Modeling credit risk with a Tobit model of days past due

Abstract

In this paper we propose a novel credit risk modelling approach where number of days past due is modeled instead of a binary indicator of default. In line with regulatory requirements, the number of days overdue on loan repayments are transformed to a binary variable by applying 90-days past due threshold, and use it as the dependent variable in default probability models. However, potentially useful information is lost with this transformation. Lower levels of days past due are expected to be good predictors of future incidence of default. We show that a dynamic Tobit model, where number of days overdue is used as a censored continuous dependent variable, significantly outperforms models based on binary indicators of default. It correctly identifies more than 70% of defaulters and issues less than 1% of false alarms. Its superiority is confirmed also by more accurate rating classification, higher rating stability over the business cycle and more timely identification of defaulted borrowers. The implications for banks are clear. By modelling number of days past due they can significantly improve risk identification and reduce procyclicality of IRB capital requirements. Moreover, we show how modelling of days past due can be used also for stage allocation for the purposes of IFRS9 reporting.