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

Paper: arXiv 2502.14479

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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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

Cited References (69)

1. Defining and comparing SICR-events for classifying impaired loans under IFRS 9 — → 2303.03080
2. A procedure for loss-optimising the timing of loan recovery under uncertainty (2021) — link
3. Simulation-based optimisation of the timing of loan recovery across different portfolios (2021) — link
4. Modelling the term-structure of default risk under IFRS 9 within a multistate regression framework [Source Code] (2025) — link
5. Credit risk scorecards: developing and implementing intelligent credit scoring (2005)
6. Consumer Credit Models: Pricing, Profit and Portfolios (2009) — link
7. Credit risk analytics: Measurement techniques, applications, and examples in SAS (2016)
8. Credit scoring and its applications (2002) — link

1 of 69 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.