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Survival models with time-varying covariates (TVCs) are widely used in the literature on credit risk prediction. However, when these covariates are endogenous, the inclusion procedure has been limited to practices such as lagging these variables or treating them as exogenous. That leads to possible biased estimators (depending on the strength of the exogeneity assumption) and a lack of prediction framework that consolidates the joint evolution of the survival process and the endogenous TVCs. The use of joint models is a suitable approach for handling endogeneity, however, it comes at a high computational cost. We propose a joint model for bivariate endogenous TVCs and discrete survival data using integrated nested Laplace approximation (INLA). We illustrate the implementation via simulations and build a model for full-prepayment consumer loans. We also propose a methodology for individual survival prediction using the Laplace method that leads to more accurate approximations than comparable approaches. We evidence the superiority of joint models over the traditional survival approach for an out-of-sample and out-of-time analysis.

The inclusion of time-varying covariates into survival analysis has led to better predictions of the time to default in behavioural credit scoring models. However, when these time-varying covariates are endogenous, there are two major problems: estimation bias of the survival model and lack of a prediction framework for future values of both the event and the endogenous time-varying covariates. Joint models for longitudinal and survival data is an appropriate framework to model the mutual evolution of the survival time and the endogenous time-varying covariates. To the best of our knowledge,this paper explores for the first time the application of discrete-time joint models to credit scoring. Moreover, we propose a novel extension to the joint model literature by including autoregressive terms in modelling the endogenous time-varying covariates. We present the method via simulations and by applying it to US mortgage loans. The empirical analysis shows, first, that discrete joint models can increase the discrimination performance compared to survival models. Second, when an autoregressive term is included, this performance can be further improved.

This article focuses on modelling the contagion effects - both between and within groups - on small business failures in London. Small business clusters can be defined based on different companies’ characteristics, for example, economic sector or geographical location. These aspects are usually included as fixed effects to predict the defaults of small- and medium-sized enterprises (SMEs). However, this approach however ignores the interactions between the company groups and only captures the heterogeneity across the clusters. To include both contagion effects between and within groups, a Bayesian spatial hierarchical model for binary data is proposed and applied to a dataset of SMEs located in London in 2016. The empirical analysis shows that the contagion component at the lower level, based on the geographical location, is not significant if the industry clustering is ignored. However, it becomes significant if the industry group effect is included,and also the upper-level interdependence also becomes significant. Finally, the suggested model improves the predictive accuracy and the expected shortfall estimate compared to standard scoring models.

The scale of the UK government's response to the Covid-19 crisis after the first lockdown in March 2020 was unprecedented. For the business sector, two financing schemes were particularly relevant: the Coronavirus Business Interruption Loan Scheme (CBILS) and the Bounce Back Loan Scheme (BBLS). Both were designed to support the capitalization of businesses through this difficult trading period. In this paper, we use data covering the first two quarters of the Covid-19 crisis to explore the dynamics of small and medium-sized enterprise (SME) financing and in particular the role of government support schemes. Our findings show that 92.1% of all debt funds provided in this period were backed by the UK government, which compares to less than 5% under normal circumstances. We find that the demand, supply and government share of SME lending increased from Covid-19 quarter 1 (April–June 2020) to quarter 2 (July–September 2020), that micro and small businesses had the highest demand for loans, and that better-performing firms were more likely to receive loans. Further, in a world where more loan requests than ever were granted, the government share of this pool of loans had a different risk profile than the small pool of non-government-backed loans.

Open banking (OB) creates an opportunity for financial institutions to oer more personalised services by better differentiating between a specific customer (reference subject) and similar customers (comparison group). We propose the time-varying comparative mean value as a statistical method that learns about the dynamics governing how the response of a reference subject differs from that of a comparison group, defined via covariate truncation. The proposed model can be regarded as a time-varying truncated covariate regression model of which a smooth version is devised by resorting to local polynomial regression. The simulation study suggests that our estimators accurately recover the true time-varying comparative mean value in a variety of scenarios. We showcase our methods using OB-type data from a financial service provider in the UK, with the dataset containing detailed information on customers' accounts across 70 UK financial institutions. By contrasting a specific customer against similar customers, our method offers interesting diagnostics that can be used by financial institutions to recommend personalised services.

