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

ArXiv ID: 2502.14479 “View on arXiv”

Authors: Unknown

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.

Keywords: Credit Risk Modeling, Loan Term-Structure, Semi-Markov Models, IFRS 9, Default Probability

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical techniques (beta regression, multinomial logistic regression) within a multistate framework, indicating high mathematical density. It is strongly data-driven, using residential mortgage data and evaluating model performance, which aligns with high empirical rigor.

  flowchart TD
    A["Research Goal"] --> B["Data & Inputs"]
    B --> C["Model Development"]
    C --> D["Performance Evaluation"]
    D --> E["Key Findings"]

    subgraph A ["Research Goal"]
        A1["Model loan lifetime<br/>default risk term-structure<br/>under IFRS 9"]
    end

    subgraph B ["Data & Inputs"]
        B1["Residential Mortgage Data"]
        B2["Macroeconomic Variables"]
        B3["Loan-Level Features"]
    end

    subgraph C ["Methodology"]
        C1["Markov Chain"]
        C2["Beta Regression"]
        C3["Multinomial Logistic Regression"]
    end

    subgraph D ["Computations"]
        D1["Custom Diagnostics Suite"]
        D2["Model Comparison"]
    end

    subgraph E ["Outcomes"]
        E1["Successive Models Outperform Previous"]
        E2["Enhanced IFRS 9 Loss Reserve Accuracy"]
    end