Quiz 5 Answer

Simple: Just raise implied volatility and look at the delta. If the delta rises, then the book is look OTM calls and shorter OTM puts, i.e. long skewness --you want Expectation of the cubic returns E[DS^3] to be >0. In other words look at the sign of the DDelta-Dsigma.

The problem is that the analytical derivative is not sufficient since the effect might flip if you have way out of the money options that might "wake up" at higher volatility. So you should make sure that the reaction is monotonic. In other words you might have exposures to higher ODD moments of the distribution.