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Journal of Financial Econometrics 2005 3(2):188-226; doi:10.1093/jjfinec/nbi013
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

Stochastic Migration Models with Application to Corporate Risk

Patrick Gagliardini
     University of Lugano and CREST

Christian Gouriéroux
     CREST, CEPREMAP, and University of Toronto

Address correspondence to Patrick Gagliardini, Swiss Institute of Banking and Finance, University of St. Gallen, Rosenbergstrasse 52, CH-9000 St. Gallen, Switzerland, or e-mail: patrick.gagliardinin{at}unisg.ch.

In this article we explain how to use rating histories provided by the internal scoring systems of banks and rating agencies in order to predict the future risk of a set of borrowers. The method is developed following the steps suggested by the Basle Committee. To introduce both migration correlation and non-Markovian serial dependence, we consider rating histories with stochastic transition matrices. We develop the methodology to estimate both the number and dynamics of the factors influencing the transitions and we explain how to use the model for prediction. As an illustration, the ordered probit model with unobservable dynamic factor is estimated from French data on corporate risk.

KEYWORDS: credit risk, Jacobi process, Kalman filter, migration correlation, rating, stochastic intensity

Received June 4, 2004; revised January 19, 2005; accepted January 21, 2005


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