On the parameterization of the CreditRisk + model for estimating credit portfolio risk

The CreditRisk+ 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.