Modeling default versus prepayment risk via logistic regression and Cox proportional hazards.
The main focus of our study is examining the difference in statistical modeling approaches when predicting for loan default versus prepayment as well as the interpretation of the features used to inform these models. A loan default is the failure to repay a loan by the borrower according to agreed upon terms. A loan prepayment is the early payment of a loan by the borrower, typically as a result of lower interest rates allowing for favorable refinancing. Prepayment reflects a borrower's financial capacity to pay off a loan or ability to refinance it at a more attractive level. On the other hand, default represents lack of capacity (or willingness/wherewithal) to pay. Using dv01 labels of loan status, we assume defaulted loans to be indicated as 'Charged Off' and 'Sold - Debt Sale', and prepaid loans to be indicated as 'Paid Off' in their loan statuses. In theory, we would expect borrowers that prepay to be have high debt servicing capacity/be good borrowers in order to be able to prepay. For instance, we would expect this group to thus have higher incomes, and a lower Debt to Income Ratio. On the other hand, borrowers that default will be likely to have lower incomes, and higher Debt to Income Ratios. Some variables may have less explainability due to correlated externalities. For example, it is unclear whether groups that prepay will have lower or higher credit inquiries than the average borrower, because although having a large number of inquires is a sign of someone with low credit/who was rejected multiple times, borrowers who shop around (and thus are likely to prepay if they find a better deal) will also tend to have a higher number of inquiries. We study these factors, first using a simple binary classification framework using the logistic regression Model, and then using a hazard rate approach via the cox-proportional hazards model.
- Peter Chen
- Sarang Gupta
- Ally Bouchard