1、 外文翻译 原文 Modeling Credit Risk of Portfolio of Consumer Loans Material Source: Mathematics and Computers in Simulation archive Volume 79 , Issue 8 (April 2009) table of contents Author： Madhur Malik and Lyn Thomas One of the issues that the Basel Accord highlighted was that though techniques for esti
2、mating 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 will seek to exploit the obvious para
3、llels between behavioral 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 si
4、gnificantly 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. In credit scoring the main interest is in developing a scoring system which can correctly rank the customers in terms of their rel
5、ative default risk so that the customers above some cut-off score are more or less riskier than those who are below. Credit scoring models can broadly be classified into two types, application scoring and behavioral scoring. The objective of both is to classify whether a customer will default (Bad)
6、or not default (Good) in a given time period, which leads to estimates of probability of default (PD) of the customer in that period. Application scores are used to predict customers default risk, say 12 months in future, at the time of application made for the loan. In application scoring, past cus
7、tomers are classified as Good or Bad based on whether they defaulted, which usually means 90+ days delinquent, during the first 12 months of the starting of the loan. The information available at the time of application in the form of application variables and credit bureau records is then used to e
8、stimate the probability of being good/bad in the given time period. Behavioral scoring is similar in principal to application scoring except that in behavioral scores we observe the recent, say last one year, payment and purchase behavior of customers who have been granted loan and use this informat
9、ion in addition to the information available for application scoring to predict the probability of default in next twelve months or some other fixed time horizon. As the name suggests in behavioral scoring the individuals behavior with a particular lender and on a specific product is considered in a
10、ddition to the information the lender has through credit bureaus. The above estimates of default probabilities are then transformed into scores, which are used as a basis to accept or reject a customer for credit, depending on the cut-off decided by the banks for application scorecards or to make le
11、nding decisions on current customers, like increasing/decreasing credit limit, offering new financial products, offering new interest rates, based on behavioral scores. Lenders update their behavioral scores monthly by using the most recent information on their customers. With the advent of the Base
12、l II banking regulation (BCBS, 2004) it is not just enough to correctly rank customers according to their default risk but also one needs to measure accurately the PD, as the predicted PD are used to calculate the minimum capital needed to set aside for the portfolio of consumer loans. Moreover PD h
13、as to be predicted not just at an individual level but also for segments of the loan portfolio) The limitation of the above approach of developing scorecards is that it uses a snapshot of customers who joined say during certain months in calendar time (for application score) or who are on books duri
14、ng certain months in calendar time (for behavioral scores), which does not take care of the changes in economic conditions and the quality of loans over time. Motivated by the reduced form models for portfolio credit risk in corporate lending (LAN do, 1994; Duffle, Santa and Wang, 2007) we will seek
15、 to exploit the obvious parallels between behavioral scores and the ratings ascribed to corporate bonds to build consumer lending equivalents. Similar recent studies conducted in corporate credit risk include (Duffle, Santa, and Wang, 2007) who studied multi-period corporate default prediction with
16、time varying covariates. They exploit the time-series dynamics of the macroeconomic and firm-specific covariates and combine these with a short-horizon default model to estimate the likelihood of default over several future periods. (Campbell, Holster, and Szilagyi,2007) in their recent study do not
17、 model the time-series evolution of the predictor variables but instead estimate separate lo gic models for firm default probabilities at short and long horizons. (Figlewski, Frydman and Liana, 2007) fit Cox intensity models for credit events, including defaults or major upgrades and downgrades in c
18、redit rating. Their models incorporate both firm-specific factors related to a firms credit rating history and a broad range of macroeconomic variables. Their results show that, in addition to being strongly influenced by ratings related factors, intensities of occurrence of credit evens are signifi