In 2016 the British government acknowledged the importance of reducing antimicrobial prescriptions in order to avoid the long-term harmful effects of over-prescription. Prescription needs are highly dependent on factors that have a spatio-temporal component, such as the presence of a bacterial outbreak and the population density. In this context, density-based clustering algorithms are flexible tools to analyse data by searching for group structures. The case of Scotland presents an additional challenge due to the diversity of population densities under the area of study. We present here a spatio-temporal clustering approach for highlighting the behaviour of general practitioners (GPs) in Scotland. Particularly, we consider the density-based spatial clustering of applications with noise algorithm (DBSCAN) due to its ability to include both spatial and temporal data, as well as its flexibility to be extended with further variables. We extend this approach into two directions. For the temporal analysis, we use dynamic time warping to measure the dissimilarity between warped and shifted time series. For the spatial component, we introduce a new way of weighting spatial distances with continuous weights derived from a KDE-based process. This makes our approach suitable for cases involving spatial clusters with differing densities, which is a well-known issue for the original DBSCAN. We show an improved performance compared to both the latter and the popular k-means algorithm on simulated, as well as empirical data, presenting evidence for the ability to cluster more elements correctly and deliver actionable insights., Comment: 27 pages, 11 figures, 3 tables

Automated valuation models (AVMs) are widely used by financial institutions to estimate the property value for a residential mortgage. The distribution of pricing errors obtained from AVMs generally show fat tails (Pender 2016; Demiroglu and James Management Science, 64(4), 1747–1760 2018). The extreme events on the tails are usually known as “black swans” (Taleb 2010) in finance and their existence complicates financial risk management, assessment, and regulation. We show via theory, Monte Carlo experiments, and an empirical example that a direct relation exists between non-normality of the pricing errors and goodness-of-fit of the house pricing models. Specifically, we provide an empirical example using US housing prices where we demonstrate an almost perfect linear relation between the estimated degrees-of-freedom for a Student’s t distribution and the goodness-of-fit of sophisticated evaluation models with spatial and spatialtemporal dependence.

This paper proposes a spatial discrete survival model to estimate the time to default for UK mortgages. The model includes a flexible parametric link function given by the Generalised Extreme Value Distribution and a dynamic spatially varying baseline hazard function to capture neighbourhood effects over time. We incorporate time and space varying variables into the model. The gains of the proposed model are illustrated through the analysis of a dataset on around 74,000 mortgage loans issued in England and Wales from 2006 to 2015.

This articles examines small and medium enterprises’ (SMEs) expectations of access to debt finance in times of uncertainty. In particular, we studied whether relationship lending affects British SMEs’ concerns about future access to debt finance after the UK referendum on European Union membership (the so-called Brexit referendum). By using a unique survey, we found that relationship lending significantly reduces SMEs’ expectations of being financially constrained, although the same does not hold for firms engaging in product innovation. Our results are robust after controlling for accounting information disclosure and for the relationship between the expectation of access to debt finance, the prospect of growth, and changes in business strategies.

To boost the application of machine learning (ML) techniques for credit scoring models, the blackbox problem should be addressed. The primary aim of this paper is to propose a measure based on counterfactuals to evaluate the interpretability of a ML credit scoring technique. Counterfactuals assist with understanding the model with regard to the classification decision boundaries and evaluate model robustness. The second contribution is the development of a data perturbation technique to generate a stress scenario.We apply these two proposals to a dataset on UK unsecured personal loans to compare logistic regression and stochastic gradient boosting (SBG). We show that training a blackbox model (SGB) as conditioned on our data perturbation technique can provide insight into model performance under stressed scenarios. The empirical results show that our interpretability measure is able to capture the classification decision boundary, unlike AUC and the classification accuracy widely used in the banking sector.

