The economy and loss given default: evidence from two UK retail lending data sets

Loss given default (LGD) models predict losses as a proportion of the outstanding loan, in the event a debtor goes into default. The literature on corporate sector LGD models suggests LGD is correlated to the economy and so changes in the economy could translate into different predictions of losses. In this work, the role of macroeconomic variables in loan-level retail LGD models is examined by testing the inclusion of macroeconomic variables in two different retail LGD models: a two-stage model for a residential mortgage loans data set and an ordinary least squares model for an unsecured personal loans data set. To improve loan-level predictions of LGD, indicators relating to the macroeconomy are considered with mixed results: the selected macroeconomic variable seemed able to improve the predictive performance of mortgage loan LGD estimates, but not for personal loan LGD. For mortgage loan LGD, interest rate was most beneficial but only predicted better during downturn periods, underestimating LGD during non-downturn periods. For personal loan LGD, only net lending growth is statistically significant but including this variable did not bring any improvement to R².     

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.     

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.     

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.     

Cyclical adjustment of point-in-time PD

Banking regulation stipulates that to calculate minimum capital requirements a long-term average of annual default probability (PD) should be used. Typically, logistic regression is applied with a 12-month sample period to obtain retail PD estimates. Thus the output will reflect the default rate in the sample, and not the long-term average. The ensuing calibration problem is addressed in the paper by a ‘variable scalar methodology’, based on an actual application in a commercial bank. Using quarterly intra-bank loss data over 15 years, a state-space model of the credit cycle is estimated by a Kalman filter, resulting in a structural decomposition of the credit cycle. This yields an adjustment factor for each point in the cycle for each of two client segments. The regulatory compliance aspects of such a framework, as well as some practical issues are presented and discussed.     

Modeling credit portfolio derivatives,including both a default and a prepayment feature

Apart from heteronomy exit events such as, for example credit default or death, several financial agreements allow policy holders to voluntarily terminate the contract. Examples include callable mortgages or life insurance contracts. For the contractual counterpart, the result is a cash‐flow uncertainty called prepayment risk. Despite the high relevance of this implicit option, only few portfolio models consider both a default and a cancellability feature. On a portfolio level, this is especially critical because empirical observations of the mortgage market suggest that prepayment risk is an important determinant for the pricing of mortgage‐backed securities. Furthermore, defaults and prepayments tend to occur in clusters, and there is evidence for a negative association between the two risks. This paper presents a realistic and tractable portfolio model that takes into account these observations. Technically, we rely on an Archimedean dependence structure. A suitable parameterization allows to fit the likelihood of default and prepayment clusters separately and accounts for the postulated negative interdependence. Moreover, this structure turns out to be tractable enough for real‐time evaluation of portfolio derivatives. As an application, the pricing of loan credit default swaps, an example of a portfolio derivative that includes a cancellability feature, is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

P2P网贷违约人是否具有区域性特征——来自湖南省的例证

借助网络爬虫技术手段获取"人人贷"平台上借款人的各项信息,提取两个样本:分为全国随机样本和湖南省随机样本,构建二元Logit回归模型,分析其中对违约率有显著影响的变量.研究表明,负债收入比、借款期限、学历、房产、房贷、描述指数对违约行为有负向影响,而借款利率、车产、认证个数对借款者违约行为有正向影响.同时,通过对两个样本最终回归模型的比较,发现湖南省违约人特征与全国随机样本中体现的违约人特征基本一致,但其中较为特殊的是,在湖南拥有房产和车产不能作为网络借款人履约能力提升的标志.     

汽车消费、住房抵押贷款违约特性及对策

本通过对比住房抵押贷款和汽车消费贷款的违约特性，得出在利率由央行统一规定的条件下，对住房抵押贷款和汽车消费贷款，实行同样的首付款政策是不合理的，这导致目前汽车消费贷款的违约率居高不下。对于住房抵押贷款，银行可以适当降低首付款，来提高本银行住房抵押贷款在市场的竞争力，对于汽车消费贷款，可以通过采取提高汽车贷款首付款的措施，来降低违约率，控制抵押贷款风险。     

Efficient frontier cutoff policies in credit portfolios

Historically, account acquisition in scored retail credit and loan portfolios has focused on risk management in the sense of minimizing default losses. We believe that acquisition policies should focus on a broader set of business measures that explicitly recognize tradeoffs between conflicting objectives of losses, volume and profit. Typical business challenges are: ‘How do I maximize portfolio profit while keeping acceptance rate (volume, size) at acceptable levels?’ ‘How do I maximize profit without incurring default losses above a given level?’ ‘How do I minimize the risk of large loss exposures for a given market share?’ In this paper we are not concerned with which combination of objectives are appropriate, but rather focus on the cutoff policies that allow us to capture a number of different portfolio objectives. When there are conflicting objectives we show that optimal policies yield meaningful tradeoffs and efficient frontiers and that optimal shadow prices allow us to develop risk-adjusted tradeoffs between profit and market share. Some of the graphical solutions that we obtain are simple to derive and easy to understand without explicit mathematical formulations but even simple constraints may require formal use of non-linear programming techniques. We concentrate on models and insights that yield decision strategies and cutoff policies rather than the techniques for developing good predictors.     

