A decomposition of the term structure model of Heath, Jarrow and Morton

Abstract

This paper demonstrates that the term structure model of Heath, Jarrow and Morton (HJM, 1992) can be decomposed into two component functions, such that if one can represent the observed initial forward rate curve, then the other is the dynamic evolution of the forward rates. This decomposition simplifies the practical implementation of the HJM model for allowing the parameters of the model to be estimated from the initial forward rate function, since the evolution of the forward function has the same parameters. Because the estimation is essentially a cross-sectional curvefitting to which the treasury securities are sufficient, interest rate contingent claims are not required for the calibration of the HJM model; thus, the costly path-dependent computation can be completely avoided. Utilizing the functionality of the HJM model, this paper derives a simple and accurate estimation procedure. The empirical results show that a three-factor HJM specification is a consistent representation of the term structure...