Model combination for credit risk assessment: A stacked generalization approach

The development of credit risk assessment models is often considered within a classification context. Recent studies on the development of classification models have shown that a combination of methods often provides improved classification results compared to a single-method approach. Within this context, this study explores the combination of different classification methods in developing efficient models for credit risk assessment. A variety of methods are considered in the combination, including machine learning approaches and statistical techniques. The results illustrate that combined models can outperform individual models for credit risk analysis. The analysis also covers important issues such as the impact of using different parameters for the combined models, the effect of attribute selection, as well as the effects of combining strong or weak models.     

Enhanced decision support in credit scoring using Bayesian binary quantile regression

Fierce competition as well as the recent financial crisis in financial and banking industries made credit scoring gain importance. An accurate estimation of credit risk helps organizations to decide whether or not to grant credit to potential customers. Many classification methods have been suggested to handle this problem in the literature. This paper proposes a model for evaluating credit risk based on binary quantile regression, using Bayesian estimation. This paper points out the distinct advantages of the latter approach: that is (i) the method provides accurate predictions of which customers may default in the future, (ii) the approach provides detailed insight into the effects of the explanatory variables on the probability of default, and (iii) the methodology is ideally suited to build a segmentation scheme of the customers in terms of risk of default and the corresponding uncertainty about the prediction. An often studied dataset from a German bank is used to show the applicability of the method proposed. The results demonstrate that the methodology can be an important tool for credit companies that want to take the credit risk of their customer fully into account.     

Unsupervised quadratic surface support vector machine with application to credit risk assessment

Unsupervised classification is a highly important task of machine learning methods. Although achieving great success in supervised classification, support vector machine (SVM) is much less utilized to classify unlabeled data points, which also induces many drawbacks including sensitive to nonlinear kernels and random initializations, high computational cost, unsuitable for imbalanced datasets. In this paper, to utilize the advantages of SVM and overcome the drawbacks of SVM-based clustering methods, we propose a completely new two-stage unsupervised classification method with no initialization: a new unsupervised kernel-free quadratic surface SVM (QSSVM) model is proposed to avoid selecting kernels and related kernel parameters, then a golden-section algorithm is designed to generate the appropriate classifier for balanced and imbalanced data. By studying certain properties of proposed model, a convergent decomposition algorithm is developed to implement this non-covex QSSVM model effectively and efficiently (in terms of computational cost). Numerical tests on artificial and public benchmark data indicate that the proposed unsupervised QSSVM method outperforms well-known clustering methods (including SVM-based and other state-of-the-art methods), particularly in terms of classification accuracy. Moreover, we extend and apply the proposed method to credit risk assessment by incorporating the T-test based feature weights. The promising numerical results on benchmark personal credit data and real-world corporate credit data strongly demonstrate the effectiveness, efficiency and interpretability of proposed method, as well as indicate its significant potential in certain real-world applications.     

Identifying future defaulters: A hierarchical Bayesian method

Traditional methods of applying classification models into the area of credit scoring may ignore the effect from censoring. Survival analysis has been introduced with its ability to deal with censored data. The mixture cure model, one important branch of survival models, is also applied in the context of credit scoring, assuming that the study population is a mixture of never-default and will-default customers.     

Estimation and status prediction in a discrete mover‐stayer model with covariate effects on stayer's probability

A discrete‐time mover‐stayer (MS) model is an extension of a discrete‐time Markov chain, which assumes a simple form of population heterogeneity. The individuals in the population are either stayers, who never leave their initial states or movers who move according to a Markov chain. We, in turn, propose an extension of the MS model by specifying the stayer's probability as a logistic function of an individual's covariates. Such extension has been recently discussed for a continuous time MS but has not been considered before for a discrete time one. This extension allows for an in‐sample classification of subjects who never left their initial states into stayers or movers. The parameters of an extended MS model are estimated using the expectation‐maximization algorithm. A novel bootstrap procedure is proposed for out of sample validation of the in‐sample classification. The bootstrap procedure is also applied to validate the in‐sample classification with respect to a more general dichotomy than the MS one. The developed methods are illustrated with the data set on installment loans. But they can be applied more broadly in credit risk area, where prediction of creditworthiness of a loan borrower or lessee is of major interest.     

