IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v79y2024ics0927539824000744.html
   My bibliography  Save this article

Using the Bayesian sampling method to estimate corporate loss given default distribution

Author

Listed:
  • Zhang, Xiaofei
  • Zhao, Xinlei

Abstract

We use Markov chain Monte Carlo (MCMC) sampling to draw model coefficients to generate LGD distributions. We find that applying this Bayesian method on a sophisticated model, such as the zero-one-inflated beta (ZOIB) model, that accounts for the bi-modal distribution of the LGDs can generate LGD distributions that mimic the observed distributions well. By contrast, applying this Bayesian sampling approach on a simple model such as Tobit cannot capture the bi-modal LGD distributions accurately. Finally, we argue that this Bayesian sampling approach to generate LGD distributions is better fit for the stress testing purpose than the typical approach to estimate LGD model coefficients and then stress the macro variables. The latter approach yields stressed LGDs that may not be conservative enough, even if the macro variables are stressed to their worst historical values.

Suggested Citation

  • Zhang, Xiaofei & Zhao, Xinlei, 2024. "Using the Bayesian sampling method to estimate corporate loss given default distribution," Journal of Empirical Finance, Elsevier, vol. 79(C).
    • Handle: RePEc:eee:empfin:v:79:y:2024:i:c:s0927539824000744
    DOI: 10.1016/j.jempfin.2024.101540
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927539824000744
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jempfin.2024.101540?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    2. Katarzyna Bijak & Lyn C Thomas, 2015. "Modelling LGD for unsecured retail loans using Bayesian methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(2), pages 342-352, February.
    3. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Edward I. Altman & Vellore M. Kishore, 1996. "Almost Everything You Wanted to Know about Recoveries on Defaulted Bonds," Financial Analysts Journal, Taylor & Francis Journals, vol. 52(6), pages 57-64, November.
    6. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    7. Altman, Edward I. & Kalotay, Egon A., 2014. "Ultimate recovery mixtures," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 116-129.
    8. Jobst, Rainer & Kellner, Ralf & Rösch, Daniel, 2020. "Bayesian loss given default estimation for European sovereign bonds," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1073-1091.
    9. Loterman, Gert & Brown, Iain & Martens, David & Mues, Christophe & Baesens, Bart, 2012. "Benchmarking regression algorithms for loss given default modeling," International Journal of Forecasting, Elsevier, vol. 28(1), pages 161-170.
    10. Sigrist, Fabio & Stahel, Werner A., 2011. "Using the Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 673-710, November.
    11. Abraham (Avri) Ravid, S. & Sverdlove, Ronald & Bris, Arturo & Coiculescu, Gabriela, 2015. "Conflicts in Bankruptcy and the Sequence of Debt Issues," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 50(6), pages 1353-1388, December.
    12. Yashkir, Olga & Yashkir, Yuriy, 2013. "Loss Given Default Modelling: Comparative Analysis," MPRA Paper 46147, University Library of Munich, Germany.
    13. Hartmann-Wendels, Thomas & Miller, Patrick & Töws, Eugen, 2014. "Loss given default for leasing: Parametric and nonparametric estimations," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 364-375.
    14. Ellen Tobback & David Martens & Tony Van Gestel & Bart Baesens, 2014. "Forecasting Loss Given Default models: impact of account characteristics and the macroeconomic state," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(3), pages 376-392, March.
    15. Hurlin, Christophe & Leymarie, Jérémy & Patin, Antoine, 2018. "Loss functions for Loss Given Default model comparison," European Journal of Operational Research, Elsevier, vol. 268(1), pages 348-360.
    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. Hwang, Ruey-Ching & Chu, Chih-Kang & Yu, Kaizhi, 2020. "Predicting LGD distributions with mixed continuous and discrete ordinal outcomes," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1003-1022.
