Interest rate volatility and the shape of the term structure

Abstract

This paper analyses the effect of interest rate uncertainty on the shape of the forward rate curve. We consider a broad class of term structure models characterized by an affine relation between the drift and diffusion coefficients of the stochastic process describing the evolution of the state variables and the level of the state variables. For these models, a simple relation exists between the shape of the forward rate curve, the sensitivity of the zero-coupon yield curve to the state variables and the variance-covariance matrix of the state variables. In single factor models this relation implies that minus the convexity of the forward rate curve with respect to a measure of ‘duration’ is equal to the variance of the short rate. The paper explores why it is that, despite the well known shortcomings of single factor models, attempts to fit such models to cross-sections of nominal bond prices nonetheless produce reasonable estimates of interest rate volatility.