Credit scoring model development is very important for the lending decisions of financial institutions. The creditworthiness of borrowers is evaluated by assessing their hard and soft information. However, microfinance borrowers are very sensitive to a local economic downturn and extreme (weather or climate) events. Therefore, this paper is devoted to extending the standard credit scoring models by taking into account the spatial dependence in credit risk. We estimate a credit scoring model with spatial random effects using the distance matrix based on the borrowers’ locations. We find that including the spatial random effects improves the ability to predict defaults and non-defaults of both individual and group loans. Furthermore, we find that several loan characteristics and demographic information are important determinants of individual loan default but not group loans. Our study provides valuable insights for professionals and academics in credit scoring for microfinance and rural finance.

Summary We analyse the dependence between defaults in peer-to-peer lending and credit bureaus. To achieve this, we propose a new flexible bivariate regression model that is suitable for binary imbalanced samples. We use different copula functions to model the dependence structure between defaults in the two credit markets. We implement the model in the R package BivGEV and we explore the empirical properties of the proposed fitting procedure by a Monte Carlo study. The application of this proposal to a comprehensive data set provided by Lending Club shows a significant level of dependence between the defaults in peer-to-peer and credit bureaus. Finally, we find that our model outperforms the bivariate probit and univariate logit models in predicting peer-to-peer default, in estimating the value at risk and the expected shortfall.

The main aim of this study is to analyze the joint effects of customer segmentation, borrower characteristics and modeling techniques on the classification accuracy of a scoring model for agribusinesses. To this end, we used data provided by a Chilean company on 161 163 loans from January 2007 to December 2013. We considered random forest, neural network and logistic regression models as analytical methods. Regarding borrowers’ profiles, we examined the effects of sociodemographic, repayment behavior, agribusiness-specific and credit-related variables. We also segmented the customers as individuals, small and medium-sized enterprises, and large holdings. As the segments show different risk behaviors, we obtained a better performance when we estimated a scoring model for each segment instead of using a segmentation variable. In terms of the value of each set of variables, behavioral variables increased the predictive capability of the model by double the amount achieved by including agribusiness-related variables. The random forest is the model with the best classification accuracy.

Using the UK SMEs Finance Monitor data over 2011-2017, we explore the determinants of bank debt rejections for UK SMEs. In the wake of the global financial crisis, business overdrafts and term loans show slightly different trends although the factors affecting rejections are similar. We find that since 2014 rejection rates reduced for both facilities and they remained stable in the run-up to the Brexit referendum and its immediate aftermath, although export and import SMEs operating in industries with a high share of EU trade experienced tigher conditions. Further, we present robust evidence that firms with female owners, organised in partnerships, and with a higher initial credit balance are more likely to have their credit application approved. Finally, younger, smaller and more innovative SMEs are more likely to be rejected, while their chance of being successful in their credit applications increases substantially after 2014.

This paper focuses on the impact of financial fragmentation on small and medium enterprises’ (SMEs) access to finance. We combine country-level data on financial fragmentation and the ECB’s SAFE (Survey on the Access to Finance of Enterprises) data for 12 European Union (EU) countries over 2009–2016. Our findings indicate that an increase in financial fragmentation not only raises the probability of all firms to be rationed but also to be charged higher loan rates; in addition, it increases the likelihood of borrower discouragement and it impairs firms’ perceptions of the future availability of bank funds. Less creditworthy firms are even more likely to become credit rationed, suggesting a flight to quality effect in lending. However, our study also documents a potential adverse effect of increasing bank market power resulting from greater integration. This suggests that financial integration could impair firms’ financing, if not accompanied by policy initiatives aimed at maintaining an optimal level of competition in the banking sector.

