Adverse selection and non-take inference with coherent risk and response scoring

The authors offer a mathematical model for adverse selection by individual borrowers based on preferences for offers and the default (Bad) or non-default (Good) status of booked accounts. We define the condition for borrower risk and response when there is no adverse selection (NAS). This definition provides us with a direct comparison between the prior and posterior conditional probabilities of default by an individual borrower who Takes an offer; this allows us to obtain estimates of differential response rates for individual borrowers and the Good/Bad odds for Take, Non-Take and Accept sub-populations. Performance of different response-risk segments allows us to compare price-driven risk elasticity and price-driven response elasticity in the presence of Good or Bad adverse selections; a special case applies when the borrower's capacity to repay is not an issue. We offer limited experimental results for selected price-risk segments where action-based risk and response scores are used to estimate borrower preferences. The critical role of Non-Take inference is described.     

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.     

Risk analysis with contractual default. Does covenant breach matter?

Mergers and acquisitions (M&A), private equity and leveraged buyouts, securitization and project finance are characterized by the presence of contractual clauses (covenants). These covenants trigger the technical default of the borrower even in the absence of insolvency. Therefore, borrowers may default on loans even when they have sufficient available cash to repay outstanding debt. This condition is not captured by the net present value (NPV) distribution obtained through a standard Monte Carlo simulation. In this paper, we present a methodology for including the consequences of covenant breach in a Monte Carlo simulation, extending traditional risk analysis in investment planning. We introduce a conceptual framework for modeling technical and material breaches from the standpoint of both lenders and shareholders. We apply this framework to a real case study concerning the project financing of a 64-million euro biomass power plant. The simulation is carried out on the actual model developed by the financial advisor of the project and made available to the authors. Results show that both technical and material breaches have a statistically significant impact on the net present value distribution, and this impact is more relevant when leverage and cost of debt increase.     

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.     

Optimal ROE loan pricing with or without adverse selection

The authors describe the structural solution of the loan rate as a function of default and response risk that maximizes expected return on equity for a lender's portfolio of risky loans. Under the assumptions of our model, the non-linear differential equation for the optimizing price is found to be separable in transformed financial, response and risk variables. With an end-point condition where default-free borrowers are willing to borrow at loan rates higher than the lender's cost of funds, general solutions are obtained for cases where default probabilities may depend explicitly on the offered loan rate and where adverse selection may or may not be present. For the general solution, we suggest a numerical algorithm that involves the sequential solutions of two separate transcendental equations each one of which depends on parameters of the risk and response scores. For the special case where the borrower's default probability is conditionally independent of loan rate, it is shown that the optimal solution is independent of Basel regulations on equity capital.     

Effects of missing data in credit risk scoring. A comparative analysis of methods to achieve robustness in the absence of sufficient data

The 2004 Basel II Accord has pointed out the benefits of credit risk management through internal models using internal data to estimate risk components: probability of default (PD), loss given default, exposure at default and maturity. Internal data are the primary data source for PD estimates; banks are permitted to use statistical default prediction models to estimate the borrowers’ PD, subject to some requirements concerning accuracy, completeness and appropriateness of data. However, in practice, internal records are usually incomplete or do not contain adequate history to estimate the PD. Current missing data are critical with regard to low default portfolios, characterised by inadequate default records, making it difficult to design statistically significant prediction models. Several methods might be used to deal with missing data such as list-wise deletion, application-specific list-wise deletion, substitution techniques or imputation models (simple and multiple variants). List-wise deletion is an easy-to-use method widely applied by social scientists, but it loses substantial data and reduces the diversity of information resulting in a bias in the model's parameters, results and inferences. The choice of the best method to solve the missing data problem largely depends on the nature of missing values (MCAR, MAR and MNAR processes) but there is a lack of empirical analysis about their effect on credit risk that limits the validity of resulting models. In this paper, we analyse the nature and effects of missing data in credit risk modelling (MCAR, MAR and NMAR processes) and take into account current scarce data set on consumer borrowers, which include different percents and distributions of missing data. The findings are used to analyse the performance of several methods for dealing with missing data such as likewise deletion, simple imputation methods, MLE models and advanced multiple imputation (MI) alternatives based on MarkovChain-MonteCarlo and re-sampling methods. Results are evaluated and discussed between models in terms of robustness, accuracy and complexity. In particular, MI models are found to provide very valuable solutions with regard to credit risk missing data.     

