Generalized Extreme Value Regression: an Application to Credit Defaults.

In order to model credit defaults we propose a Generalized Linear Model (McCullagh and Neleder, 1989) whose link function is the quantile function of the Generalized Extreme Value (GEV) distribution (Kotz and Nadarajah, 2000). In particular, the dependent variable is binary and describes the rare event of a credit default. The goal of this paper is to overcome the drawbacks shown by the logistic regression in rare events. By using the logit link function the probability of rare events could be underestimated. Furthermore, the logit link is a symmetric function, not appropriated when the dependent variable is a rare event. We choose the GEV quantile function as skewed link function since we focus our attention on the tail of the response curve for the values close to 1. We define the proposed model GEV regression