Adaptive credit scoring with kernel learning methods

Credit scoring is a method of modelling potential risk of credit applications. Traditionally, logistic regression and discriminant analysis are the most widely used approaches to create scoring models in the industry. However, these methods are associated with quite a few limitations, such as being instable with high-dimensional data and small sample size, intensive variable selection effort and incapability of efficiently handling non-linear features. Most importantly, based on these algorithms, it is difficult to automate the modelling process and when population changes occur, the static models usually fail to adapt and may need to be rebuilt from scratch. In the last few years, the kernel learning approach has been investigated to solve these problems. However, the existing applications of this type of methods (in particular the SVM) in credit scoring have all focused on the batch model and did not address the important problem of how to update the scoring model on-line. This paper presents a novel and practical adaptive scoring system based on an incremental kernel method. With this approach, the scoring model is adjusted according to an on-line update procedure that can always converge to the optimal solution without information loss or running into numerical difficulties. Non-linear features in the data are automatically included in the model through a kernel transformation. This approach does not require any variable reduction effort and is also robust for scoring data with a large number of attributes and highly unbalanced class distributions. Moreover, a new potential kernel function is introduced to further improve the predictive performance of the scoring model and a kernel attribute ranking technique is used that adds transparency in the final model. Experimental studies using real world data sets have demonstrated the effectiveness of the proposed method.     

Tail behaviour of credit loss distributions for general latent factor models

Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the co‐movements in defaults over time, we assume that defaults are triggered by a general, possibly non‐linear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk⁺. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model's functional form and the tail properties of the model's risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk⁺ approach to modeling portfolio credit risk.     

贝叶斯方法在信用风险度量中的应用研究综述

贝叶斯方法可以有效的处理信用风险度量中常见的数据缺失问题,而且为科学使用专家意见等主观经验提供了有效途径,已被广泛应用于信用风险度量领域。本文从模型构建、估计方法及模型比较三个方面对应用贝叶斯方法度量信用风险的重要文献进行综述,重点关注信用风险的违约相关性和风险蔓延性等最新研究热点,为深入研究信用风险度量问题提供参考,并引起国内风险分析人员对贝叶斯方法的兴趣。     

Empirical Evaluation of Hybrid Defaultable Bond Pricing Models

A four‐factor model (the extended model of Schmid and Zagst) is presented for pricing credit risk related instruments such as defaultable bonds or credit derivatives. It is an advancement of an earlier three‐factor model. In addition to a firm‐specific credit risk factor, a new systematic risk factor in the form of GDP growth rate is included. This new model is set in the context of other hybrid defaultable bond pricing models and empirically compared to specific representatives. We find that a model based only on firm‐specific variables is unable to capture changes in credit spreads completely. However, it is shown that in this model, market variables such as GDP growth rates, non‐defaultable interest rates and firm‐specific variables together significantly influence credit spread levels and changes.     

A multicriteria approach for rating the credit risk of financial institutions

Within the new bank regulatory context, the assessment of the credit risk of financial institutions is an important issue for supervising authorities and investors. This study explores the possibility of a developing risk assessment model for financial institutions using a multicriteria classification method. The analysis is based on publicly available financial data for UK firms. The results indicate that the proposed multicriteria methodology provides promising results compared to well known statistical methods.     

