A Joint Model for the Term Structure of Interest Rates and Realized Volatility

Abstract

This paper presents a term structure model for no-arbitrage bond yields and realized bond market volatility. Based on well-known results, realized yield curve covariation is linked to GARCH-type conditional covariation. The model is tractable and its latent state variables can be filtered using an exact algorithm. In an empirical study of U.S. Treasury bond data, the model shows that conditional yield curve covariation is priced in long-term yields. Moreover, the model proves useful for multi-step ahead forecasting of realized covariation. Finally, I use the model to quantify interest-rate risk and risk compensation.

Keywords: Term structure modeling, yield curve covariation, interest-rate risk, real- ized covariation, multivariate GARCH, non-linear Kalman filter

JEL Classification: C13, C32, G12