Retail credit stress testing using a discrete hazard model with macroeconomic factors

Retail credit models are implemented using discrete survival analysis, enabling macroeconomic conditions to be included as time-varying covariates. In consequence, these models can be used to estimate changes in probability of default given downturn economic scenarios. Compared with traditional models, we offer improved methodologies for scenario generation and for the use of them to predict default rates. Monte Carlo simulation is used to generate a distribution of estimated default rates from which Value at Risk and Expected Shortfall are computed as a means of stress testing. Several macroeconomic variables are considered and in particular factor analysis is employed to model the structure between these variables. Two large UK data sets are used to test this approach, resulting in plausible dynamic models and stress test outcomes.     

Joint survival probability via truncated invariant copula

Given an intensity-based credit risk model, this paper studies dependence structure between default intensities. To model this structure, we use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. Through very lengthy algebra, we obtain explicitly the joint survival probability of the integrated intensities by using the truncated invariant Farlie–Gumbel–Morgenstern copula with exponential marginal distributions. We also apply our theoretical result to pricing basket default swap spreads. This result can provide a useful guide for credit risk management.     

Credit scoring with macroeconomic variables using survival analysis

Survival analysis can be applied to build models for time to default on debt. In this paper, we report an application of survival analysis to model default on a large data set of credit card accounts. We explore the hypothesis that probability of default (PD) is affected by general conditions in the economy over time. These macroeconomic variables (MVs) cannot readily be included in logistic regression models. However, survival analysis provides a framework for their inclusion as time-varying covariates. Various MVs, such as interest rate and unemployment rate, are included in the analysis. We show that inclusion of these indicators improves model fit and affects PD yielding a modest improvement in predictions of default on an independent test set.     

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.     

基于贝叶斯方法的低违约组合违约率估计

现代信用风险建模的核心是估计违约率,违约率估计是否准确将直接影响信用风险建模的质量。在估计违约率的众多文献中,频率法或logistic回归等统计方法的运用非常广泛,此类统计模型的基础是大样本,它客观上需要最低数量或最优数量的违约数据,而低违约组合(LDP)是指只有很少违约数据甚至没有违约数据的组合,如何估计LDP的违约率、反映违约率的非预期波动是一个值得关注的现实问题。本文针对银行贷款LDP缺乏足够历史违约数据的情况,采用贝叶斯方法估计LDP的违约率,并进一步探讨了根据专家判断或者根据同类银行LDP违约数量的历史数据来确定先验分布的方法。在贝叶斯估计中,通过先验分布的设定,不仅可以实现违约率估计的科学性和合理性,而且可以反映违约的非预期波动,有助于银行实施谨慎稳健的风险管理。     

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.     

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。     

基于数据的银行信贷行业的信用风险研究

目前多数研究利用美国旧金山市KMV公司于1997年建立的模型(KMV模型)计算企业年违约距离来评估具体企业的信用风险,但缺乏信贷行业的信用风险评估方法,也不能给出随时间变化的信用风险.首先提出基于数据的信贷行业随时间动态演化的信用风险评估模型,然后利用2016年18个行业的数据得到了中国信贷行业动态演化的信用风险,该信用风险随时间演化特征可分为波动上升、下降后波动、下降后稳定、稳定四种类型.进一步研究发现金融业、科学研究和技术服务业、信息传输软件和技术服务业这三个行业动态演化的信用风险平均值高且不稳定,住宿和餐饮业的信用风险很高但是比较平稳,其他行业的信用风险较低且较平稳.     

基于双因子CIR强度式定价的信用债券投资组合优化

信用风险和利率风险是相互关联影响的。资产组合优化不能将这两种风险单独考虑或简单的相加,应该进行整体的风险控制,不然会造成投资风险的低估。本文的主要工作:一是在强度式定价模型的框架下,分别利用CIR随机利率模型刻画利率风险因素“无风险利率”和信用风险因素“违约强度”的随机动态变化,衡量在两类风险共同影响下信用债券的市场价值,从而构建CRRA型投资效用函数。以CRRA型投资效用函数最大化作为目标函数,同时控制利率和信用两类风险。弥补了现有研究中仅单独考虑信用风险或利率风险、无法对两种风险进行整体控制的弊端。二是将无风险利率作为影响违约强度的一个因子,利用“无风险利率因子”和“纯信用因子”的双因子CIR模型拟合违约强度,考虑了市场利率变化对于债券违约强度的影响,反映两种风险的相关性。使得投资组合模型中既同时考虑了信用风险和利率风险、又考虑了两种风险的交互影响。避免在优化资产组合时忽略两种风险间相关性、可能造成风险低估的问题。     

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.     