Subagging for credit scoring models

The logistic regression framework has been for long time the most used statistical method when assessing customer credit risk. Recently, a more pragmatic approach has been adopted, where the first issue is credit risk prediction, instead of explanation. In this context, several classification techniques have been shown to perform well on credit scoring, such as support vector machines among others. While the investigation of better classifiers is an important research topic, the specific methodology chosen in real world applications has to deal with the challenges arising from the real world data collected in the industry. Such data are often highly unbalanced, part of the information can be missing and some common hypotheses, such as the i.i.d. one, can be violated. In this paper we present a case study based on a sample of IBM Italian customers, which presents all the challenges mentioned above. The main objective is to build and validate robust models, able to handle missing information, class unbalancedness and non-iid data points. We define a missing data imputation method and propose the use of an ensemble classification technique, subagging, particularly suitable for highly unbalanced data, such as credit scoring data. Both the imputation and subagging steps are embedded in a customized cross-validation loop, which handles dependencies between different credit requests. The methodology has been applied using several classifiers (kernel support vector machines, nearest neighbors, decision trees, Adaboost) and their subagged versions. The use of subagging improves the performance of the base classifier and we will show that subagging decision trees achieve better performance, still keeping the model simple and reasonably interpretable.     

基于核主元分析的带可变惩罚因子最小二乘模糊支持向量机模型及其在信用分类中的应用

信用分类是信用风险管理中一个重要环节,其主要目的是根据信用申请客户提供的资料从申请客户中区分出可信客户和违约客户,以便为信用决策者提供决策依据.为了正确区分不同的信用客户,特别是违约客户,结合核主元分析和支持向量机算法构造基于核主元分析的带可变惩罚因子最小二乘模糊支持向量机模型对信用数据进行了分类处理.在基于核主元分析的带可变惩罚因子最小二乘模糊支持向量机模型中,首先对样本数据进行预处理,然后利用核主元分析以非线性方式降低数据的维数,最后利用带可变惩罚因子最小二乘模糊支持向量机模型对降维后数据进行分类分析.为了验证,选择两个公开的信用数据集来进行实证分析.实证结果表明：基于核主元分析的带可变惩罚因子最小二乘模糊支持向量机模型取得了较好的分类结果,可为信用决策者提供重要的决策参考依据.     

Discovering Credit Cardholders’ Behavior by Multiple Criteria Linear Programming

In credit card portfolio management, predicting the cardholder’s spending behavior is a key to reduce the risk of bankruptcy. Given a set of attributes for major aspects of credit cardholders and predefined classes for spending behaviors, this paper proposes a classification model by using multiple criteria linear programming to discover behavior patterns of credit cardholders. It shows a general classification model that can theoretically handle any class-size. Then, it focuses on a typical case where the cardholders’ behaviors are predefined as four classes. A dataset from a major US bank is used to demonstrate the applicability of the proposed method.     

基于多目标进化聚类的信用风险特征识别

在信用风险识别领域,聚类算法常被用于区分不同风险等级的样本并识别风险特征。然而该领域中通常面临高维数据处理问题,导致传统聚类算法存在不适应此类问题的缺陷：易陷入局部最优、受冗余特征干扰、鲁棒性不强等。采用高维信用风险数据,研究上市公司信用风险,建立信用风险特征识别的三目标优化模型,设计基于分解的多目标子空间聚类算法进行求解。通过算法的横向对比实验,展示了所提出的算法在聚类精度和鲁棒性方面的优势,并根据聚类算法的权重分配结果,归纳总结上市公司信用风险评估过程中应重点关注的指标。     

A bi‐level neural‐based fuzzy classification approach for credit scoring problems

The credit scoring is a risk evaluation task considered as a critical decision for financial institutions in order to avoid wrong decision that may result in huge amount of losses. Classification models are one of the most widely used groups of data mining approaches that greatly help decision makers and managers to reduce their credit risk of granting credits to customers instead of intuitive experience or portfolio management. Accuracy is one of the most important criteria in order to choose a credit‐scoring model; and hence, the researches directed at improving upon the effectiveness of credit scoring models have never been stopped. In this article, a hybrid binary classification model, namely FMLP, is proposed for credit scoring, based on the basic concepts of fuzzy logic and artificial neural networks (ANNs). In the proposed model, instead of crisp weights and biases, used in traditional multilayer perceptrons (MLPs), fuzzy numbers are used in order to better model of the uncertainties and complexities in financial data sets. Empirical results of three well‐known benchmark credit data sets indicate that hybrid proposed model outperforms its component and also other those classification models such as support vector machines (SVMs), K‐nearest neighbor (KNN), quadratic discriminant analysis (QDA), and linear discriminant analysis (LDA). Therefore, it can be concluded that the proposed model can be an appropriate alternative tool for financial binary classification problems, especially in high uncertainty conditions. © 2013 Wiley Periodicals, Inc. Complexity 18: 46–57, 2013     

