I would like to test how accurate are SABR volatility surfaces with respect to historical volatility over a given time period and for a specific equity index.

Reading a few papers I realised that one way to do so is to go through the entire SABR calibration process, find its IV and then compare the resulting surface with historical volatility for those options over various maturities.

What do you think and how would you go about it?

  • $\begingroup$ Please note that any kind of volatility model fit can only be ‘valid’ for the point in time you are fitting it. But you can of course come up with some accuracy metric per calibration time point, e.g. by calculating a (weighted) mean squared IVOL error or such. $\endgroup$ Jul 30 at 9:18
  • $\begingroup$ Yes, that makes sense and it's a good starting point. Now, problem is that, in order to verify that IV is close to market volatility for that asset, I would need to retrieve historical calls and puts data for previous times. Just don't know where to get that without paying a large premium $\endgroup$ Jul 30 at 11:53

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