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Bayesian estimation of probabilities of default for low default portfolios

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  • Tasche, Dirk

Abstract

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well-established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the estimation. The Bayesian estimator for the PD based on the uninformed, uniform prior distribution is an obvious alternative that avoids the choice of a confidence level. It is demonstrated in this paper that in the case of independent default events the upper confidence bounds can be represented as quantiles of a Bayesian posterior distribution based on a prior that is slightly more conservative than the uninformed prior. The paper then describes how to implement the uninformed and conservative Bayesian estimators in the dependent one- and multi-period default data cases and compares their estimates with the upper confidence bound estimates. The comparison leads to a suggestion of a constrained version of the uninformed (neutral) Bayesian estimator as an alternative to the upper confidence bound estimators.

Suggested Citation

  • Tasche, Dirk, 2013. "Bayesian estimation of probabilities of default for low default portfolios," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 6(3), pages 302-326, July.
    • Handle: RePEc:aza:rmfi00:y:2013:v:6:i:3:p:302-326
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    Citations

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    Cited by:

    1. Andrius Grigutis, 2023. "Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche," Papers 2303.06148, arXiv.org.
    2. Blümke, Oliver, 2018. "On the cyclicality of default rates of banks: A comparative study of the asset correlation and diversification effects," Journal of Empirical Finance, Elsevier, vol. 47(C), pages 65-77.
    3. Oliver Blümke, 2020. "Estimating the probability of default for no‐default and low‐default portfolios," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(1), pages 89-107, January.
    4. Oliver Blümke, 2022. "Multiperiod default probability forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 677-696, July.
    5. Yi-Ping Chang & Chih-Tun Yu, 2014. "Bayesian confidence intervals for probability of default and asset correlation of portfolio credit risk," Computational Statistics, Springer, vol. 29(1), pages 331-361, February.
    6. Nendel, Max & Streicher, Jan, 2025. "An axiomatic approach to default risk and model uncertainty in rating systems," Center for Mathematical Economics Working Papers 725, Center for Mathematical Economics, Bielefeld University.
    7. Nendel, Max & Streicher, Jan, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    8. Denis Surzhko, 2017. "Bayesian Approach to PD Calibration and Stress-testing in Low Default Portfolios," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 7(2), pages 1-6.
    9. Baesens, Bart & Smedts, Kristien, 2025. "Boosting credit risk models," The British Accounting Review, Elsevier, vol. 57(4).

    More about this item

    Keywords

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    JEL classification:

    • G2 - Financial Economics - - Financial Institutions and Services
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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