Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model

A pivotal characteristic of credit defaults that is ignored by most credit scoring models is the rarity of\r\nthe event. The most widely used model to estimate the probability of default is the logistic regression\r\nmodel. Since the dependent variable represents a rare event, the logistic regression model shows relevant\r\ndrawbacks, for example, underestimation of the default probability, which could be very risky for banks.\r\nIn order to overcome these drawbacks, we propose the generalized extreme value regression model. In\r\nparticular, in a generalized linear model (GLM) with the binary-dependent variable we suggest the quantile\r\nfunction of the GEV distribution as link function, so our attention is focused on the tail of the response\r\ncurve for values close to one. The estimation procedure used is the maximum-likelihood method. This\r\nmodel accommodates skewness and it presents a generalisation of GLMs with complementary log–log\r\nlink function. We analyse its performance by simulation studies. Finally, we apply the proposed model to\r\nempirical data on Italian small and medium enterprises.