A Parsimonious Model of Loss Given Default in Changing Conditions

A bank loan might pay off as promised or it might default. Default exposes the bank to loss. When the loss is expressed as a fraction of the loan balance, it is known as loss given default or LGD. LGD rates, like default rates, rise in stressful conditions. Banks need to predict both rates when they engage in the stress tests required by law.

This presentation describes the LGD function, a parsimonious model of cyclical LGD behavior. The function is derived from assumptions about the distributions of loss and default. It contains no new quantities that would require calibration to a data set. Despite its parsimony, the LGD function captures broad cyclical behaviors observed in long histories of bond data, and it is a close match for behavior inferred from loan data. In part because only a few cycles of credit data exist at present, no statistically significant improvements have been found.

The LGD function might interest the mathematically inclined listener because it possesses several desirable features that do not appear to be prefigured by the assumptions made in the derivation.