    2. Kaposty, Florian & Kriebel, Johannes & Löderbusch, Matthias, 2020. "Predicting loss given default in leasing: A closer look at models and variable selection," International Journal of Forecasting, Elsevier, vol. 36(2), pages 248-266.
    3. Ruey-Ching Hwang & Chih-Kang Chu & Kaizhi Yu, 2021. "Predicting the Loss Given Default Distribution with the Zero-Inflated Censored Beta-Mixture Regression that Allows Probability Masses and Bimodality," Journal of Financial Services Research, Springer;Western Finance Association, vol. 59(3), pages 143-172, June.
    4. Kellner, Ralf & Nagl, Maximilian & Rösch, Daniel, 2022. "Opening the black box – Quantile neural networks for loss given default prediction," Journal of Banking & Finance, Elsevier, vol. 134(C).
    5. Xia, Yufei & Zhao, Junhao & He, Lingyun & Li, Yinguo & Yang, Xiaoli, 2021. "Forecasting loss given default for peer-to-peer loans via heterogeneous stacking ensemble approach," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1590-1613.
    6. Ruey-Ching Hwang & Huimin Chung & C. K. Chu, 2016. "A Two-Stage Probit Model for Predicting Recovery Rates," Journal of Financial Services Research, Springer;Western Finance Association, vol. 50(3), pages 311-339, December.
    7. Marc Gürtler & Marvin Zöllner, 2023. "Heterogeneities among credit risk parameter distributions: the modality defines the best estimation method," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 251-287, March.
    8. Salvatore D. Tomarchio & Antonio Punzo, 2019. "Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1247-1266, October.
    9. Nazemi, Abdolreza & Rezazadeh, Hani & Fabozzi, Frank J. & Höchstötter, Markus, 2022. "Deep learning for modeling the collection rate for third-party buyers," International Journal of Forecasting, Elsevier, vol. 38(1), pages 240-252.
    10. Hurlin, Christophe & Leymarie, Jérémy & Patin, Antoine, 2018. "Loss functions for Loss Given Default model comparison," European Journal of Operational Research, Elsevier, vol. 268(1), pages 348-360.
    11. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    12. Nazemi, Abdolreza & Fatemi Pour, Farnoosh & Heidenreich, Konstantin & Fabozzi, Frank J., 2017. "Fuzzy decision fusion approach for loss-given-default modeling," European Journal of Operational Research, Elsevier, vol. 262(2), pages 780-791.
    13. Olson, Luke M. & Qi, Min & Zhang, Xiaofei & Zhao, Xinlei, 2021. "Machine learning loss given default for corporate debt," Journal of Empirical Finance, Elsevier, vol. 64(C), pages 144-159.
    14. Nazemi, Abdolreza & Fabozzi, Frank J., 2024. "Interpretable machine learning for creditor recovery rates," Journal of Banking & Finance, Elsevier, vol. 164(C).
    15. Jennifer Betz & Ralf Kellner & Daniel Rösch, 2021. "Time matters: How default resolution times impact final loss rates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 619-644, June.
    16. Paolo Gambetti & Francesco Roccazzella & Frédéric Vrins, 2022. "Meta-Learning Approaches for Recovery Rate Prediction," Risks, MDPI, vol. 10(6), pages 1-29, June.
    17. Yao, Xiao & Crook, Jonathan & Andreeva, Galina, 2017. "Enhancing two-stage modelling methodology for loss given default with support vector machines," European Journal of Operational Research, Elsevier, vol. 263(2), pages 679-689.
    18. Chih-Kang Chu & Ruey-Ching Hwang, 2019. "Predicting Loss Distributions for Small-Size Defaulted-Debt Portfolios Using a Convolution Technique that Allows Probability Masses to Occur at Boundary Points," Journal of Financial Services Research, Springer;Western Finance Association, vol. 56(1), pages 95-117, August.
    19. Miller, Patrick & Töws, Eugen, 2018. "Loss given default adjusted workout processes for leases," Journal of Banking & Finance, Elsevier, vol. 91(C), pages 189-201.
    20. Yuta Tanoue & Satoshi Yamashita & Hideaki Nagahata, 2020. "Comparison study of two-step LGD estimation model with probability machines," Risk Management, Palgrave Macmillan, vol. 22(3), pages 155-177, September.

    More about this item

    Keywords

    Finance; Loss given default; Bi-modal distribution; Bayesian; Zero-one-inflated beta model;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

    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:eee:empfin:v:79:y:2024:i:c:s0927539824000744. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jempfin .

    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.