On a multivariate Markov chain model for credit risk measurement. (English) Zbl 1134.91485

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

Quant. Finance 5, No. 6, 543-556 (2005).

Summary: 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 \(O(s^{2}m^{2})\), 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.

MSC:

91B30

Risk theory, insurance (MSC2010)

Keywords:

correlated credit migrations; linear programming; transition matrices; credibility theory

Software:

Excel

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