While there is increasing interest in crypto assets, the credit risk of these exchanges is still relatively unexplored. To fill this gap, we considered a unique dataset of 144 exchanges, active from the first quarter of 2018 to the first quarter of 2021. We analyzed the determinants surrounding the decision to close an exchange using credit scoring and machine learning techniques. Cybersecurity grades, having a public developer team, the age of the exchange, and the number of available traded cryptocurrencies are the main significant covariates across different model specifications. Both in-sample and out-of-sample analyzes confirm these findings. These results are robust in regard to the inclusion of additional variables, considering the country of registration of these exchanges and whether they are centralized or decentralized.

This article studies the effects of incorporating the interdependence among London small business defaults into a risk analysis framework using the data just before the financial crisis. We propose an extension from standard scoring models to take into account the spatial dimensions and the demographic characteristics of small and medium-sized enterprises (SMEs), such as legal form, industry sector, and number of employees. We estimate spatial probit models using different distance matrices based only on the spatial location or on an interaction between spatial locations and demographic characteristics. We find that the interdependence or contagion component defined on spatial and demographic characteristics is significant and that it improves the ability to predict defaults of non–start-ups in London. Furthermore, including contagion effects among SMEs alters the parameter estimates of risk determinants. The approach can be extended to other risk analysis applications where spatial risk may incorporate correlation based on other aspects.

The aim of this paper is to measure the effect of the interaction between age for the population of males and females aged 18 to 74 and region-level GDP per capita on labour market transition probabilities in Italy. We compare different occupational states in a sample of males and females who remained in their region of residence at two points in time (12 months apart). We estimate the transition probabilities using a flexible hierarchical logit model with interaction effects between worker age and region-level GDP per capita. We apply this model using longitudinal data from the Italian Labour Force Survey that cover the 2004–2013 period. We find empirical support for the assumption that people in the same age cohort have different labour market opportunities based on the level of GDP per capita in their region of residence. These differences are particularly relevant among younger workers.

We explore the impact of financing constraints and the role of banking markets integration on the growth of small and medium enterprises (SMEs). The data are drawn from the European Central Bank/Survey on the Access to Finance of Enterprises (ECB/SAFE) on SMEs’ access to finance aggregated at the country level for the largest 11 euro area countries during 2009–2015. Our findings suggest that financing constraints hamper SMEs’ growth and that the effect is stronger for perceived, rather than actual, financing constraints. On the other hand, increased banking markets integration in the euro area appears to foster SMEs’ growth. Furthermore, we found that the reduction in financing constraints is crucial in the transmission channel from banking markets integration to growth. This effect appears significantly stronger when integration is measured by the intensity of cross-border lending than through convergence in interest rates to loans to nonfinancial corporations.

We develop a flexible binary choice model for mortgage default decisions that incorporates neighborhood effects in the disturbances. The main advantage of the model lies in its performance in providing improved estimates of the probability of default for risky mortgage loans. In addition, it can be applied to portfolios with a high number of loans. Assuming mortgage decisions with spatially dependent disturbances, the proposed approach uses the generalized extreme value distribution to flexibly model the error terms. To estimate the model on a large sample size, we use a variant of the Geweke-Hajivassiliou-Keane algorithm. We apply the proposed model and its competitors to a large dataset on almost 300,000 mortgages in Clark County, which includes Las Vegas, over 2009–2010. The results show that our proposal greatly improves the predictive accuracy of identifying loans that will default. Moreover, the competitor models underestimate credit Value at Risk.

We propose a novel approach based on the Marshall–Olkin (MO) copula to estimate the impact of systematic and idiosyncratic components on cross-border systemic risk. To use the data on non-failed banks in the suggested method, we consider the time to bank failure as a censored variable. Therefore, we propose a pseudo-maximum likelihood estimation procedure for the MO copula for a Type I censored sample. We derive the log-likelihood function, the copula parameter estimator and the bootstrap confidence intervals. Empirical data on the banking system of three European countries (Germany, Italy and the UK) shows that the proposed censored model can accurately estimate the systematic component of cross-border systemic risk.