网络借贷收窄利率定价区间的影响研究——基于倾向性分数匹配法

随着网络借贷的发展,学术界对网络借贷的研究逐渐深入。利率定价机制是网络借贷机制设计的核心,体现了金融的本质——对风险的定价,并逐渐成为学术研究的话题。Wei和Lin^[1]曾记录和分析了美国网络借贷机制变更的过程。本文选用国内一家代表性的网络借贷平台数据,用倾向性分数匹配法对其利率定价机制变化前后的交易行为进行研究,发现当平台收窄了利率区间且降低了合格借款人的审核通过率,违约率反而更高。狭窄的利率区间降低了利率区分度,而利率区分度是投资人判断具体贷款所处风险水平的重要依据,实际上恶化了信息不对称,影响投资人投资行为,具体表现为满标时间延长、单笔贷款投标占比减少,并且投资人羊群行为加重。本文以期限利率周度标准差为利率区间的代理变量,解释了上述变化产生的原因。平台收窄利率区间,降低了贷款质量优劣的区分度,使得平台和投资人风险识别效率降低,未能达到平台运营优化的结果。本文丰富了网络借贷的学术研究,为网络借贷利率定价机制的发展提供参考。     

A classification problem of credit risk rating investigated and solved by optimisation of the ROC curve

Estimation of probability of default has considerable importance in risk management applications where default risk is referred to as credit risk. Basel II (Committee on Banking Supervision) proposes a revision to the international capital accord that implies a more prominent role for internal credit risk assessments based on the determination of default probability of borrowers. In our study, we classify borrower firms into rating classes with respect to their default probability. The classification of firms into rating classes necessitates the finding of threshold values separating the rating classes. We aim at solving two problems: to distinguish the defaults from non-defaults, and to put the firms in an order based on their credit quality and classify them into sub-rating classes. For using a model to obtain the probability of default of each firm, Receiver Operating Characteristics (ROC) analysis is employed to assess the distinction power of our model. In our new functional approach, we optimise the area under the ROC curve for a balanced choice of the thresholds; and we include accuracy of the solution into the program. Thus, a constrained optimisation problem on the area under the curve (or its complement) is carefully modelled, discretised and turned into a penalized sum-of-squares problem of nonlinear regression; we apply the Levenberg–Marquardt algorithm. We present numerical evaluations and their interpretations based on real-world data from firms in the Turkish manufacturing sector. We conclude with a discussion of structural frontiers, parametrical and computational features, and an invitation to future work.     

默认模式网络与任务正网络之间相互拮抗的神经动力学分析

任务正激活与任务负激活的工作机制是认知功能实现的基本要素.这一拮抗关系的失衡或者受损可能会引发一系列严重的退行性神经疾病，然而到目前为止，尚不清楚这种拮抗现象的神经机制.该文基于默认模式网络与任务正网络在突触层面上相互抑制的假设，并结合多种刺激条件下的工作记忆模型，进行了计算机数值模拟.研究结果表明: 1) 任务正网络与任务负网络之间在神经活动上呈现出拮抗关系； 2) 伴随着工作记忆刺激方向数目的增加，任务负网络神经活动的衰减程度会随之增大； 3) 当工作记忆相关的脑区其神经活动增加时，任务负网络的神经活动减少； 4) 并且随着工作记忆任务难度的增加，任务负网络的神经活动会迅速衰减.这些计算结果都与神经科学实验数据是匹配的.由于任务负激活是默认模式网络的主要特征，因此默认模式网络与任务正网络在突触层面上的相互抑制是这两种不同性质网络之间形成拮抗关系的根本原因.     

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 reduced-form model with default intensities containing contagion and regime-switching Vasicek processes

The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps (CDSs). Numerical results are presented to show the impacts of the model parameters on the fair spreads.     

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.     

关于双曲衰减的违约相关模型及CDS定价

引进一个双曲类型的衰减函数来表示一方违约对另一方违约强度的影响．若交易双方为竞争对手(合作公司),当一方的违约时,另一方的违约强度将减小(增大)．随着时间的推移,这种影响将逐渐减小,直至为零．在这个模型下,通过测度变换,可以得到两公司违约时间的联合分布及各自的边际分布,从而可以对违约互换进行定价．     

基于不均衡数据的小企业信用风险评价

小企业信用风险评价既是银行风险管理问题,又事关经济社会稳定。针对小企业贷款实践中,违约样本远少于非违约样本、且违约客户误判对银行影响较大的现实,采用不均衡支持向量机对小企业信用风险评价指标进行赋权,进而构建了能有效区分违约客户、非违约客户的评价模型。根据有无特定评价指标、特定评价指标数值变化对贷款小企业违约状态的影响程度赋权;反映了对违约状态影响越大、评价指标权重越大的赋权思路。将违约样本正确识别率、违约样本的准确率与查全率等因素作为支持向量机赋权模型中客户识别率的度量标准,改变了样本数据不均衡所导致的样本总体精度很高、违约样本精度反而不高的现象。研究结果表明:行业景气指数、资本固定化比率、净利润现金含量、恩格尔系数、营业利润率等评价指标对小企业信用风险的影响较大。     

