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Transition Probability Matrix Methodology for Incremental Risk Charge

by Tzahi Yavin of the Royal Bank of Canada,
Hu Zhang of the Royal Bank of Canada,
Eugene Wang of the Royal Bank of Canada, and
Michael A. Clayton of the Royal Bank of Canada

January 17, 2011

Abstract: As part of Basel II's incremental risk charge (IRC) methodology, this paper summarizes our extensive investigations of constructing transition probability matrices (TPMs) for unsecuritized credit products in the trading book. The objective is to create monthly or quarterly TPMs with predefined sectors and ratings that are consistent with the bank's Basel PDs. Constructing a TPM is not a unique process. We highlight various aspects of three types of uncertainties embedded in di erent construction methods: 1) the available historical data and the bank's rating philosophy; 2) the merger of one-year Basel PD and the chosen Moody's TPMs; and 3) deriving a monthly or quarterly TPM when the generator matrix does not exist. Given the fact that TPMs and specifically their PDs are the most important parameters in IRC, it is our view that banks may need to make discretionary choices regarding their methodology, with uncertainties well understood and managed.

JEL Classification: C02, G28, G21.

Keywords: Basel II, trading book, incremental risk charge, default probability, default correlation, transition probability matrix, generator matrix, credit portfolio

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