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.     

An empirical comparison of conventional techniques,neural networks and the three stage hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) model for credit scoring analysis: The case of Turkish credit card data

The number of Non-Performing Loans has increased in recent years, paralleling the current financial crisis, thus increasing the importance of credit scoring models. This study proposes a three stage hybrid Adaptive Neuro Fuzzy Inference System credit scoring model, which is based on statistical techniques and Neuro Fuzzy. The proposed model’s performance was compared with conventional and commonly utilized models. The credit scoring models are tested using a 10-fold cross-validation process with the credit card data of an international bank operating in Turkey. Results demonstrate that the proposed model consistently performs better than the Linear Discriminant Analysis, Logistic Regression Analysis, and Artificial Neural Network (ANN) approaches, in terms of average correct classification rate and estimated misclassification cost. As with ANN, the proposed model has learning ability; unlike ANN, the model does not stay in a black box. In the proposed model, the interpretation of independent variables may provide valuable information for bankers and consumers, especially in the explanation of why credit applications are rejected.     

基于稀疏主成分的我国上市公司信用风险评价与预测

把我国2016-2018年沪深Ａ股上市公司中164家ST公司作为信用违约样本,492家非ST上市公司作为非违约样本进行实证研究.从营运能力、偿债能力、盈利能力和成长能力等4个方面选取了25个财务指标,然后运用稀疏主成分方法提取主成分因子,并加入公司规模、第一大股东持股比例和股权质押3个非财务指标,作为Logistic回归模型的输入参数.在此基础上构建Logistic模型进行信用风险评价和预测.     

基于随机市场需求的供应链融资模式研究

传统供应链融资模型大都在线性市场需求情形下分析零售商的商业信用、债权融资等内外部融资模式。本文同时了考虑零售商的股权融资、债权融资以及商业信用融资模式, 并引入随机市场需求因素, 针对一个供应商和两个具有资金约束零售商组成的两级供应链, 分析债权股权融资比例、商业信用等因素对零售商融资策略的影响, 并构建基于随机市场需求的融资模型;进一步, 利用数值示例和敏感性分析对此融资模型进行深入探讨。研究发现:当债权融资比例小于某临界值时, 零售商债权融资比例与订购量正相关, 反之债权融资比例与订购量负相关;对于一个服从均匀分布函数的随机市场需求而言, 若供应链采用外部融资模式, 那么随着其债权融资比例的增大, 利润将逐渐增加;若零售商采用商业信用融资模式, 那么其融资利率与利润负相关。相关研究结论对于供应链上中小企业融资模式的选择具有重要理论指导意义和实际引用价值。     

交通拥堵管理中可交易电子券方案的公平性分析

利用损失厌恶理论中的参照依赖模型,构建用户的感知出行成本函数,在固定需求的交通网络中加入电子券交易费用率,建立均衡条件下的变分不等式模型。通过模拟仿真,说明市场交易费用率会影响电子券交易市场,政府可通过调节交易费用率提高电子券方案公平性。选取路网中所有起讫对间出行成本变化率波动的加权平均值,度量可交易电子券方案的公平性,综合考虑最小化系统出行总成本和最大化方案公平性两个目标,构造效用函数,分析不同权重下市场交易费用率对可交易电子券方案的影响,以期对电子券方案的公平性进行优化。     

Data mining feature selection for credit scoring models

The features used may have an important effect on the performance of credit scoring models. The process of choosing the best set of features for credit scoring models is usually unsystematic and dominated by somewhat arbitrary trial. This paper presents an empirical study of four machine learning feature selection methods. These methods provide an automatic data mining technique for reducing the feature space. The study illustrates how four feature selection methods—‘ReliefF’, ‘Correlation-based’, ‘Consistency-based’ and ‘Wrapper’ algorithms help to improve three aspects of the performance of scoring models: model simplicity, model speed and model accuracy. The experiments are conducted on real data sets using four classification algorithms—‘model tree (M5)’, ‘neural network (multi-layer perceptron with back-propagation)’, ‘logistic regression’, and ‘k-nearest-neighbours’.     

