Term structure modeling under volatility uncertainty

In this paper, we study term structure movements in the spirit of Heath et al. (Econometrica 60(1):77–105, 1992) under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. 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. The drift condition allows to construct arbitrage-free term structure models that are completely robust with respect to the volatility. In particular, we obtain robust versions of classical term structure models.

Models of the Yield Curve and Term Structure

This chapter presents an overview of the modern state of term structure modeling techniques. It provides an analytical framework that is applicable to all short rate models and considers them from the point of view of the classic approach of pricing by replication. The market price of risk and its relation to the drift of a short rate model are important considerations in modeling the term structure. The notable short rate models used in the industry for relative value pricing are introduced with a brief description of the class of affine short rate models employed for forecasting the real-world dynamics of bond prices. The chapter also includes a description of the Heath-Jarrow-Morton derivative pricing framework and an analysis of the LIBOR market model.