Theta and Weekends

A number of traders, some of whom are even successful, claim you don’t need to understand the “Greeks” to trade options. They might have a point. Although the Greeks exist whether or not we keep track of them or understand them, in the final reckoning the option price is what matters. If we buy some options for $1,000 and later sell them for $2,000, we will have made $1,000 no matter why the price change happened. However, understanding the Black-Scholes-Merton paradigm and the associated Greeks is like knowing a new language. Sometimes it is simply easier to express a certain idea in a different language, and sometimes a certain trading idea can be most easily visualized with the help of the Greeks.

Here we will talk about one such trade, based on one Greek: theta. Theta is the change in the option price over a certain time interval if nothing else changes, particularly the underlying price. But over the same time interval we expect the underlying price will change. The amount the expected underlying move changes the value of the option exactly offsets the amount it is expected to decrease because of theta. So, while theta is sometimes called “decay,” an option is not actually expected to decay as time passes. This would only be the case if the underlying didn’t move. Even experienced traders sometimes get confused by this, and it has been used as an interview question at several option trading firms.

Up until now we have implicitly assumed the option is fairly priced and the implied volatility used in the pricing formula is the same as that of the underlying during the life of the option—in which case the volatility of the underlying compensates the option holder for the theta cost of holding it, and neither the buyer nor the seller will make a profit. But if the implied volatility is too high, the seller of the option will eventually make money because the underlying movement won’t be large enough before time runs out and the option expires. This is a volatility effect, but it manifests itself slowly and is often erroneously called “time decay.” Accordingly, the first important thing to remember is: Never sell an option purely to “collect theta.” You will make money selling an option only if the realized volatility of the underlying is lower than the implied volatility of the option. Variance and time are inter-linked. Sometimes traders think in terms of one and sometimes in terms of the other, but they are equivalent.

An interesting example of this, and one that leads to a profitable option trade, is what happens to options over weekends.  Many years ago, when I was a clerk on the floor of LIFFE, a young option trader (let’s call him James) had the bright idea of selling options on Friday then buying them back on Monday “when they would be cheaper.” Of course we laughed at him, pointing out that he wasn’t the only one with a calendar and that everyone took the weekend into account. It seemed clear to us that something as obvious as an upcoming weekend couldn’t possibly be the source of a profitable market inefficiency. (Incidentally, don’t feel too sorry for the ridicule James suffered. He has done extremely well for himself, and many of those who made fun of him are now selling used cars or working in fish and chip shops.)

Indeed, the option market makers did adjust for the weekend, either by lowering the volatility inputs in their pricing models (because fewer volatility-causing events could be assumed to occur over the weekend ) or by gradually moving the time input forward. But just because the market makers adjusted their prices doesn’t mean they did so perfectly. Perhaps James was actually correct, and on average it is profitable to be short options over the weekends? 

to be continued...