Re-assignment and consolidation of credit authorizations

When a customer is granted several credit lines with different risk levels, the bank usually stipulates an authorization for each credit line and a total authorization; moreover authorizations are sometimes given for sets of credit lines. The purpose of the paper is, given a set of credit lines with corresponding authorizations, and a customer's current credit utilizations, to find new utilizations of greatest risk to the bank, within the credit authorization limits and with regard to the current utilizations. These new utilizations, used as re-assigned authorizations enable the bank to assess the risks relative to residual commitment and possible overstepping for each credit line. Furthermore these risks can be aggregated over a set of customers for each credit line. An algorithm has been developed to compute these re-assigned authorizations; it is based on classical linear programming methods. This paper describes this algorithm and recommends its use to consolidate risks.     

On the simulation of portfolios of interest rate and credit risk sensitive securities

We discuss extensions of reduced-form and structural models for pricing credit risky securities to portfolio simulation and valuation. Stochasticity in interest rates and credit spreads is captured via reduced-form models and is incorporated with a default and migration model based on the structural credit risk modelling approach. Calculated prices are consistent with observed prices and the term structure of default-free and defaultable interest rates. Three applications are discussed: (i) study of the inter-temporal price sensitivity of credit bonds and the sensitivity of future portfolio valuation with respect to changes in interest rates, default probabilities, recovery rates and rating migration, (ii) study of the structure of credit risk by investigating the impact of disparate risk factors on portfolio risk, and (iii) tracking of corporate bond indices via simulation and optimisation models. In particular, we study the effect of uncertainty in credit spreads and interest rates on the overall risk of a credit portfolio, a topic that has been recently discussed by Kiesel et al. [The structure of credit risk: spread volatility and ratings transitions. Technical report, Bank of England, ISSN 1268-5562, 2001], but has been otherwise mostly neglected. We find that spread risk and interest rate risk are important factors that do not diversify away in a large portfolio context, especially when high-quality instruments are considered.     

上市公司信用风险分析模型中的变量选择

当前上市公司信用风险数据所呈现出的高维度以及高相关性的特点严重影响了信用风险模型的准确性。为此本文结合已有算法以及信用风险模型的特点设计了一种新的基于非参数的变量选择方法。通过该方法对上市公司用风险相关变量进行分析筛选可以消除数据集中包含的噪声变量以及线性相关变量。本文同时还针对该方法设计了高变量维度下最优解求解算法。文章以Logistic模型为例对上市公司信用风险做了实证分析,研究结果表明与以往的变量选择方法相比该方法可以有效的降低数据维度,消除变量间的相关性,并同时提高模型的可靠性和预测精度。     

The risk management for technology credit guarantee fund

Technology credit guarantee Fund (TCGF) supports many small and medium companies with high degree of growth potential in technology. Generally, the performance of technology credit guarantee has been evaluated focusing on the probability of default (PD) on the fund recipient companies. But PD itself does not reflect the amount of loss. In this paper, we suggest the way to find the expected loss using the PD, Exposure at Default and Loss Given Default for risk management of the TCGF. Unlike general credit measure, we use the competing risk model in order to estimate the PD for various types of defaults. It is expected that our study can contribute to provide the efficient credit risk management for TCGF and the lending institution.     

Factors' correlation in the Heath–Jarrow–Morton interest rate model

We propose a new derivation of the Heath–Jarrow–Morton risk‐neutral drift restriction that takes into account nonzero instantaneous correlations between factors. The result allows avoiding the orthogonalization of factors and provides an approach by which interest rate derivatives can be priced by preserving the economic meaning of each underlying factor. An application is given for the term structure of credit‐risky bonds, driven by two correlated factors—the risk‐free forward rate and the forward credit spreads. Copyright © 2008 John Wiley & Sons, Ltd.