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Testing SABR Implied Volatility Surfaces Against Historical Volatility

Article Quant Q&A · Author: tallsamurai
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Summary

The document asks how to assess the accuracy of SABR implied volatility surfaces for a chosen equity index and historical period. Its proposed approach is to calibrate SABR, obtain the model’s implied volatilities, and compare them with historical volatility across options of different maturities. It is a research question rather than a worked method: no calibration details, volatility estimator, data source, sample period, or test results are provided.

A meaningful evaluation would need to define what “accuracy” means and compare like with like. Historical realized volatility and option implied volatility measure different quantities, so a direct comparison needs aligned horizons and a clear treatment of strike, maturity, and observation timing. The document does not address those choices or discuss benchmarks, out-of-sample testing, or calibration error. Its main contribution is identifying a possible comparison, while leaving the validation design and interpretation open.

Key ideas

  • The proposed evaluation calibrates SABR and compares its implied volatilities with historical volatility across maturities.
  • The question focuses on a specific equity index and a defined historical period.
  • Historical realized volatility and option implied volatility are different measures and require careful alignment for comparison.
  • The document provides no data, calibration procedure, benchmark, or empirical findings.

Tags

OptionsVolatilityDerivatives pricingBacktesting
Full text
# How to measure accuracy of SABR volatility surfaces?


# How to measure accuracy of SABR volatility surfaces?












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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.