The Hull–White model under volatility uncertainty

Julian Hölzermann*

*Kontaktforfatter

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Abstract

We study the Hull–White model for the term structure of interest rates in the presence of volatility uncertainty. The uncertainty about the volatility is represented by a set of beliefs, which naturally leads to a sublinear expectation and a G-Brownian motion. The main question in this setting is how to find an arbitrage-free term structure. This question is crucial, since we can show that the classical approach, martingale modeling, does not work in the presence of volatility uncertainty. Therefore, we need to adjust the model in order to find an arbitrage-free term structure. The resulting term structure is affine with respect to the short rate and the adjustment factor. Although the adjustment changes the structure of the model, it is still consistent with the traditional Hull–White model after fitting the yield curve. In addition, we extend the model and the results to a multifactor version, driven by multiple risk factors.

OriginalsprogEngelsk
TidsskriftQuantitative Finance
Vol/bind21
Udgave nummer11
Sider (fra-til)1921-1933
ISSN1469-7688
DOI
StatusUdgivet - 2021
Udgivet eksterntJa

Bibliografisk note

Funding Information:
The author gratefully acknowledges financial support by the German Research Foundation (Deutsche Forschungsgemeinschaft) via Collaborative Research Center 1283. The author thanks Frank Riedel for valuable advice, Tolulope Fadina, Damir Filipović, Jan Obłój, and Thorsten Schmidt for fruitful conversations, and two anonymous referees for interesting suggestions.

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

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