Deriving the term-structure of loan write-off risk under IFRS 9 by using survival analysis: A benchmark study

Paper: arXiv 2603.11897

Authors: Arno Botha, Mohammed Gabru, Marcel Muller, Janette Larney

Abstract

The estimation of marginal loan write-off probabilities is a non-trivial task when modelling the loss given default (LGD) risk parameter in credit risk. We explore two types of survival models in estimating the overall write-off probability over default spell time, where these probabilities form the term-structure of write-off risk in aggregate. These survival models include a discrete-time hazard (DtH) model and a conditional inference survival tree. Both models are compared to a cross-sectional logistic regression model for write-off risk. All of these (first-stage) models are then ensconced in a broader two-stage LGD-modelling approach, wherein a loss severity model is estimated in the second stage. In expanding the model suite, a novel dichotomisation step is introduced for collapsing the write-off probability into a 0/1-value, prior to LGD-calculation. A benchmark study is subsequently conducted amongst the resulting LGD-models. We find that the DtH-model outperforms other two-stage LGD-models admirably across most diagnostics. However, a single-stage LGD-model still had the best results, likely due to the peculiar `L-shaped’ LGD-distribution in our data. Ultimately, we believe that our tutorial-style work can enhance LGD-modelling practices when estimating the expected credit loss under IFRS 9.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a rigorous application of discrete-time hazard models and conditional inference survival trees to model loan write-off term structure under IFRS 9. It combines solid theoretical survival analysis with a robust empirical design on a large real-world mortgage dataset, complete with open-source R code for high reproducibility.

Research Flowchart

  flowchart TD
    A["Research Goal: Estimate Write-Off Risk Term-Structure & Boost IFRS 9 LGD Accuracy"] --> B["Data Inputs: Default spell data with L-shaped LGD distribution"]
    
    B --> C["Stage 1: Model Write-Off Risk<br>(Logistic Regression vs DtH vs Survival Tree)"]
    
    C --> D["Novel Dichotomisation Step<br>(Collapse Write-Off Probability to 0/1)"]
    
    D --> E["Stage 2: Loss Severity Estimation<br>& Compare Two-Stage vs Single-Stage LGD"]
    
    E --> F["Key Outcome: DtH outperforms among Two-Stage models;<br>Single-Stage LGD wins overall due to data distribution"]

Cited References (71)

1. A procedure for loss-optimising the timing of loan recovery under uncertainty (2021) — link
2. A cost of capital approach to determining the LGD discount rate — → 2503.23992
3. Simulation-based optimisation of the timing of loan recovery across different portfolios (2021) — link
4. Approaches for modelling the term-structure of default risk under IFRS 9: A tutorial using discrete-time survival analysis (2026) — link
5. Towards modelling lifetime default risk: Exploring different subtypes of recurrent event Cox-regression models (2025) — link
6. Deriving the term-structure of loan write-off risk under IFRS 9 using survival analysis [Source Code] (2026) — link
7. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS (2016)
8. Credit Risk Management: Basic Concepts (2009) — link

1 of 71 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.