IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v12y2024i8p131-d1458069.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/12/8/131/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/12/8/131/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Patrick Kurth & Max Nendel & Jan Streicher, 2023. "A hypothesis test for the long-term calibration in rating systems with overlapping time windows," Papers 2312.14765, arXiv.org.
    2. Brunella Bruno & Immacolata Marino & Giacomo Nocera, 2020. "Internal Ratings, Non-Performing Loans, and Bank Opacity: Evidence from Analysts’ Forecasts," CSEF Working Papers 576, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 25 Jan 2023.
    3. 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.
    4. Francesco Columba & Federica Orsini & Stefano Tranquillo, 2024. "Rating the Raters. Some Perspective From a Central Bank," Mercati, infrastrutture, sistemi di pagamento (Markets, Infrastructures, Payment Systems) 55, Bank of Italy, Directorate General for Markets and Payment System.
    5. François Coppens & Fernando Gonzáles & Gerhard Winkler, 2007. "The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary policy operations," Working Paper Research 118, National Bank of Belgium.
    6. António R. Antunes & Homero Gonçalves & Pedro Prego, 2016. "Firm default probabilities revisited," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.
    7. Henry Penikas & Anastasia Skarednova & Mikhail Surkov, 2021. "How Do Investors Prefer Banks to Transit to Basel Internal Models: Mandatorily or Voluntarily?," Bank of Russia Working Paper Series wps74, Bank of Russia.
    8. Merikas, Andreas & Merika, Anna & Penikas, Henry I. & Surkov, Mikhail A., 2020. "The Basel II internal ratings based (IRB) model and the transition impact on the listed Greek banks," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    9. Skała, Dorota, 2020. "Shareholder shocks and loan loss provisions in Central European banks," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 69(C).
    10. Casellina, Simone & Pandolfo, Giuseppe & Quagliariello, Mario, 2020. "Applying the Pre-Commitment Approach to bottom-up stress tests: A new old story," Journal of Economics and Business, Elsevier, vol. 112(C).
    11. Liu, Cai, 2021. "The IRB model, bank regulatory arbitrage, and the Eurozone crisis," Journal of International Money and Finance, Elsevier, vol. 116(C).
    12. Bruno, Brunella & Marino, Immacolata & Nocera, Giacomo, 2023. "Internal ratings and bank opacity: Evidence from analysts’ forecasts," Journal of Financial Intermediation, Elsevier, vol. 56(C).
    13. Giorgio Calcagnini & Federico Favaretto & Germana Giombini, 2024. "The effect of 2020 lockdown on bank internal ratings," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 51(2), pages 355-396, June.
    14. Topalog̃lu Bozkurt, Ayça & Özyıldırım, Süheyla, 2025. "Firm commonality, bank connectedness and portfolio riskiness," International Review of Economics & Finance, Elsevier, vol. 97(C).
    15. Dal Borgo, Mariela, 2022. "Internal models for deposits: Effects on banks' capital and interest rate risk of assets," Journal of Banking & Finance, Elsevier, vol. 135(C).
    16. Bitetto, Alessandro & Cerchiello, Paola & Filomeni, Stefano & Tanda, Alessandra & Tarantino, Barbara, 2023. "Machine learning and credit risk: Empirical evidence from small- and mid-sized businesses," Socio-Economic Planning Sciences, Elsevier, vol. 90(C).
    17. B. Bruno & I. Marino & G. Nocera, 2023. "Internal Ratings and Bank Opacity: Evidence from Analysts’ Forecasts," Post-Print hal-04322520, HAL.
    18. Acheampong, Albert & Elshandidy, Tamer, 2021. "Does soft information determine credit risk? Text-based evidence from European banks," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    19. Natalia Nehrebecka, 2021. "COVID-19: stress-testing non-financial companies: a macroprudential perspective. The experience of Poland," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(2), pages 283-319, June.
    20. D Martens & T Van Gestel & M De Backer & R Haesen & J Vanthienen & B Baesens, 2010. "Credit rating prediction using Ant Colony Optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 561-573, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:12:y:2024:i:8:p:131-:d:1458069. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.