A two-factor model of the term structure with optimal filtering behaviour

Abstract

The rates of return of financial variables observed at high frequency are not normally distributed, mainly because of positive excess kurtosis; thus, most of the models developed in financial economics need be modified to take into account such characteristics of the data. On this respect GARCH models provide an appropriate modelling framework. Building on the convergence of an AR(1)-GARCH(1,1) model to a bivariate Ito process, we present a two-factor model for the term structure of interest rates and derive the closed-form solution for the price of zero-coupon bonds. The estimation of such a model can be carried out by means of an AR(1)-GARCH(1,1) scheme, which represents its discrete-time version.