International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 719237, 13 pages
Research Article

A Dependent Hidden Markov Model of Credit Quality

Centre for Industrial and Applied Mathematics, School of Mathematics and Statistics, University of South Australia, City West Campus, GPO Box 2471, Adelaide, SA 5001, Australia

Received 29 February 2012; Accepted 11 May 2012

Academic Editor: Yaozhong Hu

Copyright © 2012 Małgorzata Wiktoria Korolkiewicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a dependent hidden Markov model of credit quality. We suppose that the "true" credit quality is not observed directly but only through noisy observations given by posted credit ratings. The model is formulated in discrete time with a Markov chain observed in martingale noise, where "noise" terms of the state and observation processes are possibly dependent. The model provides estimates for the state of the Markov chain governing the evolution of the credit rating process and the parameters of the model, where the latter are estimated using the EM algorithm. The dependent dynamics allow for the so-called "rating momentum" discussed in the credit literature and also provide a convenient test of independence between the state and observation dynamics.