A comparison of neural networks and linear scoring models in the credit union environment

The purpose of the present paper is to explore the ability of neural networks such as multilayer perceptrons and modular neural networks, and traditional techniques such as linear discriminant analysis and logistic regression, in building credit scoring models in the credit union environment. Also, since funding and small sample size often preclude the use of customized credit scoring models at small credit unions, we investigate the performance of generic models and compare them with customized models. Our results indicate that customized neural networks offer a very promising avenue if the measure of performance is percentage of bad loans correctly classified. However, if the measure of performance is percentage of good and bad loans correctly classified, logistic regression models are comparable to the neural networks approach. The performance of generic models was not as good as the customized models, particularly when it came to correctly classifying bad loans. Although we found significant differences in the results for the three credit unions, our modular neural network could not accommodate these differences, indicating that more innovative architectures might be necessary for building effective generic models.     

基于KMV模型的我国上市公司信用风险研究

在KM V框架的基础上对股权价值计算方法进行了改进,通过改进后的方法,计算出1999年至2006年各年所有上市公司的违约距离、理论违约率、企业价值、股权价值等指标数据.从分析的结果来看,上市公司规模对信用风险有一定影响,上市公司规模越大,信用风险越小,公司规模越小,信用风险越大.从违约风险的变化情况看,2003—2006年上市公司的违约距离呈下降态势,说明近年来上市公司的违约风险加大.对比沪深300上市公司股改前和股改后信用状况,发现股改前后信用状况有显著不同,股改后上市公司的违约风险变大.通过违约距离的敏感性分析,认为股权价值波动率对违约距离最敏感.     

A multi-period bank portfolio management program

We describe a bank portfolio management program based on the complete Markowitz model, which explicitly treats risk due to unanticipated fluctuations in interest rate. Our program takes into account both inter-temporal and intra-temporal covariance. The major result of this approach is that, for the same expected return, our model yields a portfolio with significantly smaller risk than that determined by an index model. For the same risk level, our method yields a portfolio with higher expected yield. The model employs a rolling planning horizon, with time periods in the planning horizon of arbitrary length. A novelty in the model is that it permits inter-temporal transactions in the portfolio's securities by generating dummy securities to represent every possible transaction over the planning horizon. The output from the model consists of a list of portfolio strategies showing the expected after-tax return and the 1% worst case yield for each strategy. We also present an illustrative example, using real data from a large Pennsylvania bank, and compare the results from our model to the simpler variance-only and index models. The principles upon which the model is based are sufficiently general to allow the program to be expanded into a general asset-liability balance sheet management program.     

European generic scoring models using survival analysis

Credit scoring discriminates between ‘good’ and ‘bad’ credit risks to assist credit-grantors in making lending decisions. Such discrimination may not be a good indicator of profit, while survival analysis allows profit to be modelled. The paper explores the application of parametric accelerated failure time and proportional hazards models and Cox non-parametric model to the data from the retail card (revolving credit) from three European countries. The predictive performance of three national models is tested for different timescales of default and then compared to that of a single generic model for a timescale of 25 months. It is found that survival analysis national and generic models produce predictive quality, which is very close to the current industry standard—logistic regression. Stratification is investigated as a way of extending Cox non-parametric proportional hazards model to tackle heterogeneous segments in the population.     

A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach

Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided.     

债券投资组合业绩归因的多期实证研究

目前国内对投资组合的业绩归因研究主要从管理者层面着手,将超额收益的来源归结为择时能力和选股能力,但这并不适用于债券投资。本文基于Campisi模型,对债券定价公式进行分解,从债券自身的特性来研究组合的超额收益来源,并结合GRAP跨期处理方法,形成多期业绩归因模型,对长期债券投资组合进行归因分析。相对于单期的归因模型,多期归因模型可以对任意一段时间内投资组合的超额收益进行归因,而不是单期归因项的简单加总。本文以中证全债指数为基准组合,对32只债券构成的投资组合进行实证研究,结果表明模型符合市场情况和实际操作情况。因此本文提出的多期业绩归因研究具有实用性。     

面向顾客资产的三维顾客细分模型及其应用

简单依照顾客利润贡献对顾客细分未能充分考虑顾客的无形贡献,会低估顾客对企业的价值.从面向顾客资产的视角进行顾客细分,可以兼顾到顾客当前的利润贡献和顾客的潜在有形和无形贡献,从而提出基于顾客当前显性贡献、潜在显性贡献和潜在隐性贡献三维顾客细分模型及度量方法,并结合实证阐述顾客细分方法的实现过程.     

Using equity options to imply credit information

The evolution of credit derivatives has inspired many researchers to investigate the behaviour of credit spreads. Today the growing consensus is that the equity option market provides sufficient information to estimate latent credit parameters. Hull et al. (J. Credit Risk 1(1):3–28, 2005) propose a clever approach to estimate credit spreads from the equity option market. In this paper we first perform a time series analysis to test the conjecture of an existing relationship between credit spreads and implied equity volatility and find strong evidence of a positive relationship. We also propose an extension to Hull et al.’s paper that significantly improves credit spread estimation.     