Modelling credit risk with scarce default data: on the suitability of cooperative bootstrapped strategies for small low-default portfolios

Credit risk models are commonly based on large internal data sets to produce reliable estimates of the probability of default (PD) that should be validated with time. However, in the real world, a substantial portion of the exposures is included in low-default portfolios (LDPs) in which the number of defaulted loans is usually much lower than the number of non-default observations. Modelling of these imbalanced data sets is particularly problematic with small portfolios in which the absence of information increases the specification error. Sovereigns, banks, or specialised retail exposures are recent examples of post-crisis portfolios with insufficient data for PD estimates, which require specific tools for risk quantification and validation. This paper explores the suitability of cooperative strategies for managing such scarce LDPs. In addition to the use of statistical and machine-learning classifiers, this paper explores the suitability of cooperative models and bootstrapping strategies for default prediction and multi-grade PD setting using two real-world credit consumer data sets. The performance is assessed in terms of out-of-sample and out-of-time discriminatory power, PD calibration, and stability. The results indicate that combinational approaches based on correlation-adjusted strategies are promising techniques for managing sparse LDPs and providing accurate and well-calibrated credit risk estimates.     

Development and application of consumer credit scoring models using profit-based classification measures

This paper presents a new approach for consumer credit scoring, by tailoring a profit-based classification performance measure to credit risk modeling. This performance measure takes into account the expected profits and losses of credit granting and thereby better aligns the model developers’ objectives with those of the lending company. It is based on the Expected Maximum Profit (EMP) measure and is used to find a trade-off between the expected losses – driven by the exposure of the loan and the loss given default – and the operational income given by the loan. Additionally, one of the major advantages of using the proposed measure is that it permits to calculate the optimal cutoff value, which is necessary for model implementation. To test the proposed approach, we use a dataset of loans granted by a government institution, and benchmarked the accuracy and monetary gain of using EMP, accuracy, and the area under the ROC curve as measures for selecting model parameters, and for determining the respective cutoff values. The results show that our proposed profit-based classification measure outperforms the alternative approaches in terms of both accuracy and monetary value in the test set, and that it facilitates model deployment.     

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。     

基于银行下侧风险规避的第三方B2B平台激励策略研究

以电子仓单融资为例, 基于银行下侧风险规避角度, 研究联合授信和委托授信下当第三方B2B平台存在行为隐匿的道德风险时, 银行对B2B平台的激励策略设计问题。研究发现:B2B平台的最优努力水平随收益分配比例、回购比例的增大而减小, 随质押率、贷款利率、产品采购量、损失补偿比例的增大而增大;同时银行为规避违约风险, 需设置质押率、贷款利率和贷款额上限及回购比例下限, 并且银行最优收益分配比例与损失补偿比例、最优损失补偿比例与贷款损失率均成正相关关系。此外, 随着B2B平台工作效率的提高, 联合授信下最优收益分配比例将减小, 最优损失补偿比例将增大, 最终近似于委托授信下的最优损失补偿比例。最后给出数值分析。     

Default probabilities in a corporate bank portfolio: A logistic model approach

Analysis and management of credit risk has taken on an increased importance in recent years. New regulations force banks and other financial institutions to make a credible effort to chart and manage the risk associated with their client portfolio. Increased competition in the financial market has also improved the motivation of monitoring the risk/reward relationship on various clients. Modern risk measures such as Credit Risk Capital (CRC) and Risk Adjusted Return On Capital (RAROC) are now well established among banks. One problem in such risk frameworks is to find the expected loss (EL) of the bank portfolio. The EL is based on assumptions regarding the estimated default frequency (EDF) for each client or group of clients. Benchmark models for CRC calculations treat EDFs as exogenous and do not devote much attention to how they can be obtained. This article presents a method of estimating such rates for a retail bank portfolio. The analysis is based on a logistic regression model where financial variables as well as other firm characteristics affect the default probability.     

Quantile regression for robust bank efficiency score estimation

We discuss quantile regression techniques as a robust and easy to implement alternative for estimating Farell technical efficiency scores. The quantile regression approach estimates the production process for benchmark banks located at top conditional quantiles. Monte Carlo simulations reveal that even when generating data according to the assumptions of the stochastic frontier model (SFA), efficiency estimates obtained from quantile regressions resemble SFA-efficiency estimates. We apply the SFA and the quantile regression approach to German bank data for three banking groups, commercial banks, savings banks and cooperative banks to estimate efficiency scores based on a simple value added function and a multiple-input–multiple-output cost function. The results reveal that the efficient (benchmark) banks have production and cost elasticities which differ considerably from elasticities obtained from conditional mean functions and stochastic frontier functions.     

信用担保对银行向中小企业融资的决策影响分析

本文分析了中小企业能从银行获得贷款的项目风险范围,得出:提高抵押条件,可以使得风险范围扩大.当中小企业的抵押品不足时,不能从银行获得贷款的情况下,我们引入了政策性信用担保机构,分析显示了担保下企业获得担保贷款的项目风险范围,并给出了在担保机构无盈利时的担保费率公式.     

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.     

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.     

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.     

Quantile regression for longitudinal data

The penalized least squares interpretation of the classical random effects estimator suggests a possible way forward for quantile regression models with a large number of “fixed effects”. The introduction of a large number of individual fixed effects can significantly inflate the variability of estimates of other covariate effects. Regularization, or shrinkage of these individual effects toward a common value can help to modify this inflation effect. A general approach to estimating quantile regression models for longitudinal data is proposed employing ?₁ regularization methods. Sparse linear algebra and interior point methods for solving large linear programs are essential computational tools.