A few weeks ago, I wrote about what option strikes
were best to sell when harvesting the variance premium. This is part of an
ongoing project to find optimal option strategies for volatility trading,
hedging and directional trading. As the next step, today I’m going to look at
what expiration to trade when selling index volatility.

First, let’s look at the theoretical arguments in the Black-Scholes-Merton world. On average the total PL for an option sold at si when the realized volatility is (the lower) sr is

But it is the way that this comes about that is important to us here. This is actually the sum of gamma profits which occur continuously. In one time step

(Traders usually think in terms of the first equation but this second equation is probably more fundamental as it comes straight from the first term in the BSM differential equation). So instantaneous PL is directly proportional to gamma. And short term (ATM) options have more gamma than long term (ATM) options. So you can ex…

First, let’s look at the theoretical arguments in the Black-Scholes-Merton world. On average the total PL for an option sold at si when the realized volatility is (the lower) sr is

But it is the way that this comes about that is important to us here. This is actually the sum of gamma profits which occur continuously. In one time step

(Traders usually think in terms of the first equation but this second equation is probably more fundamental as it comes straight from the first term in the BSM differential equation). So instantaneous PL is directly proportional to gamma. And short term (ATM) options have more gamma than long term (ATM) options. So you can ex…