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.     

On the customer lifetime value: a mathematical perspective

The customer lifetime value (CLV) is an important concept increasingly considered in the field of general marketing and in the management of firms, of organizations to increase the captured profitability. It represents the total value that a customer produces during his or her lifetime, or better represents the measure of the potential profit generating by a customer. The companies use the customer lifetime value to segment customers, analyze probability of churn, allocate resources or formulate strategies and, therefore, they increasingly derive revenue from the creation and from sustenance of long-term relationships with their customers. For this reason, the customer lifetime value is increasingly considered a touchstone for the management of customer relationships. In this article, the authors deepen the concept and use of customer lifetime value and present some mathematical models for its determination. There is many models for this purpose but most of them are theoretic, complex and not applicable. Though not exhaustive, the major contribution of this paper is that it provides a general mathematical formulation to estimate the CLV and that it has a context less specific compared to papers, present in literature, on the customer lifetime.     

Customer retention: a behavioural model

One of the main problems currently facing CTedit-card issuersis the increasing number of cardholders who are using theircards less often (i.e. attrition) and/or returning their cards(closures). This problem is of particular concern as the totalnumber of credit cards held by consumers is declining (by approximately0.6 per cent per month in 1992) and the number of new applicantsis also running at an all time-low (less than 1 per cent permonth in 1992). Most of the published literature in the broad area of creditcards looks at credit scoring, rather than the need for cardissuers to identify and retain a profitable portfolio of cardcustomers. The overall objective of our research is ‘segmentationfor customer retention’, and this paper aims to identifythe characteristics of card customers who initiate the closureof their accounts Linear discriminant analysis is applied toa sample of approximately 17,000 UK holders of bank credit cards,using various behavioural and sociodemographic variables, andtested on a holdout sample of 10,000 cases.     

Analysis of the effectiveness of manufacturer-sponsored retailer gift cards in supply chains

Some manufacturers sponsor “free” retailer gift cards to be given to consumers who purchase their products. These gift cards are paid for by the manufacturer and are redeemable on all products at the retailer. We develop a model of such a supply chain. We analyze cases in which the gift cards’ redemption rate is constant or increasing in gift card value. The results indicate that in addition to the redemption rate and consumers’ valuation for gift card dollars, the profitability of manufacturer-sponsored gift cards depends on the average gross margin of the retailer and the type of purchases consumers make with gift cards. Furthermore, we show that under certain conditions, free gift cards will increase the expected profits of the retailer and manufacturer as well as decrease the retail price of the product. These conditions include a retailer with large average gross margin and consumers using gift cards to purchase products they would not buy with cash otherwise. Furthermore, all consumers, including those who do not redeem the gift card, are more likely to benefit from a reduced retail price when their probability of redeeming the gift card after purchase is equal to their estimated redemption probability at purchase time. We show the conditions under which gift cards are more profitable than cash mail-in rebates. We develop an incentive scheme to improve the performance of supply chains with gift cards.     

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.     

An improved customer lifetime value model based on Markov chain

Firms are increasingly looking to provide a satisfactory prediction of customer lifetime value (CLV), a determining metric to target future profitable customers and to optimize marketing resources. One of the major challenges associated with the measurement of CLV is the choice of the appropriate model for predicting customer value because of the large number of models proposed in the literature. Earlier models to forecast CLV are relatively unsuccessful, whereas simple models often provide results which are equivalent or even better than sophisticated ones. To predict CLV, Rust et al. (2011) proposed a framework model that performs better than simple managerial heuristic models, but its implementation excludes cases where customer's profit is negative and does not handle lost‐for‐good situations. In this paper, we propose a modified model that handles both negative and positive profits based on Markov chain model (MCM), hence offering a greater flexibility by covering always‐a‐share and lost‐for‐good situations. The proposed model is compared with the Pareto/Negative Binomial Distribution (Pareto/NBD), the Beta Geometric/Negative Binomial Distribution (BG/NBD), the MCM, and the Rust et al. (2011) models. Based on customer credit card transactions provided by the North African retail bank, an empirical study shows that the proposed model has better forecasting performance than competing models. Copyright © 2014 John Wiley & Sons, Ltd.     

