On the role of state variables in interest rates models

Abstract

This paper discusses the introduction and the selection of a finite set of state variable in arbitrage-free models of the term structure of interest rates. We choose a Gaussian setting which offers, as it is well known, tractable computations, hence results easier to understand and interpret. We study the mathematical conditions under which interest rates can be taken as state variables and address the key issues of time homogeneity of the model for a given set of state variables and the role of the current yield curve. Lastly, we provide explicit empirical estimations for four different swap markets (France, Italy, Japan, United Kingdom) and show that the state variables extracted through the use of a Kalman filter approach can be identified with linear combinations of interest rates. Copyright © 2000 John Wiley & Sons, Ltd.