19、cantly affected by macroeconomic factors. (Shum way, 2001) uses a discrete duration model with time dependent covariates and demonstrates that hazard models are statistically superior to static models that do not take into account the fact that a firm is exposed to the risk of a credit event over mu
20、ltiple periods. However there has been no work on building duration models for the credit risk of portfolios of consumer loans. In this paper, we incorporate consumer specific ratings (behavioral score) and macroeconomic factors in the framework of Cox Proportional Hazard to build a model for custom
21、ers default probability in the next twelve months, given all the current information available on an individual along with the values of macroeconomic factors for one year ahead. The results of our analysis show that default intensities of consumers are significantly influenced by macroeconomic fact
22、ors and the time of origination of the loan. This shows that the information contained in behavioral score, which is developed on the history of loans who started during a certain period in calendar time, could not capture in full the driving force behind the dynamics of default behavior. Finally, w
23、e will demonstrate how our model of individual consumers default risk can be used to simulate the distribution of defaults in a portfolio of consumer loans. The development of our model will not affect the rules governing Basel II but could be expected to have an impact on the way banks segment and
24、stress test their portfolios under its regulations. Such models will also be of considerable use in the segmentation and pricing of portfolios of consumer loans for securitization purposes an area where the theories of corporate and consumer risk management should, but as yet do not, meet. The idea
25、of employing survival analysis for building credit-scoring models was first introduced by (Marian, 1992) and then developed further by (Thomas et al, 1999 and 2002). Thomas et al. (1999) compared performance of exponential, Waybill and Coxs nonparametric models with logistic regression and found tha
26、t survival-analysis methods are competitive with, and sometimes superior to, the traditional logistic-regression approach. In the next section, we shall briefly discuss the notion of hazard rate and survival probability, and the theory associated with the Cox proportional hazard rate model. We then
27、develop a hazard rate model to predict future hazard rates of customers conditional on the information on customers available today. These predicted hazards are then combined to predict the probability of default for twelve months ahead. Finally, we discuss the results of the simulations to construc
28、t the default distribution of portfolio of loans and draw some conclusion. 译文 规划消费贷款的有价证券的信贷风险 资料来源 :数学计算机模型文档 2009 年 4 月份第 8 期 79 卷 作 者： Madhur Malik and Lyn Thomas 巴塞尔协议中的其中一条协议指出，虽然用于评估违约可能性的方法以及针对个体消费者的贷款的信贷风险体系建立了，但是此类贷款的有价证券的信贷风险的模式还没形成。由于企业贷款中信贷风险的降低，我们将探索如何利用行为得分和公司债券评定等级的显著相似点来构建消费者借贷等价物。我们
29、结合消费者特定等级和考克斯比例风险模型框架的宏观经济因素。这些模型是评测贷款的有价证 券的信贷风险的模拟方法的基础。 在信用评分中，主要利益在于发展一个能准确地根据客户的相对的违约风险将其排序的评分系统，因此高于分数分界点的客户或多或少比那些低于分数分界点的客户更有风险。广义上，信用评分分为两大类：申请得分和行为得分。两者的目的都是区分一个客户在给定的期限内是否会违约，从而导致在期限内客户违约可能性的评估。申请得分用于预测客户的违约风险，老客户的分类是根据他们是否违约。例如在未来的 12 个月内申请贷款，在贷款的第一个 12 个月期间达到了 90+天的拖欠账款才算违约。此信息在申请期间以应用变
30、量的形式 可获得。随后，信用局记录则用来评测指定期间内违约的可能性。行为得分在原则上类似于申请得分，除了我们目前所观察到的一个现象，那就是客户的付款和购买行为，这些客户是被授予贷款权利，能够利用这些不属于申请得分的信息来预测在未来 12 个月或者一些其它限制时期内违约的可能性。上述对于违约可能性的评价被转化成分数，这分数则作为接受或拒绝一个客户申请贷款的依据。也就是说依据银行的申请积分卡或银行对于目前客户所做的贷款决策，比如增加 /降低贷款限制，提供新金融产品，提供新利率，这些政策都是基于行为得分。贷方要利用客户的信息每月 更新行为得分。 随着巴塞尔 II 银行管理条例（巴塞尔银行监管委员会，
31、 2004）的出现，仅仅根据客户的违约风险来排列是远远不够的，而应该需要精确地审核客户的外交护照因为外交护照是用于计算客户贷款的有价证券所需的最小资金，并且，外交护照不仅仅是个人层面的，而且是贷款有价证券的一部分。上述发展积分卡的方法的缺陷在于它抓住了在特定时期内加入的客户（为了申请得分）或者在特定时期内登记的客户（为了行为得分），这种方法忽略了经济状况的变化以及随 着时间推移而不同的贷款特征。由于企业贷款中信贷风险的降低，我们将探索如何利用行为得分和公司债券评定等级的显著相似点来构建消费者借贷等价物。目前研究企业贷款风险是达菲 ,财田 ,王，他们研究了随着时间而改变的多期企业违约预测。他们利
32、用宏观经济的时序动态以及公司特有的变量 与短期违约案例结合来估算在未来几个阶段中违约的可能性。 （ Campbell， Hilscher, Szilagyi,2007）在他们最近的研究中并没有规划预测变量的时序发展而是估算独立的在短期以及长期内违约可能性的对数单位模型。（ Figlewski,Frydman 和Liang， 2007）在贷款事件中锁定了考克斯强度模型，包括违约或主要更新以及信用级别的降级。他们的模型结合了企业特有的与企业信用级别相关联的因素和宏观经济变量的广义范围。他们所得出的结论说明，贷款事件频繁发生不仅仅受到等级因素的深刻影响，还受到了宏观经济因素的显著影响。（ Shumw
33、ay， 2001）运用离散时间模型来陈述风险模式在统计上优越于静态模式。这种静态模式是不考虑在多时期内公司所遭受的信贷风险事件。然而，在构建期间模式上并没有实际工作。 在这篇论文中，我们结合了消费者特定等级（行为 得分）和考克斯比例风险框架中的宏观经济因素来构建一个模式，这种模式应用于在未来 12 个月内，假定所有的信息提前一年可获得的情况下客户违约的可能性。我们分析所得的结论表明消费者的违约密度明显受宏观经济因素以及贷款起始时间的影响。这就表明包含在行为得分内的信息不能完全捕获在违约行为背后的驱动力。最终，我们将阐述个体消费者违约风险模式是如何模拟消费者贷款的有价证券违约分布。 发展这种模式
34、不会影响巴塞尔 2 管理条例，但是将会影响到银行划分的途径以及强调其有价证券。类似的模式也运用于划分以及消费者贷款有价证券的标价。 在 构建贷款得分模式中运用存活分析的想法第一次被（ Narain， 1992）介绍进来，随后（ Thomas et al,1992 和 2002）进一步发展。 Thomas et al.(1999)运用对数衰退对指数，韦伯以及考克斯非参数模式进行比较，发现存活分析方法比传统的对数衰退法更有竞争力，有时更加优越。在接下来的章节中，我们将简要地讨论下风险率的概念，存活可能性以及跟考克斯比例风险率模式有关的理论。随后，我们研发一个风险率模式来预测特定客户的风险率。结合这些预测出来的风险来预测 12 个月内违约的可能性。最后，我们将讨 论模拟实验的结果来构建贷款有价证券的违约分布以及得出一些结论。
