Term structure modeling under volatility uncertainty: A forward rate model driven by G-Brownian Motion - Julian Hölzermann; Qian Lin (Bielefeld University, Center for Mathematical Economics (IMW), 2019)
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.
urn:nbn:de:0070-pub-29348400
Keywords: G12; 330; Robust Finance; Knightian Uncertainty; Interest Rates; No-Arbitrage