We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version of Fubini's theorem for stochastic integrals. The evolution of the forward rate in the model is described by a diffusion process , which is driven by a G-Brownian motion  . 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 , respectively, uncertainty. Furthermore, we examine the connection to short rate models and discuss some examples .
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 .
R
show how to set up
study
R
by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version of Fubini's theorem for stochastic integrals. The evolution of the forward rate in the model is described by
. The forward rate is modeled as
R
, which is driven
in the spirit of Heath, Jarrow, and Morton (1992). The uncertainty about the volatility is represented
A
, being the driver of the forward rate dynamics
R
, respectively, uncertainty. Furthermore, we examine the connection to short rate models and discuss some examples
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