Recharge and consolidation decisions for stored value cards with an application to Beijing public transit

Stored value cards (SVCs) are ubiquitous, but little investigation has been undertaken into actual and desired replenishment behaviour, or the economic impact of card consolidation on consumers and service providers (such as retailers and public transit authorities). We develop classic and joint replenishment economic order quantity models for reloadable SVCs where the card value may be lost, for example, through theft or breakage. We extend the models to consider potential benefits of discounts, and providing refunds upon card loss (via external recording of card value). We also show how SVC consolidation and service expansion decisions can benefit consumers and service providers. As a case study, we utilise the Beijing subway system ‘YiKaTong’ card to demonstrate cost optimisation at the consumer and enterprise level. Direct observations of recharging and a survey suggest that commuters take the likelihood of card loss into account and are risk averse. The results of the work help to explain and predict consumer recharge behaviour, and should assist service providers evaluating decisions relating to their market scope, technology, pricing, and service capacity.     

Credit spreads, endogenous bankruptcy and liquidity risk

In this paper, we consider a bond valuation model with both credit risk and liquidity risk to show that credit spreads are not negligible for short maturities. We adopt the structural approach to model credit risk, where the default triggering barrier is determined endogenously by maximizing equity value. As for liquidity risk, we assume that bondholders may encounter liquidity shocks during the lifetime of corporate bonds, and have to sell the bond immediately at the price, which is assumed to be a fraction of the price in a perfectly liquid market. Under this framework, we derive explicit expressions for corporate bond, firm value and bankruptcy trigger. Finally, numerical illustrations are presented.     

信贷人存货质押贷款中最优质物甄别合同研究

存货抵押贷款中,信用风险主要来源于抵押物价格和流动性风险,信贷人确定适当的利率和贷款价值比能够有效缓释信用风险。对于已知抵押物价格风险和流动性风险,以信贷市场结构作为约束条件,求解出使信贷人期望利率收益最大化合同利率和贷款价值比。当抵押物流动性风险增加时,信贷人最优贷款合同应该是名义利率和贷款价值比均下降;对于抵押物价格波动满足正态分布的情况,若抵押物价格风险增大,信贷人最优贷款合同应该是名义利率和贷款价值比均上升。数值算例的结果基本验证了以上结论,并与现实情况相接近。     

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.     

Reverse supply chain coordination by revenue sharing contract: A case for the personal computers industry

Products that are not recycled at the end of their life increasingly damage the environment. In a collection – remanufacturing scheme, these end-of-life products can generate new profits. Designed on the personal computers industry, this study defines an analytical model used to explore the implications of recycling on the reverse supply chain from an efficiency perspective for all participants in the process. The cases considered for analysis are the two- and three-echelon supply chains, where we first look at the decentralized reverse setting followed by the coordinated setting through implementation of revenue sharing contract. We define customer willingness to return obsolete units as a function of the discount offered by the retailer in exchange for recycling devices with a remanufacturing value. The results show that performance measures and total supply chain profits improve through coordination with revenue sharing contracts on both two- and three-echelon reverse supply chains.     

Modelling profitability using survival combination scores

The paper presents the first empirical investigation of the relationship between present value of net revenue from a revolving credit account and times to default and to second purchase. The analysis is based on the data for a store card which is used to buy ‘white’ durable goods in Germany. It is demonstrated that there exists a relationship between the above given measures. It appears that there is a scope for improving profit if an application for a store card is assessed by using a model which estimates the revenue and includes the survival probability of default and the survival probability of second purchase (a survival combination model) rather than merely a static probability of default predicted by a logistic regression.     

基于公路运力信用结构的供应链金融授信分析

文章首先从信用入手,分析供应链金融增信的要素,剖析公路运力信用结构组成,构建主体信用、交易信用及监管信用的具体指标,并明确三者与供应链金融授信额度的关系。其次,以融资自偿为基础,通过分析公路运力成本的构成及统计数据,确定出授信比率的基础值以及监管信用对基础值的影响。通过物流企业货量服从正态分布的特征,模拟出公路运力运费收入以及交易信用对运费收入的影响。最后,结合两者构建出受主体信用现金流约束检验的授信额度模型,并就金融机构风险偏好为风险规避的情况进行了算例分析。     

马尔可夫链模型在信用卡账户行为变化预测中的应用

对信用卡账户行为变化的监控是降低信用卡风险的关键.论文在构建马尔可夫模型的基础上,讨论了在信用卡账户无新增贷款、新增贷款固定不变和新增贷款发生周期性变化的情况下,如何预测信用卡账户不同状态的金额、已偿付态和坏账态的金额、全部应收款的现值及它们的方差计算等内容,为信用卡账户行为变化的预测、管理提供了方法和依据.     

