05 March 2007

What You Didn't Know About Time Decay

Time decay is known by the greek word "theta" and what everybody knows about theta is that it accelerates in the last month of the options life, losing a substantial whack of its value in the last few days.

In every option text I've ever read, theta is universally depicted by a graph that is something like the following:



This is a graph of the time value of the last 90 days of an ATM option. As you can see, the rate of decay is more or less linear up until the last 30 days, whereupon it starts to decay at an accelerating rate, losing the remaining value very quickly in the last few days.

This is proof that if you short options you should choose options with about a month remaining because that is when most of the decay is.

Or is it?

The above is certainly true for At The Money options. But what about Out of The Money options? What the textbooks don't tell you is that for an option that is somewhat OTM (or somewhat In The Money for that matter) is that the above scenario is not quite true. The characteristics of theta change, the further we go OTM or ITM.

Lets look at a theta graph for an option that is somewhat OTM:



Lo! It seems in this instance, that theta does not accelerate in the final 30 days at all, but rather DECELERATES.

If we are short OTM options we will collect more theta by writing expiry further out... 60 or perhaps 90 days and wind them up before the last month.

This is where "options education" can sometimes be erroneous and it pays to observe, notice things, play around with your strategy modeler and/or excel spreadsheet and really become intimate with these option concepts. It does pay.

8 comments:

Anonymous said...

As someone interested in doing out of the money option writing on futures contracts, I find it fascinating that I should be in the -90 to -30 day window. May I ask how you came up with this graph showing theta decelerating in the last 30 days?

W. Anthony Lawrence said...

It is simply a matter of plotting the extrinsic value remaining at various times till expiry using an options pricing model.

To this simple test. Pick an OTM option with 30 days remaining, compare the price with one 60-90 days remaining. Depending on how far OTM you go, IV, skew, etc There may be more premium per day on the longer dated options.

Anonymous said...

i write future options(er2) 45 days/buy back at 10 days. usually in a spread set up.

Anonymous said...

As the first commenter above and a newbie to futures options trading at that, from all my reading I concluded that the best way for me to profit is to write OTM strangles and I like the idea of the 90 to 30 day window or the 45 to 10 day window, with the debit for each strangle being worth between $600-$800. One concern I have is that in real life, I worry I'm giving up too much profit for the risk I'm taking with commissions and spreads.

My worst experiences with spreads have been with the currency options, with the grain options being somewhat bad. Coffee, cocoa, and crude oil seem fine. E-mini S&P500 is great.

Which futures markets in your experience seem to be the most cost-effective with option writing?

Anonymous said...

Correction to previous comment:

For a sale at 45 days, $600-$800 debit is the targeted amount for an OTM strangle.

For a sale at 90 days, a significantly higher debit, perhaps $1000-$1300 is the target.

W. Anthony Lawrence said...

"Which futures markets in your experience seem to be the most cost-effective with option writing?"

To be honest, the only FUTURES options I have played extensively with are the incices, where, as you have noticed, spreads are quite good.

I have a friend who does a lot of commodity options, so when I catch up next I will interrogate him on the topic. It so happens I am looking into this myself so stay tuned.

Re time frame: Depending on IV and how far OTM you actually go can make a difference. I wouldn't "automatically" look at any expiry range. Do the sums in each situation to get the best deal.

Good luck

Mike Sklut said...

Dollar falls in the time value of options being greatest for ATMs does not lead me to the conclusion you came to. Returns on the option's values is still greatest for away-from-money options as they near expiry. I've written something here (vafrous.com), and threw in a couple of graphs.

Gregory Bloom said...

I agree that the leveling off at the end of life appears to argue against holding option shorts to the bitter end. But your OTM graph also shows that the time to halve (half-life?) is much longer at the left side of your graph - going from 1600 to 800 takes six knots, while the halving from 800 to 400 takes just 3 knots, going from 400 to 200 takes just 2 knots, and going from 200 to 100 takes just one knot. So realizing 50% of the margin you've tied up on your short takes much less time (1/6th) at the end of life, despite the apparent slowdown.