Pricing interest rate derivatives under volatility uncertainty

Julian Hölzermann*

*Kontaktforfatter

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Abstract

In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility uncertainty. The uncertainty about the volatility is modeled by a G-Brownian motion, which drives the forward rate dynamics. The absence of arbitrage is ensured by a drift condition. Such a setting leads to a sublinear pricing measure for additional contracts, which yields either a single price or a range of prices and provides a connection to hedging prices. Similar to the forward measure approach, we define the forward sublinear expectation to simplify the pricing of cashflows. Under the forward sublinear expectation, we obtain a robust version of the expectations hypothesis, and we show how to price options on forward prices. In addition, we develop pricing methods for contracts consisting of a stream of cashflows, since the nonlinearity of the pricing measure implies that we cannot price a stream of cashflows by pricing each cashflow separately. With these tools, we derive robust pricing formulas for all major interest rate derivatives. The pricing formulas provide a link to the pricing formulas of traditional models without volatility uncertainty and show that volatility uncertainty naturally leads to unspanned stochastic volatility.

OriginalsprogEngelsk
TidsskriftAnnals of Operations Research
ISSN0254-5330
DOI
StatusE-pub ahead of print - 27. aug. 2022
Udgivet eksterntJa

Bibliografisk note

Funding Information:
The author thanks Frank Riedel for valuable advice, Max Nendel, Wolfgang Runggaldier, and the participants of the “13th European Summer School in Financial Mathematics” in Vienna for fruitful discussions, and two anonymous referees for their comments and suggestions. The author gratefully acknowledges financial support by the German Research Foundation (Deutsche Forschungsgemeinschaft) via Collaborative Research Center 1283.

Publisher Copyright:
© 2022, The Author(s).

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