Establishing decision tree-based short-term default credit risk assessment models

ABSTRACT

Traditional credit risk assessment models do not consider the time factor; they only think of whether a customer will default, but not the when to default. The result cannot provide a manager to make the profit-maximum decision. Actually, even if a customer defaults, the financial institution still can gain profit in some conditions. Nowadays, most research applied the Cox proportional hazards model into their credit scoring models, predicting the time when a customer is most likely to default, to solve the credit risk assessment problem. However, in order to fully utilize the fully dynamic capability of the Cox proportional hazards model, time-varying macroeconomic variables are required which involve more advanced data collection. Since short-term default cases are the ones that bring a great loss for a financial institution, instead of predicting when a loan will default, a loan manager is more interested in identifying those applications which may default within a short period of time when approving loan applications. This paper proposes a decision tree-based short-term default credit risk assessment model to assess the credit risk. The goal is to use the decision tree to filter the short-term default to produce a highly accurate model that could distinguish default lending. This paper integrates bootstrap aggregating (Bagging) with a synthetic minority over-sampling technique (SMOTE) into the credit risk model to improve the decision tree stability and its performance on unbalanced data. Finally, a real case of small and medium enterprise loan data that has been drawn from a local financial institution located in Taiwan is presented to further illustrate the proposed approach. After comparing the result that was obtained from the proposed approach with the logistic regression and Cox proportional hazards models, it was found that the classifying recall rate and precision rate of the proposed model was obviously superior to the logistic regression and Cox proportional hazards models.     

基于神经网络的贷款违约识别研究

随着国内金融市场的逐步开放,我国商业银行将面临日益激烈的市场竞争。提高商业银行的信用风险管理水平,增强市场竞争力,已经成为非常迫切的问题。除了完善信贷管理体制以外,研发信用风险模型以降低信用风险很有必要。鉴于目前的数据情况,现实的选择是研发贷款违约识别系统。本文对神经网络用于贷款违约识别做了实证研究,并与判别分析和决策树做了性能比较,得到了一些有意义的结论。     

Macro-Economic Factors in Credit Risk Calculations: Including Time-Varying Covariates in Mixture Cure Models

The prediction of the time of default in a credit risk setting via survival analysis needs to take a high censoring rate into account. This rate is because default does not occur for the majority of debtors. Mixture cure models allow the part of the loan population that is unsusceptible to default to be modeled, distinct from time of default for the susceptible population. In this article, we extend the mixture cure model to include time-varying covariates. We illustrate the method via simulations and by incorporating macro-economic factors as predictors for an actual bank dataset.     

An Empirical Comparison of Multiple Imputation Methods for Categorical Data

Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed versions of the database. Researchers have developed a variety of default routines to implement multiple imputation; however, there has been limited research comparing the performance of these methods, particularly for categorical data. We use simulation studies to compare repeated sampling properties of three default multiple imputation methods for categorical data, including chained equations using generalized linear models, chained equations using classification and regression trees, and a fully Bayesian joint distribution based on Dirichlet process mixture models. We base the simulations on categorical data from the American Community Survey. In the circumstances of this study, the results suggest that default chained equations approaches based on generalized linear models are dominated by the default regression tree and Bayesian mixture model approaches. They also suggest competing advantages for the regression tree and Bayesian mixture model approaches, making both reasonable default engines for multiple imputation of categorical data. Supplementary material for this article is available online.     

竞争风险下我国住房抵押贷款风险的实证研究

 本文利用我国住房抵押贷款持续期数据,对贷款终止的提前还款和违约这两种情形展开研究,估计了竞争风险下Cox比例危险模型,刻画我国住房抵押贷款的两类风险概率随协变量变化的时间效应。对竞争风险下的Cox比例危险模型,本文计算了相应的Cox-Snell残差和Deviance残差用于模型的拟合检验,检验表明本文估计的竞争风险模型用于抵押贷款持续期数据的分析是合适的。本文进一步讨论了基于持续期的贷款终止风险研究在银行抵押贷款证券化和信贷风险管理中的意义。     

信用风险、融资担保和动态保费估值

基于市场化信息和风险中性的概念,度量了有担保贷款的边际违约概率和累积违约概率,确定了贷款担保风险的精算现值,根据市场信用价差的变化给出了动态保费每期的调整幅度,并利用数值模拟进行了担保费率的比较静态分析,最后根据实际的担保数据给出了动态保费的实证检验.结果显示,实际的违约支付非常接近于动态保费的估值,证明动态保费估值模型是一个简单、可行和实用的定价模型.     

