On a multivariate Markov Chain model for credit risk measurement

Tak Kuen Siu*, Wai Ki Ching, Eric S. Fung, Michael K. Ng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


In this paper, we use credibility theory to estimate credit transition matrices in a multivariate Markov chain model for credit rating. A transition matrix is estimated by a linear combination of the prior estimate of the transition matrix and the empirical transition matrix. These estimates can be easily computed by solving a set of linear programming (LP) problems. The estimation procedure can be implemented easily on Excel spreadsheets without requiring much computational effort and time. The number of parameters is O(s2m2), where s is the dimension of the categorical time series for credit ratings and m is the number of possible credit ratings for a security. Numerical evaluations of credit risk measures based on our model are presented.

Original languageEnglish
Pages (from-to)543-556
Number of pages14
JournalQuantitative Finance
Issue number6
Publication statusPublished - 1 Dec 2005
Externally publishedYes


  • Correlated credit migrations
  • Credibility theory
  • Linear programming
  • Transition matrices

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