Credit risk assessment using a multicriteria hierarchical discrimination approach: A comparative analysis

Corporate credit risk assessment decisions involve two major issues: the determination of the probability of default and the estimation of potential future benefits and losses for credit granting. The former issue is addressed by classifying the firms seeking credit into homogeneous groups representing different levels of credit risk. Classification/discrimination procedures commonly employed for such purposes include statistical and econometric techniques. This paper explores the performance of the M.H.DIS method (Multi-group Hierarchical DIScrimination), an alternative approach that originates from multicriteria decision aid (MCDA). The method is used to develop a credit risk assessment model using a large sample of firms derived from the loan portfolio of a leading Greek commercial bank. A total of 1411 firms are considered in both training and holdout samples using financial information through the period 1994–1997. A comparison with discriminant analysis (DA), logit analysis (LA) and probit analysis (PA) is also conducted to investigate the relative performance of the M.H.DIS method as opposed to traditional tools used for credit risk assessment.     

Gompertz zero-inflated cure rate regression models applied to credit risk data

In the financial market, it is important to consider that there is a proportion of customers that have settled their debt in time zero, immediately recovering their ability to pay. In this context, in this paper, we propose a survival analysis methodology that allows the insertion of times equal to zero in scenarios where credit risk is observed. The proposed model addresses the survival analysis model of the zero-inflated cure rate which incorporates the heterogeneity of three subgroups (individuals having events in the initial time, and individuals not susceptible and susceptible to the event). In our proposal, all available survival data of customers are modeled considering that the number of competitive causes follows a Poisson distribution and the baseline risk function follows a Gompertz distribution. The model parameter estimation is obtained by the maximum likelihood estimation procedure and simulation studies are conducted to evaluate the estimators' performance. The studied methodology will be applied to a credit database provided by a financial institution in Brazil.     

A limit distribution of credit portfolio losses with low default probabilities

This paper employs a multivariate extreme value theory (EVT) approach to study the limit distribution of the loss of a general credit portfolio with low default probabilities. A latent variable model is employed to quantify the credit portfolio loss, where both heavy tails and tail dependence of the latent variables are realized via a multivariate regular variation (MRV) structure. An approximation formula to implement our main result numerically is obtained. Intensive simulation experiments are conducted, showing that this approximation formula is accurate for relatively small default probabilities, and that our approach is superior to a copula-based approach in reducing model risk.     

Cure events in default prediction

This paper evaluates the resurrection event regarding defaulted firms and incorporates observable cure events in the default prediction of SME. Due to the additional cure-related observable data, a completely new information set is applied to predict individual default and cure events. This is a new approach in credit risk that, to our knowledge, has not been followed yet. Different firm-specific and macroeconomic default and cure-event-influencing risk drivers are identified. The significant variables allow a firm-specific default risk evaluation combined with an individual risk reducing cure probability. The identification and incorporation of cure-relevant factors in the default risk framework enable lenders to support the complete resurrection of a firm in the case of its default and hence reduce the default risk itself. The estimations are developed with a database that contains 5930 mostly small and medium-sized German firms and a total of more than 23000 financial statements over a time horizon from January 2002 to December 2007. Due to the significant influence on the default risk probability as well as the bank’s possible profit prospects concerning a cured firm, it seems essential for risk management to incorporate the additional cure information into credit risk evaluation.     

The assignment of credit limits with a behaviour-scoring system

Received on 1 July 1991. Behaviour-scoring systems for authorizations enable the riskof a customer defaulting to be quantified. These risks mustbe incorporated into a credit strategy which assigns creditlimits and makes authorization decisions in the most effectivemanner. This paper introduces the concept of marginal risk whichhas proved a useful tool in defining credit limit strategiesfor a mail-order company. Behaviour scores for authorizations are similar to credit applicationscores in that they predict the overall risk of a customer defaulting.If a cut-off risk can be established, then the optimal strategywould appear to be to withhold credit for customers exceedingthis risk and to grant unlimited credit for the remainder (thisis analogous to application strategies). The notion of grantingunlimited credit is often commercially unacceptable (particularlyif customers are to be informed of their credit limits!) andso strategies which give all or nothing are of limited valueand need further refinement. In order to overcome this problem, the concept of marginal riskhas been devised. The marginal risk is the risk of the ‘last£’ of an account being defaulted. This reflectsthe fact that small-balance customers may well pay off theircurrent balance only to default on larger subsequent purchases.Although the overall risk of customers with a given behaviourscore defaulting is relatively constant, their marginal riskwill vary according to their outstanding balance. This paperexplores the relationships between marginal risk and overallrisk and between marginal risk and outstanding balance. A modelwhich summarizes these relationships is proposed, and contoursof equal marginal risk are built on the basis of this model.These contours provide strategies for allocating credit limitswhich are both practical and optimal for a well formulated cut-offrisk and which suggest that the probability of defaulting isnot the best criterion for allocating credit limits. The results of the application of this approach will be demonstrated.Some of the problems that have been overcome are discussed,as are some of the outstanding problems.     

