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

Abstract

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

Keywords:

• credit defaults
• small and medium enterprises
• generalized linear model
• generalized extreme value distribution
• rare events
• binary data

Notes

The drawbacks explained in Section 2 are due to a symmetric link function. This means that not only the logistic model but also the probit model show the above-mentioned disadvantages.

To compute the H measure and AUC, we use the H measure package of R-program. For the H measure we consider a severity ratio of 0.01.