IDEAS home Printed from https://ideas.repec.org/a/nbp/nbpbik/v55y2024i3p313-332.html
   My bibliography  Save this article

Credit loss modelling using beta distribution in a Bayesian approach

Author

Listed:
  • Aneta Ptak-Chmielewska

    (Warsaw School of Economics)

  • Paweł Kopciuszewski

    (Vistula University of Warsaw, ING Hubs Poland)

Abstract

The Advanced Internal Rating Based (AIRB) approach is more and more frequently applied by banks. Bank analysts decide to use their own approach to calculate basic risk parameters such as Probability of Default (PD), Exposure at Default (EAD), and Loss Given Default (LGD). The problem of small samples in LGD estimation is always a challenge for researchers and analytics. The paper proposes the basic LGD model based on splitting recoveries into two classes of recoveries: close to 0 or close to 1, and based on that split the construction of the LGD model with the combination of two binary models. The main advantage of the paper is, however, addressing the unresolved cases incorporated in the LGD estimation process by using a Bayesian approach which assumes a beta distribution of further recoveries for unresolved cases. An additional advantage of the paper is that the proposed modelling approach for LGD is illustrated on real data for mortgage loans for one of the European banks.

Suggested Citation

  • Aneta Ptak-Chmielewska & Paweł Kopciuszewski, 2024. "Credit loss modelling using beta distribution in a Bayesian approach," Bank i Kredyt, Narodowy Bank Polski, vol. 55(3), pages 313-332.
    • Handle: RePEc:nbp:nbpbik:v:55:y:2024:i:3:p:313-332
    as

    Download full text from publisher

    File URL: https://bankikredyt.nbp.pl/content/2024/03/bik_03_2024_04.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Radovan Chalupka & Juraj Kopecsni, 2009. "Modeling Bank Loan LGD of Corporate and SME Segments: A Case Study," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 59(4), pages 360-382, Oktober.
    2. A Matuszyk & C Mues & L C Thomas, 2010. "Modelling LGD for unsecured personal loans: decision tree approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 393-398, March.
    3. Gurdip Bakshi & Dilip B. Madan & Frank X. Zhang, 2001. "Investigating the sources of default risk: lessons from empirically evaluating credit risk models," Finance and Economics Discussion Series 2001-15, Board of Governors of the Federal Reserve System (U.S.).
    4. Mario Anolli & Elena Beccalli & Tommaso Giordani (ed.), 2013. "Retail Credit Risk Management," Palgrave Macmillan Studies in Banking and Financial Institutions, Palgrave Macmillan, number 978-1-137-00676-9, February.
    5. 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.
    6. 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.
    7. Marko Kosak & Jure Poljsak, 2010. "Loss given default determinants in a commercial bank lending: an emerging market case study," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 28(1), pages 61-88.
    8. Aneta Ptak-Chmielewska & Paweł Kopciuszewski & Anna Matuszyk, 2023. "Application of the kNN-Based Method and Survival Approach in Estimating Loss Given Default for Unresolved Cases," Risks, MDPI, vol. 11(2), pages 1-14, February.
    9. Dirk Tasche, 2004. "The single risk factor approach to capital charges in case of correlated loss given default rates," Papers cond-mat/0402390, arXiv.org, revised Feb 2004.
    10. 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.
    11. Aneta Ptak-Chmielewska & Paweł Kopciuszewski, 2023. "Application of the Bayesian approach in loss given default modelling," Bank i Kredyt, Narodowy Bank Polski, vol. 54(6), pages 625-650.
    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. Aneta Ptak-Chmielewska & Paweł Kopciuszewski, 2023. "Application of the Bayesian approach in loss given default modelling," Bank i Kredyt, Narodowy Bank Polski, vol. 54(6), pages 625-650.
    2. 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.
    3. Starosta, Wojciech, 2021. "Loss given default decomposition using mixture distributions of in-default events," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1187-1199.
    4. Do, Hung Xuan & Rösch, Daniel & Scheule, Harald, 2018. "Predicting loss severities for residential mortgage loans: A three-step selection approach," European Journal of Operational Research, Elsevier, vol. 270(1), pages 246-259.
    5. 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.
    6. Wojciech Starosta, 2020. "Modelling Recovery Rate for Incomplete Defaults Using Time Varying Predictors," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(2), pages 195-225, June.
    7. 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.
    8. 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).
    9. Betz, Jennifer & Kellner, Ralf & Rösch, Daniel, 2018. "Systematic Effects among Loss Given Defaults and their Implications on Downturn Estimation," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1113-1144.
    10. 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.
    11. Natalia Nehrebecka, 2019. "Bank loans recovery rate in commercial banks: A case study of non-financial corporations," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 37(1), pages 139-172.
    12. 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.
    13. 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.
    14. Chen, Xiaowei & Wang, Gang & Zhang, Xiangting, 2019. "Modeling recovery rate for leveraged loans," Economic Modelling, Elsevier, vol. 81(C), pages 231-241.
    15. Christophe Hurlin & Jérémy Leymarie & Antoine Patin, 2018. "Loss functions for LGD model comparison," Working Papers halshs-01516147, HAL.
    16. 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.
    17. Thamayanthi Chellathurai, 2017. "Probability Density Of Recovery Rate Given Default Of A Firm’S Debt And Its Constituent Tranches," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-34, June.
    18. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    19. Tong, Edward N.C. & Mues, Christophe & Brown, Iain & Thomas, Lyn C., 2016. "Exposure at default models with and without the credit conversion factor," European Journal of Operational Research, Elsevier, vol. 252(3), pages 910-920.
    20. Bastos, João A. & Matos, Sara M., 2022. "Explainable models of credit losses," European Journal of Operational Research, Elsevier, vol. 301(1), pages 386-394.

    More about this item

    Keywords

    Loss Given Default (LGD); Bayesian approach; beta regression; unresolved cases; small sample;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

    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:nbp:nbpbik:v:55:y:2024:i:3:p:313-332. 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: Wojciech Burjanek (email available below). General contact details of provider: https://edirc.repec.org/data/nbpgvpl.html .

    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.