On Deficiencies and Possible Improvements of the Basel II Unexpected Loss Single-Factor Model

The goal of the Basel II regulatory formula is to model the unexpected loss on a loan portfolio. The regulatory formula is based on an asymptotic portfolio unexpected default rate estimation that is multiplied by an estimate of the loss given default parameter. This simplification leads to a surprising phenomenon where the resulting regulatory capital depends on a definition of default that plays the role of a frontier between the unexpected default rate estimate and the LGD parameter, whose unexpected development is not modeled at all or is modeled only partially. We study the phenomenon in the context of single-factor models where default and loss given default are driven by one systematic factor and by one or more idiosyncratic factors. In this theoretical framework we propose and analyze a relatively simple remedy of the problem requiring that the LGD parameter be estimated as an appropriate quantile on the required probability level.