Do people use regression to try to predict the vol skewness?What I mean is this - say I regress the implied vol of a large number of options against the greeks of the options and time to expiration. Then for an option with unknown price, I can calculate its greeks (by using some sort of average vol assumption) and plug the greeks and the time to expiration in the original regression equation to get an implied vol/price. I can of course then reiterate using this new implied vol as the input to the option pricing formula to get new greeks and so on.Does this approach ring a bell? Is this well-known and used on the Street? Any references in the academia?thanks,

People certainly use optimizers and regression-like techniques to fit volatility surfaces, both implied and local. There are various methods of vol surface parameterization, many of which tend to be more stable and practical in the long term compared to the Dupire formula.The only greek I have seen as a regressand (or whatevery you call the dependent coefficient) is the Delta. That is, implied vol is most simply practically fit as either a function of time and delta or time and strike.