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Accuracy Limits of Approximation Methods in Dynamic SABR

Article Quant Q&A · Author: erik530
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Summary

The document asks whether integration techniques developed for constant-parameter SABR can be applied to dynamic SABR volatility models. It notes that the Hagan-style analytic approximation is fast but can lose accuracy at extreme strikes or maturities, and says dynamic SABR approximations are subject to similar limitations. More accurate integration-based approximations are cited for the constant-parameter setting.

A quoted passage from a referenced paper suggests that accurate analytic approximations matter in dynamic SABR calibration because calibration results should align with pricing methods. The document treats this as a clue that the integration approach may carry over, but it does not establish that it does. It provides no derivation, numerical comparison, or conditions for extending the method, leaving applicability to dynamic specifications unresolved.

Key ideas

  • Fast analytic SABR approximations may be inaccurate at extreme strikes or maturities.
  • Integration-based methods are described as more accurate for constant-parameter SABR.
  • The discussion raises, but does not resolve, whether those methods extend to dynamic SABR.
  • Calibration approximations should be consistent with the pricing methods used in dynamic models.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Numerical/integration methods within dynamic SABR


# Numerical/integration methods within dynamic SABR












I have a question regarding volatility estimates in the dynamic SABR model. It is well known that the original Hagan et al. (2002) approximation formula for the SABR model does not work good for extreme strikes/maturities. For the dynamic SABR model, similar approximations are available with the advantage that they are fast, but they have the same flaws as the original approximations from Hagan et al. (2002).

For the constant parameter SABR model, more accurate approximations are available via integration, see for example Antonov et al (2013), called 'SABR spreads its wings'. However, as of yet I have not come across any integration methods for the dynamic SABR model. I do suspect that the currently available integration methods for the constant parameter SABR model can easily be used in the dynamic SABR model, but I'm not 100% sure.

For example, the following quote is from Antonov et al (2013), where approximations are derived for the constant parameter SABR model:

> The high accuracy of our approximation is very important for dynamic SABR models, where analytic approximation used in calibration should provide results close to those used in pricing, for example, SABR Libor market models, as in Mercurio & Morini (2009) and Rebonato, McKay & White (2009).

This seems to indicate that their method can be used within the dynamic framework as well. I hope someone can elaborate, thank you!

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