### Abstract

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(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.

Original language | English |
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Pages (from-to) | 543-556 |

Number of pages | 14 |

Journal | Quantitative Finance |

Volume | 5 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Dec 2005 |

### Keywords

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

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## Cite this

*Quantitative Finance*,

*5*(6), 543-556. https://doi.org/10.1080/14697680500383714