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Hull–White Calibration with Constant Mean Reversion and Volatility

Article Quant Q&A · Author: sigirisetti
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Summary

The document clarifies the interpretation of a calibration described for the one-factor Hull–White interest-rate model. The question asks whether the optimization produces a mean-reversion rate and diffusion parameter shared across all curve tenors, rather than separate parameter values for each tenor.

The response confirms that this setup estimates one mean-reversion parameter and one volatility parameter for the entire term structure. It identifies this as the constant-mean-reversion form of Hull–White, with parameters that do not vary over time. The exchange gives no calibration objective, market instruments, fit results, or implementation details, so it establishes the parameterization being discussed but not how well it performs or whether a constant specification is appropriate for a particular application.

Key ideas

  • The described calibration estimates one mean-reversion rate for the whole term structure.
  • It also estimates one diffusion or volatility parameter shared across tenors.
  • This is the constant-parameter Hull–White specification, with parameters not varying over time.
  • The discussion does not assess fit quality or compare constant parameters with time-dependent alternatives.

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# Calibration of Hull White One factor model in F.C.Park paper


# Calibration of Hull White One factor model in F.C.Park paper












I want to ask a question with reference to a paper from below link

http://www.cmpr.co.kr/asset/research_material/implementing_interest_rate_models.pdf

Minimization specified in Page 14:

Mean reversion rate and diffusion comes out same for all tenors?

In other words, can I state calibration is done to derive one "mean reversion rate" and diffusion for entire term structure ?

Thanks

## Answer by StevenK (score 2)

https://quant.stackexchange.com/a/30817

That's right. Calibration is done in other to obtain one 'a' (mean reversion rate) and one sigma for the entire curve. This case is referred to as the Hull White model with constant mean reversion, i.e. the parameters are not time dependent.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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