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A Hypothesis Test for the Long-Term Calibration in Rating Systems with Overlapping Time Windows

Author

Listed:
  • Patrick Kurth

    (Landesbank Baden-Württemberg, 70173 Stuttgart, Germany)

  • Max Nendel

    (Center for Mathematical Economics, Bielefeld University, 33615 Bielefeld, Germany)

  • Jan Streicher

    (Landesbank Baden-Württemberg, 70173 Stuttgart, Germany
    Center for Mathematical Economics, Bielefeld University, 33615 Bielefeld, Germany)

Abstract

We present a statistical test for the long-term calibration in rating systems that can deal with overlapping time windows as required by the guidelines of the European Banking Authority (EBA), which apply to major financial institutions in the European System. In accordance with regulation, rating systems are to be calibrated and validated with respect to the long-run default rate. The consideration of one-year default rates on a quarterly basis leads to correlation effects which drastically influence the variance of the long-run default rate. In a first step, we show that the long-run default rate is approximately normally distributed. We then perform a detailed analysis of the correlation effects caused by the overlapping time windows and solve the problem of an unknown distribution of default probabilities.

Suggested Citation

  • Patrick Kurth & Max Nendel & Jan Streicher, 2024. "A Hypothesis Test for the Long-Term Calibration in Rating Systems with Overlapping Time Windows," Risks, MDPI, vol. 12(8), pages 1-28, August.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:8:p:131-:d:1458069
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    References listed on IDEAS

    as
    1. Cucinelli, Doriana & Battista, Maria Luisa Di & Marchese, Malvina & Nieri, Laura, 2018. "Credit risk in European banks: The bright side of the internal ratings based approach," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 213-229.
    2. Sergio Caprioli & Emanuele Cagliero & Riccardo Crupi, 2023. "Quantifying Credit Portfolio sensitivity to asset correlations with interpretable generative neural networks," Papers 2309.08652, arXiv.org, revised Nov 2023.
    3. Weiping Li, 2016. "Probability of Default and Default Correlations," JRFM, MDPI, vol. 9(3), pages 1-19, July.
    4. Dirk Tasche, 2003. "A traffic lights approach to PD validation," Papers cond-mat/0305038, arXiv.org.
    5. Aussenegg, Wolfgang & Resch, Florian & Winkler, Gerhard, 2011. "Pitfalls and remedies in testing the calibration quality of rating systems," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 698-708, March.
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