基于零膨胀分位数两部模型的银行贷款违约预测研究

贷款信用风险评估是银行风控的重要内容。贷款逾期天数作为常见的风险度量指标，具有典型的零膨胀特征。对于零膨胀数据，传统的线性回归不再适用，两部模型是常用的代表方法。考虑到贷款数据具有偏态分布特征，本文构建了一个分位数两部模型—logit-quantile模型。该模型由Logistic回归和分位数回归构成，为了进行风险因素的选择，在模型的两个回归中添加了Lasso惩罚。为了求解模型，本文采用了坐标下降法和线性规划法相结合的迭代算法。模拟分析显示，对比逐步法和常用的logit-linear两部模型，新模型表现出了最好的变量选择效果，尤其在零膨胀比例为80%及高维情形时，该模型的表现仍然最优。最后对某银行的贷款数据实证分析显示，新模型具有更精简的结构，采用交叉验证技术进行预测显示新模型的预测和分类表现最好。

Loan Default Forecasting Based on Zero-inflated Quantile Two-part Model

Loan is not only a main means of solving the shortage of finances, but also an important business of financial institutions. Loan default forecasting is an essential content of bank risk management. To measure the loan credit risk of lenders, the number of days overdue is an informative variable commonly used. It shows whether the lender defaulted or not, but also the extent of default. However, this variable usually has an obvious zero-inflated characteristic, that is, there exists a quite large proportion of zero observations. Those zeros usually bring challenges to traditional credit default forecasting models.