Volatility smiles in practice
Posted: October 28th, 2014, 11:35 am
I've never been in such a position myself, but I believe that e.g. on the sell side, a volatility smile, or more generally a vol surface, is used to price instruments including vanilla options.If yes, then my question is about fitting a vol smile with calls and puts. If they are both European and the underlying pays no dividends then calls at puts at the same strike (tenor is fixed here) will have the same implied volatility by Put-Call Parity and standard theory. But in practice the theoretical assumptions are only approximations so the implied vols will be a bit off (if I recall I have observed this). Moreover, if there are dividends or the options are American then the theory may not even give the same implied vol.My question is how this is handled in practice? Is a single vol smile used? Do they live they live with the error that both calls and puts at a given strike cannot be priced correctly? Is more than one smile used, or is some adjustment made depending on whether a call or put is being priced?