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A hypothesis test for the long-term calibration in rating systems with overlapping time windows

Author

Listed:
  • Kurth, Patrick

    (Center for Mathematical Economics, Bielefeld University)

  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

  • Streicher, Jan

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We present a statistical test that can be used to verify supervisory re- quirements concerning overlapping time windows for the long-term calibration in rating systems. In a first step, we show that the long-run default rate is approximately normally distributed with respect to random effects in default realization. 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 for the long-run default rate. In this context, we present several methods for a conservative calibration test that can deal with the unknown variance in the test statistic. We present a test for individual rating grades, and then pass to the portfolio level by suitably adapting the test statistic. We conclude with comparative statics analysing the effect of persisting customers and the number of customers per reference date.

Suggested Citation

  • Kurth, Patrick & Nendel, Max & Streicher, Jan, 2025. "A hypothesis test for the long-term calibration in rating systems with overlapping time windows," Center for Mathematical Economics Working Papers 735, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:735
    as

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    File URL: https://pub.uni-bielefeld.de/download/3006162/3006163
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    References listed on IDEAS

    as
    1. Dirk Tasche, 2003. "A traffic lights approach to PD validation," Papers cond-mat/0305038, arXiv.org.
    2. Weiping Li, 2016. "Probability of Default and Default Correlations," JRFM, MDPI, vol. 9(3), pages 1-19, July.
    3. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    4. Sauer, Stephan & Coppens, François & Mayer, Manuel & Millischer, Laurent & Resch, Florian & Schulze, Klaas, 2016. "Advances in multivariate back-testing for credit risk underestimation," Working Paper Series 1885, European Central Bank.
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