Pricing Interest Rate Derivatives Under Volatility Uncertainty

We study the pricing of contracts in fixed income markets in the presence of volatility uncertainty. We consider 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. In such a setting we obtain a sublinear pricing measure for additional contracts. Similar to the forward measure approach, we define a forward sublinear expectation to simplify the valuation of cash ows. Under the forward sublinear 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, oating rate notes, interest rate swaps, swaptions, caps, and oors. For fixed coupon bonds, oating rate notes, and interest rate swaps, we obtain a single price, which is the same as in traditional models. For swaptions, caps, and oors, 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.