Forecasting Loss Given Default models: impact of account characteristics and the macroeconomic state

On the basis of two data sets containing Loss Given Default (LGD) observations of home equity and corporate loans, we consider non-linear and non-parametric techniques to model and forecast LGD. These techniques include non-linear Support Vector Regression (SVR), a regression tree, a transformed linear model and a two-stage model combining a linear regression with SVR. We compare these models with an ordinary least squares linear regression. In addition, we incorporate several variants of 11 macroeconomic indicators to estimate the influence of the economic state on loan losses. The out-of-time set-up is complemented with an out-of-sample set-up to mitigate the limited number of credit crisis observations available in credit risk data sets. The two-stage/transformed model outperforms the other techniques when forecasting out-of-time for the home equity/corporate data set, while the non-parametric regression tree is the best performer when forecasting out-of-sample. The incorporation of macroeconomic variables significantly improves the prediction performance. The downturn impact ranges up to 5% depending on the data set and the macroeconomic conditions defining the downturn. These conclusions can help financial institutions when estimating LGD under the internal ratings-based approach of the Basel Accords in order to estimate the downturn LGD needed to calculate the capital requirements. Banks are also required as part of stress test exercises to assess the impact of stressed macroeconomic scenarios on their Profit and Loss (P&L) and banking book, which favours the accurate identification of relevant macroeconomic variables driving LGD evolutions.     

A Dynamic Model for Strategically Allocating Retail Space

The allocation of shelf space is a major determinent of a retailer's sales and operating costs. All the existing models of this problem focus on static optimization. But to the retailer, anticipating and adapting to new tastes and changing product life cycles is the central strategic problem. This paper shows how the static model can be extented to incorporate such market dynamics. The new model is more plausible than earlier static models in encouraging the retailer to allocate more space to new products and divest earlier from declining ones.     

On pricing of credit spread options

This paper describes and analyses different pricing models for credit spread options such as Longstaff–Schwartz, Black, Das–Sundaram and Duan (GARCH-based) models. The first two models, Longstaff–Schwartz and Black, assume respectively a mean-reverting dynamic and a lognormal distribution for the spread and are representative of the so-called “spread models”. Such models consider the spread as a unique variable and provide closed form solutions for option pricing. On the contrary Das–Sundaram propose a recursive backward induction procedure to price credit spread options on a bivariate tree, which describes the dynamic of the term structure of forward risk-neutral spread and risk-free rate. This model belongs to the class of structural models, which can be used to price a wider range of credit risk derivatives. Finally, we consider the pricing of credit spread options assuming a discrete time GARCH model for the spread.     

Logistic回归模型在信用风险分析中的应用

通过运行SPSS,建立L og istic回归信用评价模型(cred it eva luation m odel),用来对中国2000年106家上市公司进行两类模式分类,这两类模式是指按照公司的经营状况分为“差”和“正常”两个小组.对每一家上市公司,考虑其经营状况的4个主要财务指标:每股收益、每股净资产、净资产收益率和每股现金流量.仿真结果表明,L og istic回归信用评价模型对总体106个样本,判别准确率达到99.06%.此外,本文的研究结果还发现,当利用SPSS的D iscrim inan t给出的模型系数建立的线性判别分析模型和利用SPSS的M u ltinom ia lL og istic给出的模型参数建立的L og istic回归模型,L og istic回归模型的判别结果不如线性判别模型.但如果剔除不合格的样本,或是将样本数据规格化,则可以提高L og istic回归模型的分类准确率.     

Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities

Guaranteed lifetime withdrawal benefits (GLWB) embedded in variable annuities have become an increasingly popular type of life annuity designed to cover systematic mortality risk while providing protection to policyholders from downside investment risk. This paper provides an extensive study of how different sets of financial and demographic parameters affect the fair guaranteed fee charged for a GLWB as well as the profit and loss distribution, using tractable equity and stochastic mortality models in a continuous time framework. We demonstrate the significance of parameter risk, model risk, as well as the systematic mortality risk component underlying the guarantee. We quantify how different levels of equity exposure chosen by the policyholder affect the exposure of the guarantee providers to systematic mortality risk. Finally, the effectiveness of a static hedge of systematic mortality risk is examined allowing for different levels of equity exposure.     

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.