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 cashflows. 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, 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.
We study the pricing of contracts in fixed income markets in the presence of volatility 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 . 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 bond options. 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.
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In such a setting we obtain
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we show how to price
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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.
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rules for the most common
formulas for all major
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: 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
. The pricing formulas provide a link to the pricing formulas of traditional models without volatility uncertainty and show that volatility uncertainty naturally leads to