IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v69y2020i1p89-107.html
   My bibliography  Save this article

Estimating the probability of default for no‐default and low‐default portfolios

Author

Listed:
  • Oliver Blümke

Abstract

The paper proposes a sequential Bayesian updating approach to estimate default probabilities on rating grade level for no‐ and low‐default portfolios. Bayesian sequential updating enables default probabilities to be obtained also for those rating grades for which no defaults have been observed. The advantage of this approach is that it preserves the rank order of rating grades in the case of no defaults. Rank preservation is not ensured when using an identical prior distribution across all rating grades. We discuss Bayesian sequential updating for the beta–binomial model and a model incorporating the asymptotic single‐risk factor model of the Basel Accord. Practical aspects such as incorporating information from external sources and the margin of conservatism are addressed.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:69:y:2020:i:1:p:89-107
    DOI: 10.1111/rssc.12381
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12381
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssc.12381?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
    ---><---

    References listed on IDEAS

    as
    1. Fuertes, Ana-Maria & Kalotychou, Elena, 2007. "On sovereign credit migration: A study of alternative estimators and rating dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3448-3469, April.
    2. 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.
    3. Claudia Czado & Carolin Pflüger, 2008. "Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(3), pages 237-259, May.
    4. Mark Thackham & Jun Ma, 2019. "Exposure at default without conversion factors—evidence from Global Credit Data for large corporate revolving facilities," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1267-1286, October.
    5. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    6. Carling, Kenneth & Jacobson, Tor & Linde, Jesper & Roszbach, Kasper, 2007. "Corporate credit risk modeling and the macroeconomy," Journal of Banking & Finance, Elsevier, vol. 31(3), pages 845-868, March.
    7. McNeil, Alexander J. & Wendin, Jonathan P., 2007. "Bayesian inference for generalized linear mixed models of portfolio credit risk," Journal of Empirical Finance, Elsevier, vol. 14(2), pages 131-149, March.
    8. Koopman, Siem Jan & Kräussl, Roman & Lucas, André & Monteiro, André B., 2009. "Credit cycles and macro fundamentals," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 42-54, January.
    9. Pesaran, M. Hashem & Schuermann, Til & Treutler, Bjorn-Jakob & Weiner, Scott M., 2006. "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1211-1261, August.
    10. Kiefer, Nicholas M., 2009. "Default estimation for low-default portfolios," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 164-173, January.
    11. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    12. Feng, D. & Gourieroux, C. & Jasiak, J., 2008. "The ordered qualitative model for credit rating transitions," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 111-130, January.
    13. Aysun Alp, 2013. "Structural Shifts in Credit Rating Standards," Journal of Finance, American Finance Association, vol. 68(6), pages 2435-2470, December.
    14. Giesecke, Kay & Longstaff, Francis A. & Schaefer, Stephen & Strebulaev, Ilya, 2011. "Corporate bond default risk: A 150-year perspective," Journal of Financial Economics, Elsevier, vol. 102(2), pages 233-250.
    15. 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.
    16. Justin Sirignano & Apaar Sadhwani & Kay Giesecke, 2016. "Deep Learning for Mortgage Risk," Papers 1607.02470, arXiv.org, revised Mar 2018.
    17. Bernd Schwaab & Siem Jan Koopman & André Lucas, 2017. "Global Credit Risk: World, Country and Industry Factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 296-317, March.
    18. Koopman, Siem Jan & Lucas, André & Schwaab, Bernd, 2011. "Modeling frailty-correlated defaults using many macroeconomic covariates," Journal of Econometrics, Elsevier, vol. 162(2), pages 312-325, June.
    19. Nicholas M. Kiefer, 2011. "Default estimation, correlated defaults, and expert information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 173-192, March.
    20. Justin Sirignano & Kay Giesecke, 2019. "Risk Analysis for Large Pools of Loans," Management Science, INFORMS, vol. 65(1), pages 107-121, January.
    21. Hanson, Samuel & Schuermann, Til, 2006. "Confidence intervals for probabilities of default," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2281-2301, August.
    22. S. Baena‐Mirabete & P. Puig, 2018. "Parsimonious higher order Markov models for rating transitions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(1), pages 107-131, January.
    23. Lando, David & Skodeberg, Torben M., 2002. "Analyzing rating transitions and rating drift with continuous observations," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 423-444, March.
