Mixture cure models in credit scoring: If and when borrowers default

Mixture cure models were originally proposed in medical statistics to model long-term survival of cancer patients in terms of two distinct subpopulations - those that are cured of the event of interest and will never relapse, along with those that are uncured and are susceptible to the event. In the present paper, we introduce mixture cure models to the area of credit scoring, where, similarly to the medical setting, a large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. We estimate a mixture cure model predicting (time to) default on a UK personal loan portfolio, and compare its performance to the Cox proportional hazards method and standard logistic regression. Results for credit scoring at an account level and prediction of the number of defaults at a portfolio level are presented; model performance is evaluated through cross validation on discrimination and calibration measures. Discrimination performance for all three approaches was found to be high and competitive. Calibration performance for the survival approaches was found to be superior to logistic regression for intermediate time intervals and useful for fixed 12 month time horizon estimates, reinforcing the flexibility of survival analysis as both a risk ranking tool and for providing robust estimates of probability of default over time. Furthermore, the mixture cure model’s ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower.     

A note on coarse classifying in acceptance scorecards

Traditionally, in credit and behavioural scoring one assumes that as all consumers have essentially the same product, its features will not affect whether the consumer defaults or not. Hence, one coarse classifies the characteristics concentrating only on the default ratio. As products and their operational features become customized for each individual (the very purpose of acceptance scoring), then decisions like whether the customer will accept the product or not must depend on the features offered. This paper investigates how one can deal with this dependency when coarse classifying the characteristics.     

基于信用利差与Logistic回归的公司违约概率测算模型与实证研究

用Logistic模型计算公司违约概率在实际应用中存在两个问题:一是在缺乏公司违约记录数据库或违约记录数据库不典型的情况下,无法应用该模型或模型计算结果不准确;二是现有Logistic违约概率模型忽视了不同行业财务指标分布特征的差异性,导致公司违约概率计算结果的准确性降低。针对问题一,本文通过公司债券信用利差计算市场隐含的公司违约概率,在Logistic变换的基础上进一步确定Logistic线性回归的参数,使得公司违约概率的计算结果符合债券市场的实际状况。针对问题二,通过不同行业关键财务指标的单因子方差分析,证实了行业间财务指标的分布特征具有显著性差异,通过拟合优度证实了区分行业建立Logistic违约概率模型可显著提高违约概率测算的准确性。本文Logistic违约概率模型的构建过程如下:通过初选财务指标的相关性分析,删除反映信息重复的财务指标;通过Logistic回归中财务指标系数的显著性检验,删除对违约概率解释能力弱的财务指标;以Logistic回归的拟合优度为标准,选取各样本行业Logistic违约概率模型的关键财务指标,建立了机械设备等5个样本行业的Logistic违约概率模型,为样本内行业公司违约概率的准确测算提供模型与方法。本文的创新与特色:一是在无套利条件下,通过公司债券信用利差计算市场隐含的公司违约概率,并对其进行Logistic变换,作为Logistic线性回归的被解释变量,解决了在缺乏公司违约记录数据情况下Logistic违约概率模型的参数估计问题;二是通过单因子方差分析方法,证实了行业间财务指标的分布特征具有显著性差异,说明应区分行业建立Logistic违约概率模型;三是通过财务指标间的相关分析删除反映信息重复的财务指标,通过财务指标系数的显著性检验删除对公司违约概率解释能力弱的财务指标,保证了Logistic违约概率模型中关键财务指标选取的合理性;四是实证研究结果表明,不同行业的Logistic违约概率模型的关键财务指标不同,同一财务指标的参数也存在显著差异。实证研究结果还表明,区分行业建立Logistic违约概率模型与不区分行业相比,前者可将拟合优度及调整后的拟合优度提高近1倍。本文研究结果对于提高公司违约概率测算的准确性具有重要参考意义,对于商业银行贷款定价、公司债券发行定价、银行信用风险管理具有重要参考意义。     

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.     

Question selection responding to information on customers from heterogeneous populations to select offers that maximize expected profit

The advent of Internet broking pages allows customers to ‘apply’ to a number of different companies at one time, leading to multiple offers made to a customer. The saturated condition of the personal financial products has led to falling ‘take’ rates. Financial institutions are trying to increase the ‘take’ rates of their personal financial products. Applicants for credit will have to provide information for risk assessment, which can be used to assess the probability of a customer accepting an offer. Interactive channels such as the Internet and telephone allow questions that are asked to depend on previous answers. The questions selected need to provide information to assess the probability of acceptance of a particular variant of financial product. In this paper, we investigate a model to predict the best offer to extend next to a customer based on the response for the questions, as well as the question selection itself.     

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.     

