On the Parameterization of the CreditRisk+ Model for Estimating Credit Portfolio Risk

by Antoine Vandendorpe of Fortis,
Ngoc-Diep Ho of the Université Catholique de Louvain,
Steven Vanduffel of Katholieke Universiteit Leuven, and
Paul Van Dooren of the Université Catholique de Louvain

August 9, 2007

Abstract: The Credit Risk+ model is one of the industry standards for estimating the credit default risk for a portfolio of credit loans. The natural parameterization of this model requires the default probability to be apportioned using a number of (non-negative) factor loadings. However, in practice only default correlations are often available but not the factor loadings. In this paper we investigate how to deduce the factor loadings from a given set of default correlations. This is a novel approach and it requires the non-negative factorization of a positive semi-definite matrix, which is by no means trivial. We also present a numerical optimization algorithm to achieve this.

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