Modelling the loss given default distribution via a family of zero-and-one inflated mixture models

The empirical distribution of the loss given default (LGD) has support [0,1], contains an excess of 0s and 1s, and is often multimodal on (0,1). Though some parametric models have been used in the credit risk literature to model the LGD distribution, these peculiarities call for more flexible approaches. Thus, we introduce a zero-and-one inflated mixture where a three-level multinomial model is considered for the membership of the LGD values to the sets {0}, (0,1) and {1}, whereas a finite mixture of distributions is used on (0,1). To allow for more flexible shapes on (0,1), we consider component distributions already defined on (0,1) and distributions on .1,1/ mapped on (0,1) via the inverse logit transformation. This yields a family of 13 zero-and-one inflated mixture models. They are applied to two data sets of LGDs on loans: one from a European Bank and the other from the Bank of Italy. The best performers in our family, selected via classical information criteria, are then compared with several wellestablished semiparameteric or non-parametric approaches via a convenient simulation-based procedure.