Hundreds of millions of people in low-income economies do not have a credit or bank account because they have insufficient credit history for a credit score to be ascribed to them. In this paper we evaluate the predictive accuracy of models using alternative data, that may be used instead of credit history, to predict the credit risk of a new account. Without alternative data, the type of data that is typically available is demographic data. We show that a model that contains email usage and psychometric variables, as well as demographic variables, can give greater predictive accuracy than a model that uses demographic data only and that the predictive accuracy is sufficiently high for the demographic and email data to be used when conventional credit history data is unavailable. The same applies if merely psychometric data is included together with demographic data. However, we show that different randomly selected training: test sample splits give a wide range of predictive accuracies. In the second part of the paper, using two datasets that include only email usage as a predictor, we compare the predictive performances of a wide range of machine learning and statistical classifiers. We find that some classifiers applied to these alternative predictors give sufficiently accurate predictions for these variables to be used when no other data is available.

The paper proposes a novel model for the prediction of bank failures, on the basis of both macroeconomic and bank-specific microeconomic factors. As bank failures are rare, in the paper we apply a regression method for binary data based on extreme value theory, which turns out to be more effective than classical logistic regression models, as it better leverages the information in the tail of the default distribution. The application of this model to the occurrence of bank defaults in a highly bank dependent economy (Italy) shows that, while microeconomic factors as well as regulatory capital are significant to explain proper failures, macroeconomic factors are relevant only when failures are defined not only in terms of actual defaults but also in terms of mergers and acquisitions. In terms of predictive accuracy, the model based on extreme value theory outperforms classical logistic regression models.

This paper develops a method for modelling binary response data in a regression model with highly unbalanced class sizes. When the class sizes are highly unbalanced and the minority class represents a rare event, conventional regression analysis, i.e. logistic regression models, could underestimate the probability of the rare event. To overcome this drawback, we introduce a flexible skewed link function based on the quantile function of the generalized extreme value (GEV) distribution in a generalized additive model (GAM). The proposed model is known as generalized extreme value additive (GEVA) regression model, and a modified version of the local scoring algorithm is suggested to estimate it. We apply the proposed model to a dataset on Italian small and medium enterprises (SMEs) to estimate the default probability of SMEs. Our proposal performs better than the logistic (linear or additive) model in terms of predictive accuracy.

This article studies the effects of incorporating the interdependence among London small business defaults into a risk analysis framework using the data just before the financial crisis. We propose an extension from standard scoring models to take into account the spatial dimensions and the demographic characteristics of small and medium-sized enterprises (SMEs), such as legal form, industry sector, and number of employees. We estimate spatial probit models using different distance matrices based only on the spatial location or on an interaction between spatial locations and demographic characteristics. We find that the interdependence or contagion component defined on spatial and demographic characteristics is significant and that it improves the ability to predict defaults of non-start-ups in London. Furthermore, including contagion effects among SMEs alters the parameter estimates of risk determinants. The approach can be extended to other risk analysis applications where spatial risk may incorporate correlation based on other aspects.

Following 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.

Due to the vital role that SMEs play in most countries, issues relating specifically to their access to bank credit remain a key concern for both academics and practitioners. To encourage banks to extend lending to SMEs , the UK government has launched several initiatives in the aftermath of the most recent financial crisis . This chapter utilises the survey data on UK SMEs to investigate the relationship between bank credit availability and awareness of government initiatives. We find some evidence that (1) SMEs that are aware of Funding for Lending Scheme are less likely to experience overdraft rejections, and (2) SMEs that are aware of the Business Growth Fund or the British Business Bank are less likely to experience loan rejections.

The internal estimates of Loss Given Default (LGD) must reflect economic downturn conditions, thus estimating the “downturn LGD”, as the new Basel Capital Accord Basel II establishes. We suggest a methodology to estimate the downturn LGD distribution to overcome the arbitrariness of the methods suggested by Basel II. We assume that LGD is a mixture of an expansion and recession distribution. In this work, we propose an accurate parametric model for LGD and we estimate its parameters by the EM algorithm. Finally, we apply the proposed model to empirical data on Italian bank loans.

