We study a forward rate model in the presence of volatility uncertainty. The forward rate is modeled as a diffusion process in the spirit of Heath, Jarrow, and Morton (1992) . The uncertainty about the volatility is represented by a G-Brownian motion, being the driver of the forward rate dynamics. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of two equations and two market prices of risk and  uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by the diffusion coefficient . Furthermore, we obtain some classical term structures under volatility uncertainty as examples of our model .
We study a forward rate model in the presence of volatility uncertainty. The forward rate is modeled as a diffusion process in the spirit of Heath, Jarrow, and Morton Econometrica 60 (1), 77-105 . The uncertainty about the volatility is represented by a G-Brownian motion, being the driver of the forward rate dynamics. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of several equations and several market prices, termed market price of risk and market prices of uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by its diffusion term . Furthermore, we obtain robust versions of classical term structure models as examples in this framework .
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(1992)
Econometrica 60 (1), 77-105
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two equations and two market prices
several equations and several market prices, termed market price
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market prices of
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the diffusion coefficient
its diffusion term
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some classical term structures under volatility uncertainty as examples of our model
robust versions of classical term structure models as examples in this framework