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Comparing Higher-Order Approximations to the SABR Formula

Article Quant Q&A · Author: jaehyukchoi49
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Summary

The document asks whether several published improvements to Hagan’s SABR implied-volatility approximation have been compared for accuracy. It names approaches associated with Obloj, Paulot, and Balland, but does not describe their formulas or report a comparative study. The author suggests measuring error against option values obtained by a finite-difference solution of the model, and asks whether an open implementation of that numerical method is available.

No answer, data, or recommended benchmark is included, so the document does not establish which approximation performs best or how a comparison should be designed. It raises a practical research question: a useful evaluation would need to specify model and market parameters, option cases, numerical boundary conditions, and a stable reference solution. Those details are absent here. The material is therefore most useful as a pointer to the problem of validating approximations against numerical pricing, rather than as guidance on implementing SABR or selecting among the named methods.

Key ideas

  • The document identifies Obloj, Paulot, and Balland as proposed improvements to Hagan’s SABR approximation.
  • It asks whether the methods have been compared for pricing accuracy.
  • It proposes finite-difference option values as a possible reference for measuring error.
  • It does not provide comparative results or an available implementation.

Tags

OptionsVolatilityDerivatives pricingStatistics
Full text
# Comparison of various improvements to Hagan's SABR formula?


# Comparison of various improvements to Hagan's SABR formula?












There has been several papers improving the original Hagan's approximation formula (see this answer) to SABR model. At least, I know three below:

- Obloj

- Paulot (Also see this thread)

- Balland (Download)

Is there any research comparing the accuracy of them? I assume that the error can be measured from the option value solved with finite difference method?

Also, is there finite difference implementation openly available?

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