# 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...