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。     

Credit scoring for profitability objectives

In consumer credit markets lending decisions are usually represented as a set of classification problems. The objective is to predict the likelihood of customers ending up in one of a finite number of states, such as good/bad payer, responder/non-responder and transactor/non-transactor. Decision rules are then applied on the basis of the resulting model estimates. However, this represents a misspecification of the true objectives of commercial lenders, which are better described in terms of continuous financial measures such as bad debt, revenue and profit contribution. In this paper, an empirical study is undertaken to compare predictive models of continuous financial behaviour with binary models of customer default. The results show models of continuous financial behaviour to outperform classification approaches. They also demonstrate that scoring functions developed to specifically optimize profit contribution, using genetic algorithms, outperform scoring functions derived from optimizing more general functions such as sum of squared error.     

Neural network survival analysis for personal loan data

Traditionally, credit scoring aimed at distinguishing good payers from bad payers at the time of the application. The timing when customers default is also interesting to investigate since it can provide the bank with the ability to do profit scoring. Analysing when customers default is typically tackled using survival analysis. In this paper, we discuss and contrast statistical and neural network approaches for survival analysis. Compared to the proportional hazards model, neural networks may offer an interesting alternative because of their universal approximation property and the fact that no baseline hazard assumption is needed. Several neural network survival analysis models are discussed and evaluated according to their way of dealing with censored observations, time-varying inputs, the monotonicity of the generated survival curves and their scalability. In the experimental part, we contrast the performance of a neural network survival analysis model with that of the proportional hazards model for predicting both loan default and early repayment using data from a UK financial institution.     

基于迁移学习的客户信用评估模型研究

客户信用评估是银行等金融企业日常经营活动中的重要组成部分。一般违约样本在客户总体中只占少数,而能按时还款客户样本占多数,这就是客户信用评估中常见的类别不平衡问题。目前,用于客户信用评估的方法尚不能有效解决少数类样本稀缺带来的类别不平衡。本研究引入迁移学习技术整合系统内外部信息,以解决少数类样本稀缺带来的类别不平衡问题。为了提高对来自系统外部少数类样本信息的使用效率,构建了一种新的迁移学习模型:以基于集成技术的迁移装袋模型为基础,使用两阶段抽样和数据分组处理技术分别对其基模型生成和集成策略进行改进。运用重庆某商业银行信用卡客户数据进行的实证研究结果表明:与目前客户信用评估的常用方法相比,新模型能更好地处理绝对稀缺条件下类别不平衡对客户信用评估的影响,特别对占少数的违约客户有更好的预测精度。     

Using semi-supervised classifiers for credit scoring

In credit scoring, low-default portfolios (LDPs) are those for which very little default history exists. This makes it problematic for financial institutions to estimate a reliable probability of a customer defaulting on a loan. Banking regulation (Basel II Capital Accord), and best practice, however, necessitate an accurate and valid estimate of the probability of default. In this article the suitability of semi-supervised one-class classification (OCC) algorithms as a solution to the LDP problem is evaluated. The performance of OCC algorithms is compared with the performance of supervised two-class classification algorithms. This study also investigates the suitability of over sampling, which is a common approach to dealing with LDPs. Assessment of the performance of one- and two-class classification algorithms using nine real-world banking data sets, which have been modified to replicate LDPs, is provided. Our results demonstrate that only in the near or complete absence of defaulters should semi-supervised OCC algorithms be used instead of supervised two-class classification algorithms. Furthermore, we demonstrate for data sets whose class labels are unevenly distributed that optimising the threshold value on classifier output yields, in many cases, an improvement in classification performance. Finally, our results suggest that oversampling produces no overall improvement to the best performing two-class classification algorithms.     

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.     

Credit rating prediction using Ant Colony Optimization

The introduction of the Basel II Capital Accord has encouraged financial institutions to build internal rating systems assessing the credit risk of their various credit portfolios. One of the key outputs of an internal rating system is the probability of default (PD), which reflects the likelihood that a counterparty will default on his/her financial obligation. Since the PD modelling problem basically boils down to a discrimination problem (defaulter or not), one may rely on the myriad of classification techniques that have been suggested in the literature. However, since the credit risk models will be subject to supervisory review and evaluation, they must be easy to understand and transparent. Hence, techniques such as neural networks or support vector machines are less suitable due to their black box nature. Building upon previous research, we will use AntMiner+ to build internal rating systems for credit risk. AntMiner+ allows to infer a propositional rule set from a given data set, hereby using the principles from Ant Colony Optimization. Experiments will be conducted using various types of credit data sets (retail, small- and medium-sized enterprises and banks). It will be shown that the extracted rule sets are both powerful in terms of discriminatory power and comprehensibility. Furthermore, a framework will be presented describing how AntMiner+ fits into a global Basel II credit risk management system.     

A profit-based scoring system in consumer credit: making acquisition decisions for credit cards

Consumer credit scoring is one of the most successful applications of quantitative analysis in business with nearly every major lender using charge-off models to make decisions. Yet banks do not extend credit to control charge-off, but to secure profit. So, while charge-off models work well in rank-ordering the loan default costs associated with lending and are ubiquitous throughout the industry, the equivalent models on the revenue side are not being used despite the need. This paper outlines a profit-based scoring system for credit cards to be used for acquisition decisions by addressing three issues. First, the paper explains why credit card profit models—as opposed to cost or charge-off models—have been difficult to build and implement. Second, a methodology for modelling revenue on credit cards at application is proposed. Finally, acquisition strategies are explored that use both a spend model and a charge-off model to balance tradeoffs between charge-off, revenue, and volume.     

