Comparing two approaches for modelling the loss given default of credit cards: Run-off triangles vs regression

Paper: arXiv 2610.05926

Authors: Arno Botha, Henko Crewe, Marcel Muller, Janette Larney

Abstract

The use of run-off triangles (ROTs) is a common industry practice in estimating the loss given default (LGD) risk parameter when predicting credit losses in banking. We benchmark this industry practice using credit card data against a more sophisticated (though classical) regression-based approach, which is able to leverage various types of input variables in producing loan-level LGD-estimates. This regression-based approach can demonstrably recover the typical characteristics of the ‘U-shaped’ empirical LGD-distribution, which the ROT-based approach cannot do. First, we critically review the ROT-based approach and identify multiple demerits using data-driven diagnostics. We then estimate a two-stage regression-based LGD-model and favourably assess the model performance of each component (or ‘stage’). Finally, we aggregate the LGD-estimates produced by each approach over time, and compare each time series to the mean empirical loss rate over time. The ROT-based aggregates diverge substantially from the empirical rate over most time periods, whilst the regression-based aggregates follow the empirical trends much closer. These results underscore the greater prediction accuracy of the regression-based LGD-model, relative to the ROT-based one. By implication, the former approach is probably better than the latter ROT-based approach when estimating the LGD under the IFRS 9 accounting framework, which prioritises accuracy.

Complexity vs Empirical Score

• Math Complexity: 6.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper demonstrates strong empirical rigor through its comparative analysis of LGD models using credit card data. It also employs a reasonable level of mathematical sophistication with regression-based approaches and GLMs. The novelty comes from the direct comparison of industry-standard ROTs with more advanced regression techniques for LGD estimation.

Research Flowchart

  flowchart TD
    A[Research Goal: Compare ROT vs Regression for Credit Card LGD Modeling] --> B{Key Methodologies};
    B --> C[Run-Off Triangles (ROTs) Approach];
    B --> D[Two-Stage Regression-Based LGD Model];
    C --> E[Data Input: Credit Card Default Data];
    D --> E;
    E --> F[Computational Processes: Model Estimation & Aggregation];
    F --> G{Key Findings/Outcomes};
    G --> H[ROT: Cannot recover U-shaped LGD, aggregates diverge from empirical rate];
    G --> I[Regression: Recovers U-shaped LGD, aggregates follow empirical trends, higher prediction accuracy, better for IFRS 9];

Cited References (43)

1. A cost of capital approach to determining the LGD discount rate — → 2503.23992
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. Defining and comparing SICR-events for classifying impaired loans under IFRS 9 — → 2303.03080
5. Deriving the term-structure of loan write-off risk under IFRS 9 by using survival analysis: A benchmark study (2026) — link
6. The Management of Consumer Credit: Theory and Practice (2010)
7. Credit Risk Management: Basic Concepts (2009) — link
8. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS (2016)

2 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.