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Generalized Extreme Value Regression for Binary Rare Events Data: an Application to Credit Defaults

  • Raffaella Calabrese

    (Geary Institute, University College Dublin)

  • Silvia Angela Osmetti

    (Department of Statistics, University Cattolica del Dacro Cuore, Milan)

The 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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Paper provided by Geary Institute, University College Dublin in its series Working Papers with number 201120.

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Length: 20 pages
Date of creation: 15 Sep 2011
Date of revision:
Handle: RePEc:ucd:wpaper:201120
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  1. Dietsch, Michel & Petey, Joel, 2004. "Should SME exposures be treated as retail or corporate exposures? A comparative analysis of default probabilities and asset correlations in French and German SMEs," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 773-788, April.
  2. D. J. Hand & W. E. Henley, 1997. "Statistical Classification Methods in Consumer Credit Scoring: a Review," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 523-541.
  3. Ely Dahan & Haim Mendelson, 2001. "An Extreme-Value Model of Concept Testing," Management Science, INFORMS, vol. 47(1), pages 102-116, January.
  4. Altman, Edward I. & Haldeman, Robert G. & Narayanan, P., 1977. "ZETATM analysis A new model to identify bankruptcy risk of corporations," Journal of Banking & Finance, Elsevier, vol. 1(1), pages 29-54, June.
  5. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  6. Robert J. Barro, 2007. "Rare Disasters, Asset Prices, and Welfare Costs," NBER Working Papers 13690, National Bureau of Economic Research, Inc.
  7. Thomas C. Wilson, 1998. "Portfolio credit risk," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 71-82.
  8. Edmister, Robert O., 1972. "An Empirical Test of Financial Ratio Analysis for Small Business Failure Prediction," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(02), pages 1477-1493, March.
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