Term structure modeling under volatility uncertainty

Julian Hölzermann*

*Kontaktforfatter

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Abstract

In this paper, we study term structure movements in the spirit of Heath et al. (Econometrica 60(1):77–105, 1992) under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of several equations and several market prices, termed market price of risk and market prices of uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by its diffusion term. The drift condition allows to construct arbitrage-free term structure models that are completely robust with respect to the volatility. In particular, we obtain robust versions of classical term structure models.

OriginalsprogEngelsk
TidsskriftMathematics and Financial Economics
Vol/bind16
Udgave nummer2
Sider (fra-til)317-343
ISSN1862-9679
DOI
StatusUdgivet - apr. 2022
Udgivet eksterntJa

Bibliografisk note

Funding Information:
The author gratefully acknowledges financial support by the German Research Foundation (Deutsche Forschungsgemeinschaft) via Collaborative Research Center 1283.

Funding Information:
The author thanks Frank Riedel for valuable advice, Tolulope Fadina and Hanwu Li for fruitful conversations, and Qian Lin, Wolfgang Runggaldier, and the participants of the workshop ?New Frontiers in Stochastics for Economics and Finance? in Siena and the ?12th European Summer School in Financial Mathematics? in Padova for interesting remarks. Moreover, the author thanks the editor, Ulrich Horst, and two anonymous referees for suggestions that significantly improved the paper. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Publisher Copyright:
© 2021, The Author(s).

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