Estimating Event Implied Moves from Option Variance and Skew
Summary
The document describes estimating an event-related move from options by separating variance expected across ordinary time from the extra variance attributed to the event. It uses at-the-money implied volatilities for the first two expirations after the event to estimate forward variance, then subtracts the non-event portion from total front-expiry variance to obtain jump volatility.
It asks how to incorporate skew and offers a conceptual answer: changing the option strike changes the reference price underlying the estimated return, so estimates based on in-the-money and out-of-the-money options can differ. Under a skewed lognormal-return assumption, downside options have higher implied volatility, and the response suggests in-the-money estimates may imply a larger move than out-of-the-money estimates. It also relates jump volatility to expected absolute return under a normally distributed log return. The discussion gives no empirical comparison or validated skew adjustment, and it does not account for how volatility smiles, event timing, or distributional departures affect the estimate.
Key ideas
- The method estimates ordinary forward variance from two post-event expirations and attributes remaining front-expiry variance to the event.
- Using options at different strikes changes the reference price associated with the estimated return.
- The response links downside skew to differences in estimated event moves across strikes.
- A normal log-return assumption converts jump volatility into an expected absolute return.
Tags
Full text
# Measuring implied move priced into an event
# Measuring implied move priced into an event
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 by Yanyi Yuan (score -1)
https://quant.stackexchange.com/a/61202
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.