    24. Ramin P. Baghai & Henri Servaes & Ane Tamayo, 2014. "Have Rating Agencies Become More Conservative? Implications for Capital Structure and Debt Pricing," Journal of Finance, American Finance Association, vol. 69(5), pages 1961-2005, October.
    25. Walter Orth, 2013. "Default probability estimation in small samples--with an application to sovereign bonds," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1891-1902, December.
    26. Dirk Tasche, 2012. "The art of probability-of-default curve calibration," Papers 1212.3716, arXiv.org, revised Nov 2013.
    27. Kiefer, Nicholas M., 2010. "Default Estimation and Expert Information," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 320-328.
    28. Hannes Kazianka, 2016. "Objective Bayesian estimation of the probability of default," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 1-27, January.
    29. Justin A. Sirignano & Gerry Tsoukalas & Kay Giesecke, 2016. "Large-Scale Loan Portfolio Selection," Operations Research, INFORMS, vol. 64(6), pages 1239-1255, December.
    30. Krüger, Steffen & Rösch, Daniel & Scheule, Harald, 2018. "The impact of loan loss provisioning on bank capital requirements," Journal of Financial Stability, Elsevier, vol. 36(C), pages 114-129.
    31. Jonathan Crook & Tony Bellotti, 2010. "Time varying and dynamic models for default risk in consumer loans," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 283-305, April.
    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. Oliver Blümke, 2022. "Multiperiod default probability forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 677-696, July.
    2. 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.
    3. Bernd Schwaab & Siem Jan Koopman & André Lucas, 2017. "Global Credit Risk: World, Country and Industry Factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 296-317, March.
    4. 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.
    5. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    6. 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.
    7. Dimitris Gavalas & Theodore Syriopoulos, 2014. "Bank Credit Risk Management and Rating Migration Analysis on the Business Cycle," IJFS, MDPI, vol. 2(1), pages 1-22, March.
    8. Walter Orth, 2013. "Default probability estimation in small samples--with an application to sovereign bonds," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1891-1902, December.
    9. Hanson, Samuel G. & Pesaran, M. Hashem & Schuermann, Til, 2008. "Firm heterogeneity and credit risk diversification," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 583-612, September.
    10. Orth, Walter, 2011. "Default probability estimation in small samples - with an application to sovereign bonds," MPRA Paper 33778, University Library of Munich, Germany.
    11. Schwaab, Bernd & Koopman, Siem Jan & Lucas, André, 2014. "Nowcasting and forecasting global financial sector stress and credit market dislocation," International Journal of Forecasting, Elsevier, vol. 30(3), pages 741-758.
    12. Drew Creal & Bernd Schwaab & Siem Jan Koopman & Andr� Lucas, 2014. "Observation-Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 898-915, December.
    13. Figlewski, Stephen & Frydman, Halina & Liang, Weijian, 2012. "Modeling the effect of macroeconomic factors on corporate default and credit rating transitions," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 87-105.
    14. Tor Jacobson & Jesper Lindé & Kasper Roszbach, 2013. "Firm Default And Aggregate Fluctuations," Journal of the European Economic Association, European Economic Association, vol. 11(4), pages 945-972, August.
    15. Balios, Dimitris & Thomadakis, Stavros & Tsipouri, Lena, 2016. "Credit rating model development: An ordered analysis based on accounting data," Research in International Business and Finance, Elsevier, vol. 38(C), pages 122-136.
    16. Jeffrey R. Stokes, 2023. "A nonlinear inversion procedure for modeling the effects of economic factors on credit risk migration," Review of Quantitative Finance and Accounting, Springer, vol. 61(3), pages 855-878, October.
    17. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    18. Lee, Yongwoong & Rösch, Daniel & Scheule, Harald, 2016. "Accuracy of mortgage portfolio risk forecasts during financial crises," European Journal of Operational Research, Elsevier, vol. 249(2), pages 440-456.
    19. Orth, Walter, 2011. "Default probability estimation in small samples: With an application to sovereign bonds," Discussion Papers in Econometrics and Statistics 5/11, University of Cologne, Institute of Econometrics and Statistics.
    20. Nguyen, Ha, 2023. "An empirical application of Particle Markov Chain Monte Carlo to frailty correlated default models," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 103-121.

    More about this item

    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:bla:jorssc:v:69:y:2020:i:1:p:89-107. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.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.