A flexible Markov Chain approach for multivariate credit ratings

Eric S. Fung, Tak Kuen Siu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Modeling the dependence of credit ratings is an important issue for portfolio credit risk analysis. Multivariate Markov chain models are a feasible mathematical tool for modeling the dependence of credit ratings. Here we develop a flexible multivariate Markov chain model for modeling the dependence of credit ratings. The proposed model provides a parsimonious way to capture both the cross-sectional and temporal associations among ratings of individual entities. The number of model parameters is of the magnitude O(sm 2 + s 2m), where m is the number of ratings categories and s is the number of entities in a credit portfolio. The proposed model is also easy to implement. The estimation method is formulated as a set of s linear programming problems and the estimation algorithm can be implemented easily in a Microsoft EXCEL worksheet, see Ching et al. Int J Math Educ Sci Eng 35:921-932 (2004). We illustrate the practical implementation of the proposed model using real ratings data. We evaluate risk measures, such as Value at Risk and Expected Shortfall, for a credit portfolio using the proposed model and compare the risk measures with those arising from Ching et al. IMRPreprintSeries (2007), Siu et al. Quant Finance 5:543-556 (2005).

Original languageEnglish
Pages (from-to)135-143
Number of pages9
JournalComputational Economics
Issue number2
Publication statusPublished - Feb 2012


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