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 (PD) 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 (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 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 (SMEs).

Financial Risk Measurement and Prediction Modelling for Sustainable Development of Business Entities Using Regression Analysis

“…In this study, we test the use of a quite simple classifier, linear regression approach (similar to Guo et al [27]), for modelling the relationship between a scalar dependent variable and more explanatory variables (financial indicators) as it performs reasonably well in bankruptcy prediction, as proved by Jones et al [28]. Regression analysis if often use for bankruptcy prediction, the realized analysis is supported by the study of Calabrese et al [29] or latest researches in Romania [30] and Lithuania [31], which recommend regression models for bankruptcy prediction. A methodological framework of regression was used to construct predictive bankruptcy models for Asia, Europe and America and the results verify the superiority of the global model compared to regional models [32].…”

The effectiveness of TARP-CPP on the US banking industry: A new copula-based approach

“…When the data is in fact unbalanced, the estimate of the dependent variable tends to be biased towards the majority class, which is usually the less important class to correctly predict ( King & Zeng, 2001 ). Specifically, the use of a symmetric link function, such as the logit or probit function, may underestimate π t for the rare events { Y t = 1 } , as the response curve π t approaches zero at the same rate as it approaches one ( Calabrese & Osmetti, 2013;King & Zeng, 2001;Marra et al, 2014;Wang & Dey, 2010 ).…”

“…If we classify the rare events as ones, the major drawback of these approaches is that they underestimate the probability of binary rare events for values close to one, such as bank defaults or bail-outs ( Calabrese & Osmetti, 2015;King & Zeng, 2001;Wang & Dey, 2010 ). To overcome this limitation, a model has been proposed in the operational research literature ( Andreeva, Calabrese, & Osmetti, 2016;Calabrese & Osmetti, 2013;2015;Marra, Calabrese, & Osmetti, 2014 ) -the Binary Generalised Extreme Value Additive model, BGEVA (GEV model in the parametric form). This approach is particularly suitable for binary rare events data, i.e.…”

The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

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