Risk Factor Transformations Relating CreditRisk+ and CreditMetrics

CreditRisk+ and CreditMetrics furnish special cases of general credit risk factor models. On a respective model space, there is a symmetry of factor transformations that relates identical though differently represented models. In the simplest case of homogeneous one-factor one-band-models, there is an approximate symmetry between consistently parametrized CreditRisk+ and CreditMetrics. This can be viewed as evidence that there exists in general a consistent parametrization of both models that results in the same loss distribution.