On the role of state variables in interest rates models (Q2744950)

The main task of this paper is to discuss, within a Gaussian setting, the introduction and the selection of a finite number of state variables in arbitrage free interest rates models. The Gaussian specification gives the possibility of fully investigating the topic, both from a theoretical and an operational point of view.NEWLINENEWLINENEWLINEFor instance, in Sections 3 and 4 of the article results for Heath-Jarrow-Morton Gaussian multifactor models are discussed and conditions under which state variables can be identified with interest rates are presented. Finally, an explicit empirical analysis of four different swap markets (France, Italy, Japan, UK) was carried out showing that the state variables extracted through the use of a Kalman filter approach can be identified with linear combinations of interest rates. In all four markets two factors suffice to explain more than 95 per cent of the variance of interest rates.