基于混合模型的利润驱动违约判别临界点研究

违约判别临界点是金融机构是否接受客户贷款申请的重要参考,合适的违约判别临界点对减少金融机构贷款损失实现稳健经营具有重要意义。本文研究的问题是如何保证计算客户违约概率的准确性,并找到利润最大化的违约判别临界点。本文的创新与特色:一是通过将多个不同类型的违约判别模型计算的客户违约概率进行加权平均,保证了计算客户违约概率的的整体准确性,避免了使用单一模型计算客户违约概率不准确的弊端;二是通过定义金融机构从贷款中获得利润的计算公式,以利润最大为目标,求解违约判别临界点,避免了现有计算临界点的方法如广义对称点估计和经验似然法等方法得到的临界点利润不是最大的弊端。研究发现:混合模型比单一模型的准确性高,AUC值显著提高;在人人贷数据集中本文的违约判别临界点下贷款利润远高于其他方法下临界点的利润。     

Predicting default of a small business using different definitions of financial distress

The paper introduces a number of risk-rating models for UK small businesses applying an accounting-based approach, which uses financial ratios to predict corporate bankruptcy. An enhancement to these models is considered through features typical to retail credit risk modelling. A common problem of default prediction consists in the relatively small number of bankruptcies or real defaults available for model-building. In order to expand the ‘default’ group beyond bankrupt companies, the paper considers adopting four different definitions of ‘a failing business’ by investigating combinations of financial distress levels. The impact of each default definition on the choice of predictor variables and on the model's predictive accuracy is explored. In addition, the paper examines the value of categorizing financial ratios used as predictor variables.     

基于贝叶斯方法的低违约组合违约率估计

现代信用风险建模的核心是估计违约率,违约率估计是否准确将直接影响信用风险建模的质量。在估计违约率的众多文献中,频率法或logistic回归等统计方法的运用非常广泛,此类统计模型的基础是大样本,它客观上需要最低数量或最优数量的违约数据,而低违约组合(LDP)是指只有很少违约数据甚至没有违约数据的组合,如何估计LDP的违约率、反映违约率的非预期波动是一个值得关注的现实问题。本文针对银行贷款LDP缺乏足够历史违约数据的情况,采用贝叶斯方法估计LDP的违约率,并进一步探讨了根据专家判断或者根据同类银行LDP违约数量的历史数据来确定先验分布的方法。在贝叶斯估计中,通过先验分布的设定,不仅可以实现违约率估计的科学性和合理性,而且可以反映违约的非预期波动,有助于银行实施谨慎稳健的风险管理。     

Stress test for a technology credit guarantee fund based on survival analysis

A technology credit guarantee policy has been established to provide financial support to technology-based SMEs with a limited asset base. For an effective technology credit guarantee policy, risk management is essential. In this paper, we investigate a survival model that predicts start-up SMEs’ loan default probability at a given time based on technology attributes along with the economic environment and the firm’s characteristics at the time of the technology credit guarantee fund application. This, in turn, is used for the estimation of the technology fund risk along with a stress test. Our work is expected to contribute to reducing the risks associated with technology financing.     

A pricing model for secondary market yield based floating rate notes subject to default risk

The purpose of this article is to price secondary market yield based floating rate notes (SMY-FRNs) subject to default risk. SMY-FRNs are derivatives on the default-free term structure of interest rates, on the term structures for default-risky credit classes, and on the structure of a determined pool of bonds. The main problem in SMY-FRN pricing (as compared to the pricing of standard interest rate or credit derivatives) is market incompleteness, which makes traditional no-arbitrage pricing by replication fail. In general, SMY-FRNs are subject to two types of default risk. First, the SMY-FRN issuer may go bankrupt (direct default risk). Second, the possibility of the bankruptcy of the issuers in the underlying pool has an influence on the SMY-FRN coupons (indirect default risk). This article is the first one which provides a no-arbitrage pricing model for SMY-FRNs with direct and indirect default risks. It is also the first article applying incomplete market pricing methodology to SMY-FRNs.     

Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.     

农村信用社信贷违约识别模型及其应用

构建农村信用社信用风险模型对完善农村金融风险管理体系、提高农村信用社经营管理意义重大.基于还款意愿和还款能力两方面,系统分析了影响农信社贷款债务人违约率的主要因素,在此基础上应用logistic方法建立农信社债务人违约率预测模型,并通过Gini系数对模型区分能力和识别能力进行验证评估.实证结果表明,模型中债务人年龄、所在地区、贷款额所占家庭收入比例、与信用社信贷关系密切程度以及户口状况等因素都表现显著;违约率预测模型在样本内和样本外均有较好的违约识别能力,从而可为农信社放贷前的债务人信用评估、贷款发放和风险管理提供有力参考.     

Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model

In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a subfiltration structure. The Euler–Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical scheme for pricing. Finally, the antithetic variable technique is used to reduce the variance of credit default swap option prices.     

Comparison results for exchangeable credit risk portfolios

This paper is dedicated to risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the convex ordering of their corresponding mixture distributions. Thus we can proceed to some comparisons between stop-loss premiums, CDO tranche premiums and convex risk measures on aggregate losses. This methodology provides a unified analysis of dependence for a number of CDO pricing models based on factor copulas, multivariate Poisson and structural approaches.     

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.     

信用违约互换的定价方法

通过对信用违约互换的结构的分析,在Merton的结构化方法框架下,用偏微分方程求出公司的违约概率密度,最后给出信用违约互换的一种定价方法.     

A time-dependent proportional hazards survival model for credit risk analysis

In the consumer credit industry, assessment of default risk is critically important for the financial health of both the lender and the borrower. Methods for predicting risk for an applicant using credit bureau and application data, typically based on logistic regression or survival analysis, are universally employed by credit card companies. Because of the manner in which the predictive models are fit using large historical sets of existing customer data that extend over many years, default trends, anomalies, and other temporal phenomena that result from dynamic economic conditions are not brought to light. We introduce a modification of the proportional hazards survival model that includes a time-dependency mechanism for capturing temporal phenomena, and we develop a maximum likelihood algorithm for fitting the model. Using a very large, real data set, we demonstrate that incorporating the time dependency can provide more accurate risk scoring, as well as important insight into dynamic market effects that can inform and enhance related decision making.     

A preference disaggregation decision support system for financial classification problems

Classification is one of the most extensively studied problems in the fields of multivariate statistical analysis, operations research and artificial intelligence. Decisions involving a classification of the alternative solutions are of major interest in finance, since several financial decision problems are best studied by classifying a set of alternative solutions (firms, loan applications, investment projects, etc.) in predefined classes. This paper proposes an alternative approach to the classical statistical methodologies that have been extensively used for the study of financial classification problems. The proposed methodology combines the preference disaggregation approach (a multicriteria decision aid method) with decision support systems. More specifically, the FINancial CLASsification (FINCLAS) multicriteria decision support system is presented. The system incorporates a plethora of financial modeling tools, along with powerful preference disaggregation methods that lead to the development of additive utility models for the classification of the considered alternatives into predefined classes. An application in credit granting is used to illustrate the capabilities of the system.     

A reduced-form model with default intensities containing contagion and regime-switching Vasicek processes

The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps (CDSs). Numerical results are presented to show the impacts of the model parameters on the fair spreads.     

Support vector machines for default prediction of SMEs based on technology credit

In Korea, many forms of credit guarantees have been issued to fund small and medium enterprises (SMEs) with a high degree of growth potential in technology. However, a high default rate among funded SMEs has been reported. In order to effectively manage such governmental funds, it is important to develop an accurate scoring model for selecting promising SMEs. This paper provides a support vector machines (SVM) model to predict the default of funded SMEs, considering various input variables such as financial ratios, economic indicators, and technology evaluation factors. The results show that the accuracy performance of the SVM model is better than that of back-propagation neural networks (BPNs) and logistic regression. It is expected that the proposed model can be applied to a wide range of technology evaluation and loan or investment decisions for technology-based SMEs.