Friday, September 10, 2010

The Dynamics of Time Decay

When asked how to define Theta, the textbook answer is it allows traders to measure how much money an option position will make or lose per day. Though that may be adequate for an elementary understanding, there are many questions that arise when considering how time decay plays out in the real world where weekends and holidays are interspersed throughout an options life.

Having never been a market maker and never needed to generate quotes for options on a day to day basis, I must admit my understanding of the finer nuances of how time is calculated into an option's premium is certainly not as exhaustive as some. So when I received the following thoughtful question from Bill, I passed it along to Mark Wolfinger of Options for Rookies to take a stab at. Rather than post the original question, which was rather lengthy, the gist was as follows:

How does the options market account for weekends and holidays when pricing in time decay? Do options lose value over the weekend or has the weekend decay already been priced in by the close on Friday? If that's the case, does that mean options lose more value toward the end of the week relative to how much they're losing at the beginning?

The Black-Scholes and other formulas that calculate the value of an option use time as an important consideration. Time is defined as the number of days (hours, minutes, seconds, or whatever unit appeals to you) until expiration arrives. Thus, yes, you can be certain that the weekend is included in the process that determines the value of an option.

But if your question is: Will I see that time decay every day - then the answer is 'no'. Market makers set their clocks - the ones used to determine the value of an option - any way they prefer. And they prefer accelerating time prior to a weekend. When you come in Monday morning, you will never see options priced as if 3 days just passed. That decay - most, almost all, or all, has already been priced into the price of the options at the end of the prior week.

There is no set formula. Each market maker, specialist, and off-floor market maker, is free to establish his/her own program that determines the value of an option - and thus the bid/ask quote. Anyone who believes a big error has been made in the option price is free to sell the bid or pay the offer to take advantage of that 'mistake'.

[Note- This is part of the question] When I look at option pricing, there are too many factors influencing the price for me to tell the EXACT effect of theta over the weekends.

And you can never see the exact effect over the weekend. Why? Because of the way that options are priced. Each market participant gets to move the clock at whatever rate he/she sees fit. They set the bid/ask and you can trade with them, make higher bids or lower offers, but you cannot tell them how to set the clock. And the truth is that you can never know if a small change has been made to the volatility used to calculate the theoretical option values.

One simple plan is to have the clock move 7 days over the 5-day week. A more reasonable approach is to move the clock 7 days over the 5-day week, but with time accelerating during the week. Thus, it would pass much faster on Friday than on Monday. More than that, each day is not consistent, and time would pass more rapidly in the afternoon than in the morning - steadily accelerating throughout the week.

Other traders may use an algorithm that allows some passage of time over the weekend. Why? Although there is no trading, events happen, wars begin etc... Just allowing for a market-moving event makes sense. But just how much of the one week's worth of time does one devote to the weekend? I have no answer, but there's big money at stake and my wager is that the methods used to determine the clock algorithm for each trader group is a closely guarded secret.

If you take the time to look at the numbers, you will discover, all things being equal (quiet news weekend and a flat opening) the options open where they closed. There is no big price drop. In fact, it's possible for options to move up a bit in price to counter the effect of over-discounting them on the previous Friday.

For related posts, readers can check out:
Theta
Greeks
Gamma vs. Theta Part I
Gamma vs. Theta Part II

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