A Dynamic Model for the Forward Curve

Abstract

This paper develops and estimates a dynamic arbitrage-free model for the current forward curve as the sum of (i) an unconditional component, (ii) a maturity-specific component and (iii) a date-specific component. The model combines features of the Preferred Habitat model,the Expectation Hypothesis and affine yield curve models. We show how to construct alternative parametric examples of the three components from a sum of exponential functions, verify that the resulting forward curves satisfy the Heath-Jarrow-Morton conditions, and derive the risk-neutral dynamics for the purpose of pricing interest rate derivatives. We select a model from alternative affine examples that are fitted to the Fama-Bliss Treasury data over an initial training period and use it to generate out-of-sample forecasts for forward rates and yields. For forecast horizons of 6-months or longer, the forecasts of this model significantly outperform forecasts from common benchmark models.