Comparing Implied Volatility with Historical Volatility Cones
Summary
The answer explains why implied volatility surfaces and realized volatility are not directly comparable across strike or moneyness. An implied volatility surface may vary by strike because it reflects the volatility required by a pricing model to match option prices. Realized volatility of the underlying, by contrast, is not strike-specific, so its representation can omit the moneyness dimension. This reframes the comparison: rather than constructing a historical surface with the same strike axis, compare implied volatility with historical volatility estimates across time horizons.
A suggested tool is the volatility cone. Calculate rolling realized volatility for several holding periods using a chosen estimator, adjust for the bias caused by overlapping observations, and plot confidence intervals. These ranges provide a visual context for judging current implied volatility against historical outcomes. The response points to established reading on volatility trading and option cheapness, but gives no dataset, estimator specification, or worked empirical example. A volatility cone is therefore a useful comparison framework, not proof that an option is mispriced or a standalone trading signal.
Key ideas
- Implied volatility can vary by strike, while realized volatility is a property of the underlying over a period.
- A historical volatility comparison can omit moneyness and instead compare estimates across horizons.
- Volatility cones summarize rolling realized volatility distributions for multiple time windows.
- Overlapping observations can bias estimates and call for an adjustment.
- Historical ranges offer context for implied volatility but do not alone establish mispricing.
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# How do I compare implied and historic volatility? # 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. ## Answer by user508 (score 12, accepted) https://quant.stackexchange.com/a/1309 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" Edit: See an application of the Burghart, Lane paper
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