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Time-Dependent Hull–White Volatility in Hybrid Models

Article Quant Q&A · Author: Benedict
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Summary

The document asks whether a hybrid interest-rate and stochastic-volatility model can use a deterministic, time-varying volatility for its Hull–White interest-rate process instead of constant volatility. The answer says this extension can be made by representing the volatility as piecewise constant over time.

With that representation, the characteristic-function derivation is said to remain intact, with the relevant expressions extended through simple sums. The note offers no derivation, numerical example, or empirical comparison, so it provides only a high-level modeling suggestion. It also does not specify conditions for choosing the time intervals or discuss calibration and implementation details; readers would need further sources to assess those aspects.

Key ideas

  • A deterministic time-varying Hull–White volatility can be represented as piecewise constant.
  • The answer states that extending the hybrid model then requires simple sums.
  • The characteristic-function derivation is said to be unaffected by this extension.
  • The note provides no detailed derivation or calibration guidance.

Tags

Fixed incomeVolatilityDerivatives pricing
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# Hybrid Models - Hull white with Heston / SchobelZhu / BS


# Hybrid Models - Hull white with Heston / SchobelZhu / BS












I was looking at literature and found that for hybrid models, most of the literature only gives hybrid models where the volatility of the interest rate process(e.g Hull White) is constant.

Is there a way to generalize this to a deterministic time dependent vol for the IR process in the hybrid model? Could i just replace it with a term-structure dependent model vol and it works fine?

Best, Ben

## Answer by Lech (score 1)

https://quant.stackexchange.com/a/66504

You can simply introduce a piece-wise constant vol parameter. The extension is rather trivial as it will involve simple sums. Also, the derivations of the ChF will not be affected by this extension.

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.