Generalized Extreme Value Regression for Binary Rare Events Data: an Application to Credit Defaults
AbstractThe most used regression model with binary dependent variable is the logistic regression model. When the dependent variable represents a rare event, the logistic regression model shows relevant drawbacks. In order to overcome these drawbacks we propose the Generalized Extreme Value (GEV) regression model. In particular, in a Generalized Linear Model (GLM) with 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 is the maximum likelihood method. This model accommodates skewness and it presents a generalization of GLMs with log-log link function. In credit risk analysis a pivotal topic is the default probability estimation. Since defaults are rare events, we apply the GEV regression to empirical data on Italian Small and Medium Enterprises (SMEs) to model their default probabilities.
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Bibliographic InfoPaper provided by Geary Institute, University College Dublin in its series Working Papers with number 201120.
Length: 20 pages
Date of creation: 15 Sep 2011
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-09-22 (All new papers)
- NEP-BAN-2011-09-22 (Banking)
- NEP-ECM-2011-09-22 (Econometrics)
- NEP-ORE-2011-09-22 (Operations Research)
- NEP-RMG-2011-09-22 (Risk Management)
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