Bayesian inference of the inverse Weibull mixture distribution using type-I censoring

A large number of models have been derived from the two-parameter Weibull distribution including the inverse Weibull (IW) model which is found suitable for modeling the complex failure data set. In this paper, we present the Bayesian inference for the mixture of two IW models. For this purpose, the Bayes estimates of the parameters of the mixture model along with their posterior risks using informative as well as the non-informative prior are obtained. These estimates have been attained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. For the former case, Bayes estimates are obtained under three loss functions while for the latter case only the squared error loss function is used. Simulation study is carried out in order to explore numerical aspects of the proposed Bayes estimators. A real-life data set is also presented for both cases, and parameters obtained under case when shape parameter is known are tested through testing of hypothesis procedure.     

基于GCRM模型的信用经济资本测度和贷款定价研究

GCRM模型与ASRF模型相比,能给出与经济资本测度目标相一致的资本数量,而现有文献对GCRM模型的到期收益率没有给出明确的刻画,本文则通过假设资产的到期收益率与其信用经济资本相关,得出了基于GCRM模型的信用经济资本测度和贷款定价方法,它能够刻画借款者的违约概率、违约损失率,以及商业银行的风险偏好（目标支付概率）和资本融资成本对经济资本和贷款定价的影响,为商业银行相关领域的决策提供了参考。     

Correlated defaults,temporal correlation,expert information and predictability of default rates

ABSTRACT

Dependence among defaults both across assets and over time is an important characteristic of financial risk. A Bayesian approach to default rate estimation is proposed and illustrated using prior distributions assessed from an experienced industry expert. Two extensions of the binomial model are proposed. The first allows correlated defaults yet remains consistent with Basel II’s asymptotic single-factor model. The second adds temporal correlation in default rates through autocorrelation in the systemic factor. Implications for the predictability of default rates are considered. The single-factor model generates more forecast uncertainty than does the parameter uncertainty. A robustness exercise illustrates that the correlation indicated by the data is much smaller than that specified in the Basel II regulations.     

Use of asymmetric loss functions in sequential estimation problems for multiple linear regression

When estimating in a practical situation, asymmetric loss functions are preferred over squared error loss functions, as the former is more appropriate than the latter in many estimation problems. We consider here the problem of fixed precision point estimation of a linear parametric function in beta for the multiple linear regression model using asymmetric loss functions. Due to the presence of nuissance parameters, the sample size for the estimation problem is not known beforehand and hence we take the recourse of adaptive multistage sampling methodologies. We discuss here some multistage sampling techniques and compare the performances of these methodologies using simulation runs. The implementation of the codes for our proposed models is accomplished utilizing MATLAB 7.0.1 program run on a Pentium IV machine. Finally, we highlight the significance of such asymmetric loss functions with few practical examples.     

Default Bayesian goodness-of-fit tests for the skew-normal model

In this paper we propose a series of goodness-of-fit tests for the family of skew-normal models when all parameters are unknown. As the null distributions of the considered test statistics depend only on asymmetry parameter, we used a default and proper prior on skewness parameter leading to the prior predictive p-value advocated by G. Box. Goodness-of-fit tests, here proposed, depend only on sample size and exhibit full agreement between nominal and actual size. They also have good power against local alternative models which also account for asymmetry in the data.     

A semi-markov approach to stochastic compartmental models

In the past, various methods using either differential equations or differential-difference equations have been used to analyze stochastic compartmental models. In this paper a semi-Markov process approach is used to provide a framework for analyzing such models. The distribution function of the number of particles in each of the compartments is derived along with the stationary distributions. Various models found in the literature arising from biological and reliability applications are analyzed here using the semi-Markov process technique.     

A family of models for uniform and serial dependence in repeated measurements studies

Data arising from a randomized double-masked clinical trial for multiple sclerosis have provided particularly variable longitudinal repeated measurements responses. Specific models for such data, other than those based on the multivariate normal distribution, would be a valuable addition to the applied statistician's toolbox. A useful family of multivariate distributions can be generated by substituting the integrated intensity of one distribution into a second (outer) distribution. The parameters in the second distribution are then used to create a dependence structure among observations on a unit. These may either be a form of serial dependence for longitudinal data or of uniform dependence within clusters. These are respectively analogous to the Kalman filter of state space models and to copulas, but they have the major advantage that they do not require any explicit integration. One useful outer distribution for constructing such multivariate distributions is the Pareto distribution. Certain special models based on it have previously been used in event history analysis, but those considered here have much wider application.     

