; the Implied Volatility (IV) circled in green. The Sept08 options have all but 7 days to expire, the Oct options have 35 days and Dec, 98 days. Their respective Implied Volatilities :

Sept08 = 37%
Oct08 = 46%
Dec08 = 41%

Note that Oct08 has the highest IV. Please note that this is not to say that there is an error in the pricing model. The market is almost always perfectly efficient; especially when one is looking at such a liquid counter as GOOG. No one can tell the reasons for sure why the Oct's IV is higher than Dec's IV. What reasons accorded, can only be speculative, just as it speculative as to why a stock dropped 10% on a given day, without any apparent reasons. However, one can positively conclude that there exists a great deal of interests in GOOG's Oct options. The demand for these options, whether the buy or sell side, is the reason for this increased IV. It is simple economics 101. Mooncakes are most expensive becuase there is a higher demand for mooncakes during the Mooncake Festival and cheaper outside this period. Anticipated events can cause IV to increase.

However, there are always suggestions of market makers being responsible for artificially pumping up the next month's IV for all the reasons one can think of.

Now back to Theta.

Let's compare and contrast :

Within the same month, Theta exhibits this pattern

ATM options will have the highest theta assigned, as are the cases with Sept430 Call and Sept440. The reason is that, the best chances of success of any purchased options to get ITM (of cos other than those already ITM), will always be the ATM options. So, it is fair for options pricing model to allocate most premium to them, and that includes making the buyer of that ATM options, pay more for time decay. The seller of their ATM options, obviously, taking all the risks of writing, will demand a higher premium for ATM options.
Therefore, those ITM options, such as Sept400 Call, and OTM options like Sept470, will always contain comparatively lesser amounts of extrinsic value. Extrinsic value means, the additional premium an option pays for having the right to those options. With most extrinsic values attached to ATM options, correspondingly, Theta is highest always at those ATM options, both Puts and Calls.


Between Different Months, Theta Behaves in Discernable Pattern

Look at Theta for all Sept and Dec options. Across all strikes, Theta is smaller in Dec options than in Sept. For example, Sept 400 Call has a - 0.26 theta and Dec 400 Call has a - 0.18 theta. The reason that further out month has lesser theta attached to the options, is because there are many more days before those options expire.
Theta, or time decay, is experienced most when the options nears expiration. The effect is accelerated 30 days before expiration. So, in this Sept400Call, where theta is - 0.26, theoretically, ceteris paribus, theta will decay the option value by 26cents with every passing day and will decay the option value even more aggressively come closer and closer to the final expiration date.
At expiration date, all ITM, ATM and OTM options theta will revert to ZERO value. The value that time accords to these expired options, are no longer in existence. Hence, all options will lose their extrinsic value at the final second on expiration date.
In short, Theta is totally decayed at expiration date.

Now, if further out months options are supposed to have smaller theta, than why do Oct's options (being further out) have higher theta values across all similar strikes, when compared to Sept's? This is exactly opposite of what I described above.
There's no anomaly here. The only reason for Oct's options theta to be higher than Sept's is because of the markedly increased IV in the month of Oct. All that's been described about theta being highest at the ATM Oct option still applies.
But it should now be evidently clear to all that IV has a potent effect on other Greeks, including Theta. But had Oct's options IV be closer to ~39%, then those theta will likely be lower than their corresponding partners in Sept.

Increased IV will increase theta and a decreasing IV will decrease theta, everything else being constant.

This is the reason, that many traders will SELL options during HIGH Implied Volatility days and the reason why Asian traders shd NOT buy options (puts or calls) when HSI, SSE, STI do a stunning move...those warrants are very expensively priced. Since asian retail traders cannot SELL warrants, you are being forced to BUY them, if you wana trade warrants !!!! when the dust settles, and IV drops back to sane level, even if the index or stock price remain unchanged, your warrant values will drop very drastically....becos IV dropped.

Puts and Calls of Same Strike have Same Theta

There's is usually very difference in Theta figure for Calls and Puts of the similar strikes.

Theta can kill Long option traders, silently...