考虑网络平台服务的电子零售商运营模式选择

针对供应商竞争情形下拥有网络平台的电子零售商运营模式选择问题,考虑网络平台服务对网络平台绩效的影响,研究电子零售商运营模式决策与供应商销售模式选择。本文构建了网络平台服务内生的供应商竞争模型,识别电子零售商选择转销模式或平台模式运营的条件,揭示实现帕累托改进的收益分享契约特征。研究结果显示:当产品间竞争不激烈且服务增值成本指数相对较高时,若收益分享比例小于某临界值,电子零售商偏好平台模式运营,且平台模式中网络平台服务水平高而零售价格低;当产品间竞争较激烈时,电子零售商总偏好转销模式运营;当产品市场规模不高且收益分享比例在某区域时,电子零售商和供应商都偏好平台模式。     

灰色市场条件下基于收益共享契约的供应链协调

考虑灰色市场条件下由一个制造商和两个分别处于不同国家的分销商构成的供应链,分别分析了完全分散化、部分分散化和集中化决策下的供应链定价策略。考察了各种决策模式下,消费者对灰市产品价值的认可程度对制造商定价策略的影响。通过比较得出分散化和部分分散化决策下的最优定价策略偏离集中化决策下的最优定价策略。并以供应链集中化决策下的利润为基准,通过引入收益共享契约针对灰色市场条件下的完全分散化和部分分散化供应链进行协调,并给出保证供应链节点企业达到帕累托改进的收益分享系数取值范围。最后通过数值分析给出了消费者对灰市产品价值的认可程度与供应链利润、灰市产品销量及收益分享系数之间的关系。     

基于报表数据的上市公司顾客资产测量与提升——中国联通公司的应用研究

顾客资产体现企业在市场竞争中获取顾客资源的能力,本研究旨在利用报表数据对上市公司的顾客资产进行测量,并依据测量结果提出提升策略。首先,运用Matlab编程模拟上市公司的每期期末顾客存量适用的技术替代模型,进而求得顾客资产。其次,依据β转换模型原理估算企业现有顾客的终身价值总和,在同时考虑顾客的获取与流失的前提下求得顾客资产可持续比率。再次,依据顾客资产可持续比率和顾客资产的计算结果构建二维坐标图,以分析企业顾客资产的时间序列特征,作为提升顾客资产的依据。最后,将该方法在中国联通公司进行了应用。研究结果表明,该方法对上市公司的顾客资产测量和提升具有较好的适用性和可操作性。研究结果对于上市公司的顾客资产管理具有一定的参考价值。     

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。     

Trade credit competition between two retailers in a supply chain under credit-linked retail price and market demand

The paper considers a supply chain system in which the sole manufacturer supplies the same product to two retailers who compete in offering trade credit period to customers. Both the market demand and retail prices vary with the trade credit periods offered by the retailers. The manufacturer also provides a trade credit period to both the retailers to settle down their accounts. The net profit function of the supply chain is derived considering possible relationships among the trade credit periods offered by the manufacturer and the retailers and the time when each retailer receives the last payment from his customer. An algorithm is developed to find the optimal solution of the proposed model. From the numerical study, it is observed that a two-level trade credit financing can increase profits not only for the manufacturer and the retailers but also for the whole supply chain.     

Credit card pricing and impact of adverse selection

Variable pricing is one way of improving the profitability of credit cards when the price is the interest rate to be charged. However, choosing the appropriate price for each risk grade of default is not straightforward, as one of the main problems is adverse selection, when the lender finds that the borrowers who actually take a specific offer have a higher default rate than expected. We show that modelling the choice of credit card by the borrower as an auction process means that the winner's curse can lead to adverse selection. By modelling the way lenders use the credit score of a borrower in their pricing decision we are able to show that there is a simple relationship between the actual probability of a borrower repaying and what the successful lender believes this probability to be, regardless of the distribution of the errors caused by adverse selection. This allows one to assess the impact on profitability of these errors.