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

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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.
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Keywords: binary data; credit defaults; generalized extreme value distribution; generalized linear model; rare events; small and medium enterprises

Document Type: Research Article

Affiliations: 1: Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy 2: Departement of Statistical Sciences, University Cattolica del Sacro Cuore, Milan, Italy

Publication date: June 1, 2013

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