Intensity models and transition probabilities for credit card loan delinquencies

We estimate the probability of delinquency and default for a sample of credit card loans using intensity models, via semi-parametric multiplicative hazard models with time-varying covariates. It is the first time these models, previously applied for the estimation of rating transitions, are used on retail loans. Four states are defined in this non-homogenous Markov chain: up-to-date, one month in arrears, two months in arrears, and default; where transitions between states are affected by individual characteristics of the debtor at application and their repayment behaviour since. These intensity estimations allow for insights into the factors that affect movements towards (and recovery from) delinquency, and into default (or not). Results indicate that different types of debtors behave differently while in different states. The probabilities estimated for each type of transition are then used to make out-of-sample predictions over a specified period of time.     

Developing a measure of risk adjusted revenue (RAR) in credit cards market: Implications for customer relationship management

Current models of customer lifetime value (CLV) consider the discounted value of profits that a customer generates over an expected lifetime of relationship with the firm. This practice can be misleading in the financial services markets because it ignores the risk posed by the customer (such as delinquency and default). Specifically, in the credit card market, the correlation between revenue and risk is positive. Therefore, firms need to adjust a customer’s profits for the associated risk before developing a measure of customer lifetime value. We propose a new measure, risk adjusted revenue (RAR), that can incorporate multiple sources of risk and demonstrate the usefulness of the proposed measure in correctly assessing the value of a customer in the credit card market. The model can be extended to compute risk adjusted lifetime value (RALTV). We use the RAR metric to understand the effectiveness of different modes of acquisition, and of retention strategies such as affinity cards and reward cards. We find that both reward- and affinity-cardholders generate higher RAR than non-reward and non-affinity cardholders respectively. The ordering of different modes of acquisition with respect to RAR (in decreasing order) is as follows: Internet, direct mail, telesales, and direct selling.     

Lookahead scorecards for new fixed term credit products

Standard approaches to scorecard construction require that a body of data has already been collected for which the customers have known good/bad outcomes, so that scorecards can be built using this information. This requirement is not satisfied by new financial products. To overcome this lack, we describe a class of models based on using information about the length of time customers have been using the product, as well as any available information which does exist about true good/bad outcome classes. These models not only predict the probability that a new customer will go bad at some time during the product's term, but also evolve as new information becomes available. Particular choices of functional form in such models can lead to scorecards with very simple structures. The models are illustrated on a data set relating to loans.     

Modelling credit risk of portfolio of consumer loans

One of the issues that the Basel Accord highlighted was that, though techniques for estimating the probability of default and hence the credit risk of loans to individual consumers are well established, there were no models for the credit risk of portfolios of such loans. Motivated by the reduced form models for credit risk in corporate lending, we seek to exploit the obvious parallels between behavioural scores and the ratings ascribed to corporate bonds to build consumer-lending equivalents. We incorporate both consumer-specific ratings and macroeconomic factors in the framework of Cox Proportional Hazard models. Our results show that default intensities of consumers are significantly influenced by macro factors. Such models then can be used as the basis for simulation approaches to estimate the credit risk of portfolios of consumer loans.     

基于客户信用度的物流配送车辆路径问题研究

针对当前城市物流配送过程中普遍存在的客户中途取消订单、无故退换货等交易违约问题,引入客户信用度的测度方法。根据客户历史交易违约数据计算客户信用值,并转化求解客户信用度,构建了包含车辆配送成本、租赁成本以及违反时间窗惩罚成本的配送路径优化模型。设计了一种遗传(GA)-禁忌搜索(TS)混合算法进行模型求解,在算法过程中应用精英保留策略进行循环迭代寻优。结合重庆某外卖物流配送网络的实例数据,验证了模型和算法的有效性和可行性。实验结果给出了不同服务策略下的物流配送调度方案,并进行了基于客户信用度的客户配送服务序列调整比较和敏感度分析。研究表明客户信用等级的合理划分可以有效降低物流配送成本和提高客户服务水平。     

Bankruptcy prediction by generalized additive models

We compare several accounting‐based models for bankruptcy prediction. The models are developed and tested on large data sets containing annual financial statements for Norwegian limited liability firms. Out‐of‐sample and out‐of‐time validation shows that generalized additive models significantly outperform popular models like linear discriminant analysis, generalized linear models and neural networks at all levels of risk. Further, important issues like default horizon and performance depreciation are examined. We clearly see a performance depreciation as the default horizon is increased and as time goes by. Finally a multi‐year model, developed on all available data from three consecutive years, is compared with a one‐year model, developed on data from the most recent year only. The multi‐year model exhibits a desirable robustness to yearly fluctuations that is not present in the one‐year model. Copyright © 2006 John Wiley & Sons, Ltd.