【作者】 刘艳；

【导师】 林路；

【作者基本信息】 山东大学 ， 概率论与数理统计， 2014， 硕士

【摘要】 本文应用logistic逐步回归求某银行数据的违约概率,在变量选择的过程中,我们选择了AIC准则跟BIC准则,我们对两种模型进行样本内及样本外的模型区分能力对比,发现样本内BIC准则优于AIC准则,但是样本外AIC准则优于BIC准则。考虑到我们的样本为银行的违约客户数据,不可避免的,违约客户的数据相比而言少很多。为了建立好模型,我们样本内数据中违约客户与非违约客户的比为1：1,但是样本外的数据大部分是非违约客户。因此我们对AIC准则的结果是不是对非违约客户特别适合产生怀疑,此时我们引入分位数回归,在不同分位点下对比两种模型的预测优劣。最终得出结论,AIC模型对非违约客户的预测更准确些,BIC模型对违约客户的预测更准确些。本文主要分为四章。第一章分为四小部分,分别从研究背景、意义与目的、前人的成果及研究思路与结构框架这四个部分进行介绍。第二章也是分为了四个小部分,通过这四个小部分,我们可以了解Logistic逐步回归违约概率模型的建立过程以及模型评价标准。这四个小部分分别为模型的定义、模型的参数估计方法、模型的变量选择标准和变量选择方法以及模型风险区分能力的检验问题。在测算模型的风险区分能力时,我们同时用三个检验标准,这三个标准分别为：KS检验、ROC曲线和AUC值检验以及CAP曲线和AR值检验。第三章主要介绍了与分位数回归相关的理论,主要涉及分位数回归的定义、优越性、求解方法以及分位数回归的参数检验统计量问题。第四章中,我们对某银行某行业中企业客户的实际财务指标数据建立Logistic逐步回归违约概率模型,并进行了实证分析。在建立模型的时候,我们的因变量为客户的违约情况,当客户违约时因变量为1,非违约时因变量为0,我们自变量选择的为企业的财务指标数据。在选择变量的时候我们采用了逐步回归AIC准则和BIC准则两种方法,然后分别进行样本内及样本外的模型区分能力的检验,我们发现,样本内的BIC准则模型优于AIC准则模型,而样本外的AIC准则模型优于BIC准则模型。考虑到我们数据的特殊性,即违约客户很少,而我们样本外数据中大部分为非违约客户,我们怀疑是AIC模型对非违约客户的预测更为准确。为了进一步研究所建立模型的预测准确性,我们引入分位数回归,利用分位数回归来分析两种模型在不同分位点下的表现。此外,我们还通过设定样本中好坏客户的比率,即不断的提高样本中好客户的比率来比较AIC模型与BIC模型。通过两种方法比较,我们最终得出结论：AIC模型对非违约客户的预测更准确些,BIC模型对违约客户的预测更准确些。更多还原

【Abstract】 This article aims to apply the logistic stepwise regression to the calcu-lation of the bank’s default probability. We chose the AIC criterion and the BIC criterion in variable selection and built the models. When compare the distinguish ability of the two models in train sample and test sample, we found out that the BIC criterion model is better than the AIC criterion model in the train sample, the test sample otherwise. In consideration of our sample are the bank’s customer, inevitably, the default customer are very few. In order to establish a good model, in the train sample, we chose100customer and set the ratio of good customer and bad customer as1:1, that is to say, in the train sample, there are50good customer and50bad customer, whereas in the test sample, the bad customer are very few. Consequently, we doubt that maybe the AIC criterion model is especially suited for the distinguish of the good customer. In order to solve the problem, we use the quantile regression to analyze the two models under different quantiles. The result of the quantile regression shows that the AIC model is more accurate in forecasting a good customer and the BIC model is more accurate in forecasting a bad customer.This artile mainly divided into four chapters. The first chapter main-ly introduces the research background, the research significance, the research purpose, the research achievements of predecessors and the structure of the framework. The second chapter mostly discusses the logistic stepwise regres-sion default probability model, including model definition, model parameter estimation, the variable selection and the risk model distinguish ability inspec- tion. The model distinguish ability inspection contains the KS indicators, the ROC curve、AUC value inspection and the CAP、AR value inspection。The third chapter largely tells the theory of quantile regression, which contains the definition, advantages, solving method, parameter test of the quantile regres-sion. The fourth chapter is the empirical analysis of a bank’s default data. We built a model, the independent variable is the financial index data, the dependent variable is the customer’s default situation, with1implies a bad customer and0implies a good customer. When selecting the independent variable, we adopted the step regression AIC criterion and BIC criterion and built two models with the train sample. We found out that, when we compare the two models’ distinguish ability with the train sample, the BIC criterion model is better; but when use the test sample to compared, the AIC criterion model is better. Considering the particularity of our data, that is to say, there are far more less bad customer in the test sample than the good customer, we suspect the AIC model is more accurate in forecast the good customers. For further and more information, we used the quantile regression to analyse the performance of the two models under different quantiles. In addition, we also try to compare the two models by setting the ratio of the sample of good or bad customer, namely continuously improve the ratio of good customer to compare the AIC and BIC model. By this two methods, we finally draw the conclusion:when forecasting a good customer, the AIC model is more accurate and the BIC model is more accurate when forecasting a bad customer.更多还原