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).

We introduce a binary regression accounting-based model for bankruptcy prediction of Small and Medium Enterprises (SMEs). The main advantage of the model lies in its predictive performance in identifying defaulted SMEs. Another advantage, which is especially relevant for banks, is that the relationship between the accounting character-istics of SMEs and response is not assumed a priori (e.g., linear, quadratic or cubic) and can be determined from the data. The proposed approach uses the quantile function of the generalized extreme value distribution as link function as well as smooth functions of accounting characteristics to flexibly model covariate effects. Therefore, the usual assumptions in scoring models of symmetric link function and linear or pre-specified covariate-response relationships are relaxed. Out-of-sample and out-of-time validation on Italian data shows that our proposal outperforms the commonly used (logistic) scoring model for different default horizons.

This paper presents a cross-country comparison of significant predictors of small business failure between Italy and the UK. Financial measures of profitability, leverage, coverage, liquidity, scale and non-financial information are explored, some commonalities and differences are highlighted. Several models are considered, starting with the logistic regression which is a standard approach in credit risk modelling. Some important improvements are investigated. Generalised Extreme Value (GEV) regression is applied to correct for the symmetric link function of the logistic regression. The assumption of non-linearity is relaxed through application of BGEVA, non-parametric additive model based on the GEV link function. Two methods of handling missing values are compared: multiple imputation and Weights of Evidence (WoE) transformation. The results suggest that the best predictive performance is obtained by BGEVA, thus implying the necessity of taking into account the relative volume of defaults and non-linear patterns when modelling SME performance. WoE for the majority of models considered show better prediction as compared to multiple imputation, suggesting that missing values could be informative and should not be assumed to be missing at random.

a b s t r a c tFollowing the 2008 financial crisis, regulatory authorities and governments provided distressed banks with equity infusions in order to strengthen national banking systems. However, the effectiveness of these interventions for financial stability has not been extensively researched in the literature. In order to understand the effectiveness of these bailouts for the solvency of banks this paper proposes a new model: the Longitudinal Binary Generalised Extreme Value (LOBGEV) model. Differing from the existing models, the LOBGEV model allows us to analyse the temporal structure of the probability of failure for banks, for both those that received a bailout and for those that did not. In particular, it encompasses both the flexibility of the D-vine copula and the accuracy of the generalised extreme value model in estimating the probability of bank failure and of banks receiving approval for capital injection. We apply this new model to the US banking system from 2008 to 2013 in order to investigate how and to what extent the Troubled Asset Relief Program (TARP)-Capital Purchase Program (CPP) reduced the probability of the failure of commercial banks. We specifically identify a set of macroeconomic and bank-specific factors that affect the probability of bank failure for TARP-CCP recipients and for those that did not receive capital under TARP-CCP. Our results suggest that TARP-CPP provided only short-term relief for US commercial banks.

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