How do I compare implied and historic volatility?

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.

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How did you produce the chart? With R? – vonjd Jun 6 '11 at 6:07
@vonjd no with Excel. I am shamed to say that I while I am an experienced trader and programmer, I am not a quant, and am only beginning to learn R. So the data comes from Bloomberg, which gives the ATM, RR, and flys for each tenor and delta and I have backed out the outright vols for each point. – Thomas Browne Jun 6 '11 at 7:31

Implied volatility is the volatility implied by some model. You will have a skew if your model is implying different volatilities for different strikes. However, the realized volatility of the underlying will be the same for all strikes. So, when you are dealing with realized vol, you can drop the "moneyness" axis.

Volatility cones can help you compare implied vol to historic vol. Volatility cones are constructed using any historic volatility estimator to calculate n-day vols for several n's using a rolling window. Multiply by an adjustment factor to take out the bias introduced by using overlapping data. Then you can plot confidence intervals.

See Euan Sinclair's book, Volatility Trading, or the 1990 paper by Burghart and Lane, "How to Tell if Options are Cheap"

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How to tell if options are cheap can be found here: nuclearphynance.com/User%20Files/1915/… – vonjd Jun 17 '11 at 7:06
thanks for the links to the paper and the book. So there is no point in trying to compare the skew and kurtosis of the historic distribution, to the risk reversal pricing and smile of the curve, analagous to how macro traders will compare historic with implied ATM vol? That's what I was wondering basically. Second, what do you mean by overlapping data? I am using bloomberg "last price" closing prices, so there should be no overlap? For completeness I take log returns of that series and multiply by sqrt(262) to get the annualized vol. What would you do differently? – Thomas Browne Jun 17 '11 at 7:15
@vonjd I have found the following two papers to be interesting wrt to this question as well: bcb.gov.br/ingles/estabilidade/2002_nov/ref200201c62i.pdf and rbnz.govt.nz/research/discusspapers/dp02_04.pdf – Thomas Browne Jun 20 '11 at 12:03
@vonjd Thank you for the link! I have been looking for a digital copy of that paper forever! – Tal Fishman Jul 21 '11 at 19:56