IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/57244.html
   My bibliography  Save this paper

Estimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models

Author

Listed:
  • Yang, Bill Huajian

Abstract

In this paper, we propose a Vasicek-type of models for estimating portfolio level probability of default (PD). With these Vasicek models, asset correlation and long-run PD for a risk homogenous portfolio both have analytical solutions, longer external time series for market and macroeconomic variables can be included, and the traditional asymptotic maximum likelihood approach can be shown to be equivalent to least square regression, which greatly simplifies parameter estimation. The analytical formula for long-run PD, for example, explicitly quantifies the contribution of uncertainty to an increase of long-run PD. We recommend the bootstrap approach to addressing the serial correlation issue for a time series sample. To validate the proposed models, we estimate the asset correlations for 13 industry sectors using corporate annual default rates from S&P for years 1981-2011, and long-run PD and asset correlation for a US commercial portfolio, using US delinquent rate for commercial and industry loans from US Federal Reserve.

Suggested Citation

  • Yang, Bill Huajian, 2013. "Estimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models," MPRA Paper 57244, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:57244
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/57244/1/MPRA_paper_57244.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Maria Soledad Martinez Peria & Mr. Giovanni Majnoni & Mr. Matthew T Jones & Mr. Winfrid Blaschke, 2001. "Stress Testing of Financial Systems: An Overview of Issues, Methodologies, and FSAP Experiences," IMF Working Papers 2001/088, International Monetary Fund.
    4. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 37-52, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Bill Huajian & Yang, Jenny & Yang, Haoji, 2020. "Modeling Portfolio Loss by Interval Distributions," MPRA Paper 102219, University Library of Munich, Germany.
    2. Yang, Bill Huajian & Wu, Biao & Cui, Kaijie & Du, Zunwei & Fei, Glenn, 2019. "IFRS9 Expected Credit Loss Estimation: Advanced Models for Estimating Portfolio Loss and Weighting Scenario Losses," MPRA Paper 93634, University Library of Munich, Germany.
    3. M. Dietsch & K. Düllmann & H. Fraisse & P. Koziol & C. Ott, 2016. "Support for the SME Supporting Factor - Multi-country empirical evidence on systematic risk factor for SME loans," Débats économiques et financiers 23, Banque de France.

    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. Yang, Bill Huajian, 2014. "Modeling Systematic Risk and Point-in-Time Probability of Default under the Vasicek Asymptotic Single Risk Factor Model Framework," MPRA Paper 59025, University Library of Munich, Germany.
    2. Yang, Bill Huajian & Du, Zunwei, 2015. "Stress Testing and Modeling of Rating Migration under the Vasicek Model Framework - Empirical approaches and technical implementation," MPRA Paper 65168, University Library of Munich, Germany.
    3. Nuno Silva & António Santos, 2019. "Sectoral concentration risk in Portuguese banks’ loan exposures to non-financial firms," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.
    4. repec:onb:oenbwp:y:2002:i:3:b:3 is not listed on IDEAS
    5. John Y. Campbell & Jens Hilscher & Jan Szilagyi, 2008. "In Search of Distress Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2899-2939, December.
    6. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 37-52, January.
    7. François Gourio, 2013. "Credit Risk and Disaster Risk," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 1-34, July.
    8. Asis, Gonzalo & Chari, Anusha & Haas, Adam, 2021. "In search of distress risk in emerging markets," Journal of International Economics, Elsevier, vol. 131(C).
    9. Kraft, Holger & Steffensen, Mogens, 2008. "How to invest optimally in corporate bonds: A reduced-form approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 348-385, February.
    10. Breuer, Thomas & Jandacka, Martin & Rheinberger, Klaus & Summer, Martin, 2010. "Does adding up of economic capital for market- and credit risk amount to conservative risk assessment?," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 703-712, April.
    11. Yang, Bill Huajian, 2017. "Point-in-time PD term structure models for multi-period scenario loss projection: Methodologies and implementations for IFRS 9 ECL and CCAR stress testing," MPRA Paper 76271, University Library of Munich, Germany.
    12. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    13. Adithi Ramesh & C. B Senthil Kumar, 2017. "Structure and Intensity Based Approach in Credit Risk Models: A Literature Review," International Journal of Economics and Financial Issues, Econjournals, vol. 7(3), pages 609-612.
    14. Sigrist, Fabio & Leuenberger, Nicola, 2023. "Machine learning for corporate default risk: Multi-period prediction, frailty correlation, loan portfolios, and tail probabilities," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1390-1406.
    15. Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007. "Multi-period corporate default prediction with stochastic covariates," Journal of Financial Economics, Elsevier, vol. 83(3), pages 635-665, March.
    16. Choroś, Barbara & Härdle, Wolfgang Karl & Okhrin, Ostap, 2009. "CDO and HAC," SFB 649 Discussion Papers 2009-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. Nikola A. Tarashev & Haibin Zhu, 2006. "The pricing of portfolio credit risk," BIS Working Papers 214, Bank for International Settlements.
    18. Mark Clintworth & Dimitrios Lyridis & Evangelos Boulougouris, 2023. "Financial risk assessment in shipping: a holistic machine learning based methodology," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 25(1), pages 90-121, March.
    19. Kreis, Yvonne & Leisen, Dietmar P.J., 2018. "Systemic risk in a structural model of bank default linkages," Journal of Financial Stability, Elsevier, vol. 39(C), pages 221-236.
    20. Matteo Accornero & Giuseppe Cascarino & Roberto Felici & Fabio Parlapiano & Alberto Maria Sorrentino, 2018. "Credit risk in banks’ exposures to non‐financial firms," European Financial Management, European Financial Management Association, vol. 24(5), pages 775-791, November.
    21. Anand Deo & Sandeep Juneja, 2021. "Credit Risk: Simple Closed-Form Approximate Maximum Likelihood Estimator," Operations Research, INFORMS, vol. 69(2), pages 361-379, March.

    More about this item

    Keywords

    Portfolio level PD; long-run PD; asset correlation; time series; serial correlation; bootstrapping; binomial distribution; maximum likelihood; least square regression; Vasicek model;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    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:pra:mprapa:57244. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.