# Pricing Interest Rate Derivatives under Volatility Uncertainty

*Julian Hölzermann*

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Julian Hölzermann: Center for Mathematical Economics, Bielefeld University

No 633, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

**Abstract:**
We study the pricing of contracts in fixed income markets in the presence of volatil- ity uncertainty. We consider an arbitrage-free bond market under volatility uncer- tainty. 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. In such a setting we obtain a sublinear pricing measure for ad- ditional contracts. Similar to the forward measure approach, we define a forward sublinear expectation to simplify the valuation of cashflows. Under the forward sub- linear expectation, we obtain a robust version of the expectations hypothesis and a valuation method for bond options. With these tools, we derive robust pricing rules for the most common interest rate derivatives:fixed coupon bonds, floating rate notes, interest rate swaps, swaptions, caps, and floors. For fixed coupon bonds, floating rate notes, and interest rate swaps, we obtain a single price, which is the same as in traditional models. For swaptions, caps, and floors, we obtain a range of prices, which is bounded by the prices from traditional models with the highest and lowest possible volatility. Due to these pricing formulas, the model naturally exhibits unspanned stochastic volatility.

**Keywords:** Robust Finance; Model Uncertainty; Fixed Income Markets (search for similar items in EconPapers)

**Date:** 2020-03-10

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https://pub.uni-bielefeld.de/download/2941772/2941773 First Version, 2020 (application/pdf)

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**Persistent link:** https://EconPapers.repec.org/RePEc:bie:wpaper:633

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