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.
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