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Volume 5/Number 4, Winter 2009/10
An improved multivariate Markov chain model for credit risk Wai-Ki Ching
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong; email: wching@hkusua.hku.hk Tak-Kuen Siu
Department of Actuarial Studies and Centre of Financial Risk, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia; email: ktksiu2005@gmail.com Li-min Li
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong; email: liminli@hkusua.hku.hk Hao Jiang
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong; email: jiang_hao_191@163.com Tang Li
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong; email: litang@hkusua.hku.hk In this paper we use Ching's multivariate Markov chain model to model the dependency of rating transitions of several credit entities. The model is an enhancement of the multivariate Markov chain model for ratings considered by Siu et al. Our model is more parsimonious, flexible and empirically competent than the model
used by Siu et al. We adopt an efficient method to calibrate the model parameters and formulate the estimation problem as a linear programming problem that can easily be solved using spreadsheets. We compare the estimation results and the computational efficiency of the enhanced model with that also empirically investigate the effect of incorporating both positive and negative associations on portfolio credit risks.
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