Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/305799 
Year of Publication: 
2022
Citation: 
[Journal:] Annals of Operations Research [ISSN:] 1572-9338 [Volume:] 336 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 153-182
Publisher: 
Springer US, New York, NY
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.
Subjects: 
Fixed income markets
Fixed income derivatives
Ambiguous volatility
Knightian uncertainty
Model uncertainty
Robust finance
JEL: 
G12
G13
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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