IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2508.15651.html
   My bibliography  Save this paper

Through-the-Cycle PD Estimation Under Incomplete Data -- A Single Risk Factor Approach

Author

Listed:
  • Barbara Domotor
  • Ferenc Ill'es

Abstract

Banks are required to use long-term default probabilities (PDs) of their portfolios when calculating credit risk capital under internal ratings-based (IRB) models. However, the calibration models and historical data typically reflect prevailing market conditions. According to Basel recommendations, averaging annual PDs over a full economic cycle should yield the long-term PD. In practice, the available data are often temporally incomplete - even for high-risk portfolios. In this paper, we present a method for the simultaneous calibration of long-term PDs across all sub-portfolios, based on the single risk factor model embedded in the Basel framework. The method is suitable even for smaller, budget-constrained institutions, as it relies exclusively on the bank's own default data. A complete dataset is not required - not even for any individual sub-portfolio - as the only prerequisite is the presence of overlapping data before and after the missing values, a mild condition that is typically met in practical situations.

Suggested Citation

  • Barbara Domotor & Ferenc Ill'es, 2025. "Through-the-Cycle PD Estimation Under Incomplete Data -- A Single Risk Factor Approach," Papers 2508.15651, arXiv.org.
    • Handle: RePEc:arx:papers:2508.15651
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2508.15651
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. L. J. Basson & Gary van Vuuren, 2023. "Through-the-cycle to Point-in-time Probabilities of Default Conversion: Inconsistencies in the Vasicek Approach," International Journal of Economics and Financial Issues, Econjournals, vol. 13(6), pages 42-52, November.
    2. Zoltán Novotny-Farkas, 2016. "The Interaction of the IFRS 9 Expected Loss Approach with Supervisory Rules and Implications for Financial Stability," Accounting in Europe, Taylor & Francis Journals, vol. 13(2), pages 197-227, May.
    3. Lopez, Jose A., 2004. "The empirical relationship between average asset correlation, firm probability of default, and asset size," Journal of Financial Intermediation, Elsevier, vol. 13(2), pages 265-283, April.
    4. Bernd Engelmann, 2024. "A simple and consistent credit risk model for Basel II/III, IFRS 9 and stress testing when loan data history is short," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 1-29, September.
    5. García-Céspedes, Rubén & Moreno, Manuel, 2017. "An approximate multi-period Vasicek credit risk model," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 105-113.
    6. S Ingolfsson & B T Elvarsson, 2010. "Cyclical adjustment of point-in-time PD," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 374-380, March.
    7. Aguais, Scott, 2008. "Designing and Implementing a Basel II Compliant PIT-TTC Ratings Framework," MPRA Paper 6902, University Library of Munich, Germany.
    8. T Bellotti & J Crook, 2009. "Credit scoring with macroeconomic variables using survival analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1699-1707, December.
    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. Joseph L. Breeden, 2024. "An Age–Period–Cohort Framework for Profit and Profit Volatility Modeling," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    2. Tomáš Vaněk & David Hampel, 2017. "The Probability of Default Under IFRS 9: Multi-period Estimation and Macroeconomic Forecast," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(2), pages 759-776.
    3. Anton van Dyk & Gary van Vuuren, 2023. "Measurement and Calibration of Regulatory Credit Risk Asset Correlations," JRFM, MDPI, vol. 16(9), pages 1-19, September.
    4. Arno Botha & Tanja Verster & Roelinde Bester, 2024. "The TruEnd-procedure: Treating trailing zero-valued balances in credit data," Papers 2404.17008, arXiv.org, revised Nov 2025.
    5. Michel Alexandre & Giovani A. S. Brito & Theo C. Martins, . "Default contagion among credit modalities: evidence from Brazilian data," Journal of Credit Risk, Journal of Credit Risk.
    6. Eva Catarineu-Rabell & Patricia Jackson & Dimitrios Tsomocos, 2005. "Procyclicality and the new Basel Accord - banks’ choice of loan rating system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 537-557, October.
    7. William Gornall & Ilya A. Strebulaev, 2013. "Financing as a Supply Chain: The Capital Structure of Banks and Borrowers," NBER Working Papers 19633, National Bureau of Economic Research, Inc.
    8. Quirini Lorenzo & Vannucci Luigi & Quirini Giovanni, 2025. "Modelling Prepayment and Default under Changing Credit Market Conditions for a Net Present Value Analysis," Papers 2508.07774, arXiv.org.
    9. Trueck, Stefan & Rachev, Svetlozar T., 2008. "Rating Based Modeling of Credit Risk," Elsevier Monographs, Elsevier, edition 1, number 9780123736833.
    10. Xia Li & Hanghang Zheng & Xiao Chen & Hong Liu & Mao Mao, 2025. "Class-Imbalanced-Aware Adaptive Dataset Distillation for Scalable Pretrained Model on Credit Scoring," Papers 2501.10677, arXiv.org, revised Jan 2025.
    11. Linda Allen & Anthony Saunders, 2004. "Incorporating Systemic Influences Into Risk Measurements: A Survey of the Literature," Journal of Financial Services Research, Springer;Western Finance Association, vol. 26(2), pages 161-191, October.
    12. García Osma, Beatriz & Mora, Araceli & Porcuna-Enguix, Luis, 2019. "Prudential supervisors’ independence and income smoothing in European banks," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 156-176.
    13. Ghulam, Yaseen, 2025. "A further examination of sovereign domestic and external debt defaults," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    14. Ismail Tijjani Idris & Sabri Nayan, 2016. "The Moderating Role of Loan Monitoring on the Relationship between Macroeconomic Variables and Non-performing Loans in Association of Southeast Asian Nations Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 6(2), pages 402-408.
    15. Arno Botha & Tanja Verster, 2025. "Approaches for modelling the term-structure of default risk under IFRS 9: A tutorial using discrete-time survival analysis," Papers 2507.15441, arXiv.org, revised Oct 2025.
    16. Ferreira Filipe, Sara & Grammatikos, Theoharry & Michala, Dimitra, 2016. "Pricing default risk: The good, the bad, and the anomaly," Journal of Financial Stability, Elsevier, vol. 26(C), pages 190-213.
    17. Wolff, Christian & Bams, Dennis & Pisa, Magdalena, 2015. "Credit risk characteristics of US small business portfolios," CEPR Discussion Papers 10889, C.E.P.R. Discussion Papers.
    18. Dirick, Lore & Claeskens, Gerda & Vasnev, Andrey & Baesens, Bart, 2022. "A hierarchical mixture cure model with unobserved heterogeneity for credit risk," Econometrics and Statistics, Elsevier, vol. 22(C), pages 39-55.
    19. Kritzinger, Nico & van Vuuren, Gary Wayne, 2021. "Non-capital calibration of bureau scorecards," The Quarterly Review of Economics and Finance, Elsevier, vol. 79(C), pages 260-271.
    20. Dirick, Lore & Claeskens, Gerda & Baesens, Bart, 2015. "An Akaike information criterion for multiple event mixture cure models," European Journal of Operational Research, Elsevier, vol. 241(2), pages 449-457.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2508.15651. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.