基于BP神经网络的P2P网贷借款人信用评估

评估借款人信用是P2P网贷公司控制风险的重要步骤,对于网贷公司的正常运行有着极其重要的意义。论文参考商业银行信用指标体系并根据P2P网贷自身特点,建立了P2P网贷借款人的信用评估指标体系。根据建立的指标体系构建相应的BP神经网络模型,并利用一步正切法进行优化。然后选取具有代表性的P2P网贷平台的相关数据,对该模型进行训练和仿真,证明了该模型对P2P网贷平台的风险控制起到一定的作用。     

P2P网络借贷市场利率主导权偏离程度的研究——基于双边随机前沿模型

近年来P2P网络借贷作为一种典型的互联网金融模式获得了跳跃式的发展,由于借贷双方信息不对称,导致我国P2P网贷市场利率普遍偏高。本文利用双边随机前沿分析(SFA)方法对我国P2P网贷市场借贷双方利率主导权力进行测算,并对借贷双方的主导权力对贷款利率的影响效应进行定量分析,同时对借款者个体特征对借贷双方利率主导权力的影响进行比较分析。实证结果表明,出借方拥有明显的主导权力,随着学历、年龄、收入、信用等级的增高,借款人地位将有所改善。     

基于最优负债系数的上市银行违约概率测算模型与实证

当上市银行的长期负债系数γ的取值不同时,应用KMV模型测算出的银行违约概率大相径庭。根据债券的实际信用利差可以推算出上市银行的违约概率PDi,CS,根据长期负债系数γ可以运用KMV模型确定上市银行的理论违约概率PDi,KMV。本文通过理论违约率与实际违约率的总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型的最优长期负债γ系数;通过最优长期负债系数γ建立了未发债上市银行的违约率测算模型、并实证测算了我国14家全部上市银行的违约概率。本文的创新与特色一是采用KMV模型计算的银行违约概率PDi,KMV与实际信用利差确定的银行违约概率PDi,CS总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型中的最优长期负债γ系数;使γ系数的确定符合资本市场利差的实际状况,解决了现有研究中在0和1之间当采用不同的长期负债系数γ、其违约概率的计算结果截然不同的问题。二是实证研究表明,当长期负债系数γ=0.7654时,应用KMV模型测算出的我国上市银行违约概率与我国债券市场所接受的上市银行违约概率最为接近。三是实证研究表明国有上市银行违约概率最低,区域性的上市银行违约概率较高,其他上市银行的违约概率居中。     

Investment and financing decisions in the presence of time-to-build

We study a firm’s optimal decisions on investment, default, and financing when the amount of time and the running costs for project completion are uncertain. In the presence of time-to-build, a firm makes conservative investment and financing decisions; investment is delayed, and the optimal leverage ratio is inverted U-shaped with respect to the size of the lag. Although equity holders can choose to default before the project has been completed, the default probability in the presence of time-to-build is lower than that in the absence of a lag in most cases because of the conservative investment and financing decisions. Given the lower default probability, equity holders may benefit more from debt financing in the presence of time-to-build than they would in the absence of a lag. When firms can shorten their expected time-to-build by bearing more costs, unlevered firms strive to reduce the lag more than optimally levered firms do. However, highly levered firms utilize more resources to reduce the lag than all-equity firms do because equity holders are more concerned about the possibility of default before the project’s completion.     

A comparison of strategies to develop a customer default scoring model

Behavioural scoring models are generally used to estimate the probability that a customer of a financial institution who owns a credit product will default on this product in a fixed time horizon. However, one single customer usually purchases many credit products from an institution while behavioural scoring models generally treat each of these products independently. In order to make credit risk management easier and more efficient, it is interesting to develop customer default scoring models. These models estimate the probability that a customer of a certain financial institution will have credit issues with at least one product in a fixed time horizon. In this study, three strategies to develop customer default scoring models are described. One of the strategies is regularly utilized by financial institutions and the other two will be proposed herein. The performance of these strategies is compared by means of an actual data bank supplied by a financial institution and a Monte Carlo simulation study.     

Hurdle models of loan default

Some models of loan default are binary, simply modelling the probability of default, while others go further and model the extent of default (eg number of outstanding payments; amount of arrears). The double-hurdle model, originally due to Cragg (Econometrica, 1971), and conventionally applied to household consumption or labour supply decisions, contains two equations, one which determines whether or not a customer is a potential defaulter (the ‘first hurdle’), and the other which determines the extent of default. In separating these two processes, the model recognizes that there exists a subset of the observed non-defaulters who would never default whatever their circumstances. A Box-Cox transformation applied to the dependent variable is a useful generalization to the model. Estimation is relatively easy using the Maximum Likelihood routine available in STATA. The model is applied to a sample of 2515 loan applicants for whom loans were approved, a sizeable proportion of whom defaulted in varying degrees. The dependent variables used are amount in arrears and number of days in arrears. The value of the hurdle approach is confirmed by finding that certain key explanatory variables have very different effects between the two equations. Most notably, the effect of loan amount is strongly positive on arrears, while being U-shaped on the probability of default. The former effect is seriously under-estimated when the first hurdle is ignored.