Modelling the term-structure of default risk under IFRS 9 within a multistate regression framework

TL;DR

This paper compares three multistate regression techniques for modeling the lifetime default risk of loans, demonstrating that more sophisticated models improve accuracy and proposing diagnostics for model assessment.

Contribution

It introduces a comparative framework for modeling loan default risk using increasing model complexity and develops diagnostics for evaluating model performance.

Findings

Successive models outperform simpler ones in predicting default risk.

Incorporating macroeconomic and loan-level variables improves model accuracy.

Proposed diagnostics help assess sampling and model performance.

Abstract

The lifetime behaviour of loans is notoriously difficult to model, which can compromise a bank's financial reserves against future losses, if modelled poorly. Therefore, we present a data-driven comparative study amongst three techniques in modelling a series of default risk estimates over the lifetime of each loan, i.e., its term-structure. The behaviour of loans can be described using a nonstationary and time-dependent semi-Markov model, though we model its elements using a multistate regression-based approach. As such, the transition probabilities are explicitly modelled as a function of a rich set of input variables, including macroeconomic and loan-level inputs. Our modelling techniques are deliberately chosen in ascending order of complexity: 1) a Markov chain; 2) beta regression; and 3) multinomial logistic regression. Using residential mortgage data, our results show that each successive model outperforms the previous, likely as a result of greater sophistication. This finding required devising a novel suite of simple model diagnostics, which can itself be reused in assessing sampling representativeness and the performance of other modelling techniques. These contributions surely advance the current practice within banking when conducting multistate modelling. Consequently, we believe that the estimation of loss reserves will be more timeous and accurate under IFRS 9.