The goal of this paper is to provide a cohesive description and a critical comparison of the main estimators proposed in the literature for spatial binary choice models. The properties of such estimators are investigated using a theoretical and simulation study. To the authors' knowledge, this is the first paper that provides a comprehensive Monte Carlo study of the estimators' properties. This simulation study shows that the Gibbs estimator Le Sage (2000) performs best for low spatial autocorrelation, while the Recursive Importance Sampler Beron & Vijverberg (2004) performs best for high spatial autocorrelation. The same results are obtained by increasing the sample size. Finally, the linearized General Method of Moments estimator Klier & McMillen (2008) is the fastest algorithm that provides accurate estimates for low spatial autocorrelation and large sample size.

This paper proposes a new statistical estimator, to be applied to the prediction of state failures. State failures are typically conceptualised in a binary fashion—a state fails or it does not—and are rare events. Furthermore, state failures are not geographically independent events. The failure of one state can be expected to have an impact on the stability and peace in neighboring states, increasing the probability of state failures in geographical contiguous regions. Currently there is mixed evidence of such diffusion of state failure taking place Iqbal and Starr (2008). This paper proposes a new estimator to be used for estimates of the spatial interdependence among state failures and focuses on the ability to predict state failures in an international context. The most used spatial regression models for binary dependent variable consider a symmetric link function. When the dependent variable represents a rare event, a symmetric link function is not coherent. Following Calabrese and Osmetti (2013), we suggest the quantile function of the Generalized Extreme Value (GEV) distribution as link function in a spatial generalised linear model and we call this model the Spatial GEV (SGEV) regression model. To estimate the parameters of such model, a modified version of the Gibbs sampling method of LeSage (2000) and Wang and Dey (2010) is proposed. We analyse the performance of our model by Monte Carlo simulations and evaluating the prediction quality in empirical data on state failure.

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 logis- tic 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.

To represent the high concentration of recovery rates at the boundaries, we propose to consider the recovery rate as a mixed random variable, obtained as the mixture of a Bernoulli random variable and a beta random variable. We suggest to estimate the mixture weights and the Bernoulli parameter by two logistic regression models. For the recovery rates belonging to the interval 0,1, we model, jointly, the mean and the dispersion by using two link functions, so we propose the joint beta regression model that accommodates skewness and heteroscedastic errors. This methodological proposal is applied to a comprehensive survey on loan recovery process of Italian banks. In the regression model, we include some macroeconomic variables because they are relevant to explain the recovery rate and allow to estimate it in downturn conditions, as Basel II requires. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper we analyse a comprehensive database of 149,378 recovery rates on Italian bank loans. We investigate a new methodology to compute the recovery percentage that we suggest to consider as a mixed random variable. To estimate the probability density function of such a mixture, we propose the mixture of beta kernels estimator and we analyse its performance by Monte Carlo simulations. The application of these proposals to the Bank of Italy’s data shows that, even if we remove the endpoints from the support of the recovery rate, the density function estimate is far from being a beta function.

The recent European sovereign debt crisis clearly illustrates the importance of measuring the contagion effects of bank failures. Indeed, to better understand and monitor contagion risk, the European Central Bank has assumed the supervision of the largest banks in each of the member states. We propose a measure of contagion risk based on the spatial autocorrelation parameter of a binary spatial autoregressive model. Using different specifications of the interbank connectivity matrix, we estimate the contagion parameter for banks within the Eurozone, between 1996 and 2012. We provide evidence of high levels of systemic risk due to contagion during the European sovereign debt crisis.

We aim at proposing a new model for binary rare events, i.e. binary dependent variable with a very small number of ones. We extend the Generalized Extreme Value (GEV) regression model proposed by Calabrese and Osmetti (Journal of Applied Statistics 40(6):1172–1188, 2013) to a Generalized Additive Model (GAM). We suggest to consider the quantile function of the GEV distribution as a link function in a GAM, so we propose the Generalized Extreme Value Additive (GEVA) model. In order to estimate the GEVA model, a modified version of the local scoring algorithm of GAM is proposed. Finally, to model default probability, we apply our proposal to empirical data on Italian Small and Medium Enterprises (SMEs). The results show that the GEVA model has a higher predictive accuracy to identify the rare event than the logistic additive model.