Market-Based Credit Ratings

We present a methodology for rating in real-time the creditworthiness of public companies in the U.S. from the prices of traded assets. Our approach uses asset pricing data to impute a term structure of risk neutral survival functions or default probabilities. Firms are then clustered into ratings categories based on their survival functions using a functional clustering algorithm. This allows all public firms whose assets are traded to be directly rated by market participants. For firms whose assets are not traded, we show how they can be indirectly rated by matching them to firms that are traded based on observable characteristics. We also show how the resulting ratings can be used to construct loss distributions for portfolios of bonds. Finally, we compare our ratings to Standard & Poors and find that, over the period 2005 to 2011, our ratings lead theirs for firms that ultimately default.     

Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads

This article proposes a new class of copula-based dynamic models for high-dimensional conditional distributions, facilitating the estimation of a wide variety of measures of systemic risk. Our proposed models draw on successful ideas from the literature on modeling high-dimensional covariance matrices and on recent work on models for general time-varying distributions. Our use of copula-based models enables the estimation of the joint model in stages, greatly reducing the computational burden. We use the proposed new models to study a collection of daily credit default swap (CDS) spreads on 100 U.S. firms over the period 2006 to 2012. We find that while the probability of distress for individual firms has greatly reduced since the financial crisis of 2008–2009, the joint probability of distress (a measure of systemic risk) is substantially higher now than in the precrisis period. Supplementary materials for this article are available online.     

A Composite Likelihood Approach to Multivariate Survival Data

This paper is about the statistical analysis of multivariate survival data. We discuss the additive and multiplicative frailty models which have been the most popular models for multivariate survival data. As an alternative to the additive and multiplicative frailty models, we propose basing inference on a composite likelihood function that only requires modelling of the marginal distribution of pairs of failure times. Each marginal distribution of a pair of failure times is here assumed to follow a shared frailty model. The method is illustrated with a real-life example.     

On the generalized process capability under simple and mixture models

Process capability (PC) indices measure the ability of a process of interest to meet the desired specifications under certain restrictions. There are a variety of capability indices available in literature for different interest variables such as weights, lengths, thickness, and the life time of items among many others. The goal of this article is to study the generalized capability indices from the Bayesian view point under different symmetric and asymmetric loss functions for the simple and mixture of generalized lifetime models. For our study purposes, we have covered a simple and two component mixture of Maxwell distribution as a special case of the generalized class of models. A comparative discussion of the PC with the mixture models under Laplace and inverse Rayleigh are also included. Bayesian point estimation of maintenance performance of the system is also part of the study (considering the Maxwell failure lifetime model and the repair time model). A real-life example is also included to illustrate the procedural details of the proposed method.     

Conditional Euro Area Sovereign Default Risk

We propose an empirical framework to assess the likelihood of joint and conditional sovereign default from observed CDS prices. Our model is based on a dynamic skewed-t distribution that captures all salient features of the data, including skewed and heavy-tailed changes in the price of CDS protection against sovereign default, as well as dynamic volatilities and correlations that ensure that uncertainty and risk dependence can increase in times of stress. We apply the framework to euro area sovereign CDS spreads during the euro area debt crisis. Our results reveal significant time-variation in distress dependence and spill-over effects for sovereign default risk. We investigate market perceptions of joint and conditional sovereign risk around announcements of Eurosystem asset purchases programs, and document a strong impact on joint risk.     

Credit risk assessment with Bayesian model averaging

Many credit risk models are based on the selection of a single logistic regression model, on which to base parameter estimation. When many competing models are available, and without enough guidance from economical theory, model averaging represents an appealing alternative to the selection of single models. Despite model averaging approaches have been present in statistics for many years, only recently they are starting to receive attention in economics and finance applications. This contribution shows how Bayesian model averaging can be applied to credit risk estimation, a research area that has received a great deal of attention recently, especially in the light of the global financial crisis of the last few years and the correlated attempts to regulate international finance. The paper considers the use of logistic regression models under the Bayesian Model Averaging paradigm. We argue that Bayesian model averaging is not only more correct from a theoretical viewpoint, but also slightly superior, in terms of predictive performance, with respect to single selected models.     

Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

In this article, four bivariate exponential (BVE) distributions with subject to right censoring samples are presented. Bayesian estimates of the parameters of BVE are obtained through Linex and quadratic loss functions. Gamma prior distribution has been suggested to reforming the posterior function. The estimations and standard errors of parameters have also been obtained through simulation method. Markov chain Monte Carlo (MCMC) method is employed for the case of Block-Buse bivariate distribution because there was no closed form for estimator criteria. Simulation studies have been conducted to show that the computation parts can be implemented easily and comparing the estimated values due to two methods and with the true values as well.