A Functional Representation of Credit Behavior for Probability of Default Modeling

01 ABSTRACT

The paper proposes a framework for probability of default modeling via functional data analysis, representing a series of credit variables as functions and investigating whether intra-monthly information improves default predictability in linear models. The authors show that widely used variables such as available funds, utilization rate, and overdraft can all be derived from three quantities observed over time: account type, account balance, and credit limit. The authors report that functional logistic regression, when equipped with an effective functional representation, attains predictive performance on par with XGBoost while consistently outperforming ordinary logistic regression; this conclusion is the authors' report based on their framework.

02 KEY FINDINGS

1. Account type, balance, and credit limit are represented as continuous-time processes rather than reduced to monthly aggregated values, yielding a continuous faithful representation of the borrower.
2. Recurring events associated with the ordinal position among banking days are found to create strong cyclical patterns, and a relative time framework is developed to align these recurring events across borrowers.
3. The framework is assessed using functional logistic regression, which is reported to attain predictive performance on par with XGBoost while consistently outperforming logistic regression, while retaining the interpretability of linear default models.