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.     

Structural models in consumer credit

We propose a structural credit risk model for consumer lending using option theory and the concept of the value of the consumer’s reputation. Using Brazilian empirical data and a credit bureau score as proxy for creditworthiness we compare a number of alternative models before suggesting one that leads to a simple analytical solution for the probability of default. We apply the proposed model to portfolios of consumer loans introducing a factor to account for the mean influence of systemic economic factors on individuals. This results in a hybrid structural-reduced-form model. And comparisons are made with the Basel II approach. Our conclusions partially support that approach for modelling the credit risk of portfolios of retail credit.     

An incentive-compatible solution for trade credit term incorporating default risk

This paper studies the optimal trade credit term decision in an extended economic ordering quantity (EOQ) framework that incorporates a default risk component. A principal-agent bilevel programming model with costs minimization objectives is set up to derive the incentive-compatible credit term. The supplier determines the credit term as the leader in the first level programming, by balancing her/his financing capacity with the retailer’s default risk, order behavior and cost shifting. At the second level, the retailer makes decisions on ordering and payment time by reacting on the term offered by the supplier. A first order condition solution procedure is derived for the bilevel programming when credit term is confined within the practically feasible interval. Two key results are obtained – the condition to derive incentive-compatible credit term, and an equation system to derive threshold default risk criterion filtering retailers suitable for credit granting. Numerical experiments show that the capital cost of the supplier is the most important factor determining the credit term. Default risk acts like a filtering criterion for selecting retailers suitable for credit granting. Empirical evidence supporting our theoretical considerations is obtained by estimating three panel econometric models, using a dataset from China’s listed companies.     

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.     

利用传染模型对含有对手风险的信用证券定价(英文)

本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.     

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。     

On the simulation of portfolios of interest rate and credit risk sensitive securities

We discuss extensions of reduced-form and structural models for pricing credit risky securities to portfolio simulation and valuation. Stochasticity in interest rates and credit spreads is captured via reduced-form models and is incorporated with a default and migration model based on the structural credit risk modelling approach. Calculated prices are consistent with observed prices and the term structure of default-free and defaultable interest rates. Three applications are discussed: (i) study of the inter-temporal price sensitivity of credit bonds and the sensitivity of future portfolio valuation with respect to changes in interest rates, default probabilities, recovery rates and rating migration, (ii) study of the structure of credit risk by investigating the impact of disparate risk factors on portfolio risk, and (iii) tracking of corporate bond indices via simulation and optimisation models. In particular, we study the effect of uncertainty in credit spreads and interest rates on the overall risk of a credit portfolio, a topic that has been recently discussed by Kiesel et al. [The structure of credit risk: spread volatility and ratings transitions. Technical report, Bank of England, ISSN 1268-5562, 2001], but has been otherwise mostly neglected. We find that spread risk and interest rate risk are important factors that do not diversify away in a large portfolio context, especially when high-quality instruments are considered.     

A Reduced Model with Thinning-Dependence Structure

The class of reduced form models is a very important class of credit risk models, and the modelling of the default dependence structure is essential in the reduced form models. This paper models dependent defaults under a thinning-dependent structure in the reduced form framework. In our tractable model, the joint survival probability for correlated defaults can be derived, and hence the CDS premium rates (with or without counterparty risk) are given in closed form. The numerical result shows that the thinning-dependent structure is effective to model the default dependence.     

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.     

基于信息增益的小型工业企业信用评级模型

信用评级就是衡量一笔债务违约的可能性,评价债务违约风险的大小。本文利用信息增益方法建立了信用评级模型,并以小型工业企业贷款数据为对象进行了实证分析。本文的创新与特色:一是按照指标的信息增益越大、越能将违约与非违约企业区分出来的思路,筛选出对违约状态有较大影响的指标。改变了现有研究不以违约鉴别力作为指标遴选标准的不足。二是在相关程度高的一对冗余指标中,删除信息增益小、即违约鉴别能力差的指标,既避免指标间反映信息重复,又避免误删违约鉴别能力强的指标。三是利用信息增益值对指标进行赋权,保证违约鉴别能力越大的指标赋予的权重越大。改变了现有研究赋权不反映指标的违约鉴别能力大小的弊端。实证结果表明:本文遴选的包括资产负债率、行业景气指数、抵质押担保等31个指标对违约状态有显著的鉴别能力,且反映信息不重复。偿债能力是影响小型工业企业信用评级的关键要素。