what would you suggest are the starting points for comparing, in an easy, visual way, implied and delivered volatility surfaces? I'd like to see what the differences are between the historic surfaces, and the implied surfaces.
Implieds are easy enough, for example USDBRL:
But how would you go about taking a set of the past 2 years of historic returns and convert it into an equivalent surface to the above?
Perhaps there are other ways usefully to look at this problem, and where should I start? I have looked at boxplots of historic returns, but then I have the opposite problem namely, a visual representation of the historic vol but then how do I compare it to implieds?
Another thing I could do is simply to look at the historic standard deviation and compare it to the ATM vols, but then I'd be ignoring the (very useful) relative value information in the wings (because I have a sneaky suspicion that the upside wings are expensive).
My preferred tool is R (and Excel fallback if I must), or Python.