For assessing the effect of undiversified idiosyncratic risk, Basel II has established that banks should measure and control their credit concentration risk. Concentration risk in credit portfolios comes into being through an uneven distribution of bank loans to individual borrowers (single-name concentration) or through an unbalanced allocation of loans in productive sectors and geographical regions (sectoral concentration). In this paper six properties that ensure a coherent measure of single-name concentration are identified. To evaluate single-name concentration risk in the literature, Herfindahl-Hirschman index has been used. This index represents a particular case of Hannah-Kay index proposed in monopoly theory. In this work the proof that Hannah-Kay index satisfies all the six properties is given. Finally, the impact of the elasticity parameter in Hannah-Kay index on the single-name concentration measure is analysed by numerical applications. © Springer International Publishing Switzerland 2014.

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 characteristics of SMEs and response is not assumed a priori (eg, 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 considers the joint role of macroeconomic and bankspecific factors in explaining the occurrence of bank failures. As bank failures are, fortunately, rare, we apply a regression model, based on extreme value theory, that turns out to be more effective than classical logistic regression models. The application of this model to the occurrence of bank defaults in Italy shows that, while capital ratios considered by the regulatory requirements of Basel III are extremely significant to explain proper failures, macroeconomic conditions are relevant only when failures are defined also in terms of merger and acquisition. We also apply the joint beta regression model, in order to estimate the factors that most contribute to the bank capital ratios monitored by Basel III. Our results show that the Tier 1 capital ratio and the Total capital ratio are affected by similar variables, at the micro and macroeconomic level. An important outcome of this part of the analysis is that capital ratio variables can be taken as reasonable proxies of distress, at least as far as the effect sign of the determinants of failure risk is being considered.

The goal of this paper is to provide a cohesive description and a critical comparison of the main estimators proposed in the literature for spatial binary choice models. The properties of such estimators are investigated using a theoretical and simulation study. To the authors' knowledge, this is the first paper that provides a comprehensive Monte Carlo study of the estimators' properties. This simulation study shows that the Gibbs estimator Le Sage (2000) performs best for low spatial autocorrelation, while the Recursive Importance Sampler Beron & Vijverberg (2004) performs best for high spatial autocorrelation. The same results are obtained by increasing the sample size. Finally, the linearized General Method of Moments estimator Klier & McMillen (2008) is the fastest algorithm that provides accurate estimates for low spatial autocorrelation and large sample size., 22 pages, 1 figure, submitted for review and available as Working Papers 201215, Geary Institute, University College Dublin

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 p...

Basel II requires that the internal estimates of Loss Given Default (LGD) reflect economic downturn conditions, thus modelling the "downturn LGD". In this work we suggest a methodology to estimate the downturn LGD distribution. Under the assumption that LGD is a mixture of an expansion and a recession distribution, an accurate parametric model for LGD is proposed and its parameters are estimated by the EM algorithm. Finally, we apply the proposed model to empirical data on Italian bank loans.

With the implementation of the Basel II accord, the development of accurate loss given default models is becoming increasingly important. The main objective of this paper is to propose a new model to estimate Loss Given Default (LGD) for bank loans by applying generalized additive models. Our proposal allows to represent the high concentration of LGDs at the boundaries. The model is useful in uncovering nonlinear covariate effects and in estimating the mean and the variance of LGDs. The suggested model is applied to a comprehensive survey on loan recovery process of Italian banks. To model LGD in downturn conditions, we include macroeconomic variables in the model. Out-of-time validation shows that our model outperforms popular models like Tobit, decision tree and linear regression models for different time horizons.

This analysis of the Polya urn scheme focuses on proving two new important results. First, the correlation structure between draws of a Polya urn scheme is uniform. Second, fixing the number of draws and the composition of the urn, a convex stochastic ordering is induced by the number of balls replaced into the urn.