The Application Of Quantile Regression In Default Probability Models

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.