Credit Spreads Between German and Italian Sovereign Bonds: Do One-Factor Affine Models Work?

Abstract

In this paper we analyze the credit spread between Italian and German government bonds after the exchange-rate agreement in May 1998. We estimate the parameters of two mean-reverting affine models for the German term structure and the spread process—the Gaussian Vasicek and the square-root Cox-Ingersoll-Ross (CIR) model. Similar to Pearson and Sun (1994) we combine cross-sectional and time-series information of daily observations to estimate the process parameters employing a maximum likelihood method. Our empirical results show that the Vasicek and CIR model describe the German term structure dynamics equally well. Both models fail to account for all observed shapes of the credit spread structure whereas the spread residuals in the Vasicek case seem to be less volatile. Our results suggest application in the area of pricing credit-sensitive instruments such as credit derivatives or the management of credit risk, especially for European government debt. Resume Nous analysons l'etalement du credit entre les obligations d'etat italiennes et allemandes apres l'accord sur le taux d'interět de mai 1998. Nous evaluons les parametres de deux modeles de retour a la moyenne pour la structure echeanciere allemande et le processus d'etalement—le Gaussian Vasicek et le modele racine-carree Cox-Ingersoll-Ross (CIR). Similairement a Pearson et Sun (1994) nous combinons l'information echantillonnee et en serie d'observations quotidiennes afin d'evaluer les parametres employant une methode a probabilite maximum. Nos resultats empiriques demontrent que les modeles Vasicek et CIR sont incapables de considerer toutes les formes observees de la structure d'etalement du credit tandis que les soldes etales dans le cas Vasicek semblent moins volatiles. Nos resultats suggerent une application dans le domaine de la valorisation d'instruments a credit instable tels que les derives de credit ou la gestion des risques de credit, specifiquement pour la dette gouvernementale europeenne.