I had asked a quant on the Portfolio Armor team recently for a rule of thumb about the best time to sell options before time decay accelerates (so, for example, an investor could roll his protection while recouping some of the cost of hedging). He said he’d check the academic finance literature on it (he’s currently a post doctoral fellow at Princeton). He e-mailed me last week saying he hadn’t found anything in the literature, but he’d had an epiphany about it. The details still need to be worked out, but I thought it was interesting enough that I’d share the the idea here. This is from his e-mail:
As you know, the time decay is given by the Greek “theta”… the problem is that to compute an option’s theta you need a model (Black-Scholes, or some alternative), which goes against the whole premise of Portfolio Armor: it is model-free and relies on no parametric assumptions [so there's no chance of model errors].
Here he notes that you don’t need a model to figure out the time value on an option:
We can figure out the time value on any option without a model: it is the difference between the market price and the intrinsic value, where the latter is Max{(S-K),0} for calls and Max{(K-S),0} for puts.
And then here’s his epiphany to use a little calculus and discrete math to time the roll of the options before theta burn kicks in:
We can look at the discrete-time differential (approximation of the first derivative) of the time-value component and try to find the point before time-decay is accelerated (the second derivative) [...]. Once that trigger is hit, you can start emailing out reminders to users that they may want to roll their protection.
I think this feature is pretty exciting. We’re planning to add it in Q1 of next year.
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