Measuring implied move priced into an event

Question

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance between the first two expirations after the event (using ATM vols), and subtracting it from the total implied variance of the front option. This is the method suggested in Colin Bennett's book, Trading Volatility. To elaborate, if $T_1$, $T_2$ are the expirations of the first two options, and $\sigma_1$, $\sigma_2$ are their implied volatilies, then the implied forward variance is given by

$$\sigma_F^2 = \frac{\sigma_2^2 T_2 - \sigma_1^2 T_1}{T_2-T_1}$$

Then the implied jump volatility would be

$$\sigma_J = \sqrt{\sigma_1^2 T_1 - \sigma_F^2 (T_1-1)}$$

This approach does not account for skew, and I expect there's some information about the expected move priced into the OTM options that's not present in the ATM options. How do I adjust the implied move estimate to account for skew?

Answer 1

The expected stock price move post an event is the expected return of the stock price right before the event. Therefore, using ATM option IVs in the formula gives the expected return based on current stock price. If Using OTM/ITM option IVs, I think the formula gives the expected return based on the OTM/ITM option strike price. Theoretically, for stock options, skew indicates that downside strikes have greater implied volatility than upside strikes. That means using ITM options, the expected stock price move is higher as compared to using OTM options. It seems to make sense given the skewed log normal return assumption.

Also, the expected return is sqrt(2/pi)*σJ, assuming the log return is normally distributed. This is based on the mean absolute deviation formula for normal distribution.