Papale on Theta

By Steve Papale

I love Halloween.  For me it rings in the fall holiday season.  Lots of tradition.  When my kids were little I would carve the pumpkin and mom would bake the seeds.  Good stuff.  Kids were impressed.  Last night I carved the pumpkin.  Now my older kids have turned into pumpkin critics.  Eyes not centered.  Tooth missing.  Dad’s losing his touch they say.  I baked the seeds last night.  Fell asleep and left them in the oven too long.  A bit dry.  One of my kids won’t eat them.  More for me I guess.

In my mentoring I cover all the greeks.  The one greek that intuitively is probably the simplest is theta.  Most students understand fairly quickly the idea that all the extrinsic or time value of an option must go to zero by expiration day.  There is a common graph that Discover Options along with pretty much everyone else use showing an increasingly downward sloping theta curve as we get closer to expiration.  It is a nice illustration of the increasing rate of time decay over time.  But let me make a couple of clarification points regarding theta. First, the graph represents options that are at the money.  Those options have the most extrinsic value hence the front month decays at a faster rate than farther out months.

Second, those options decay at a faster rate, they don’t necessarily decay more in terms of dollars.  Most of the time front month options not only decay at faster rate but absolute dollars of decay are higher than the back month but not always.  If it is close to expiration the front month may have little extrinsic value left relative to the next month out so while the percentage of decay is higher the absolute dollar decay may be lower.  Not often but could happen.  $0.40 of extrinsic can only decay $0.40 while a $2.0 may decay more cents that day.

Third, referring back to the graph representing at the money options, options far out on the wings, i.e., far in the money and far out of the money options have very little decay.  This is simply due to there being no more extrinsic value left to decay.  In these strikes, options farther out in time have a positive decay number because they have extrinsic value with more time left until expiration.

Finally, remember theta, like all the greeks are theoretical values.  These are generated by the model and as inputs change these values can change.  What one day may appear as a large theta decay may be partly theta and partly a drop in implied volatility.  The greeks are there to help us understand the performance and behavior of our options positions but don’t bank on the numbers until the positions are closed out.

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