IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0068238.html
   My bibliography  Save this article

Curve Fitting of the Corporate Recovery Rates: The Comparison of Beta Distribution Estimation and Kernel Density Estimation

Author

Listed:
  • Rongda Chen
  • Ze Wang

Abstract

Recovery rate is essential to the estimation of the portfolio’s loss and economic capital. Neglecting the randomness of the distribution of recovery rate may underestimate the risk. The study introduces two kinds of models of distribution, Beta distribution estimation and kernel density distribution estimation, to simulate the distribution of recovery rates of corporate loans and bonds. As is known, models based on Beta distribution are common in daily usage, such as CreditMetrics by J.P. Morgan, Portfolio Manager by KMV and Losscalc by Moody’s. However, it has a fatal defect that it can’t fit the bimodal or multimodal distributions such as recovery rates of corporate loans and bonds as Moody’s new data show. In order to overcome this flaw, the kernel density estimation is introduced and we compare the simulation results by histogram, Beta distribution estimation and kernel density estimation to reach the conclusion that the Gaussian kernel density distribution really better imitates the distribution of the bimodal or multimodal data samples of corporate loans and bonds. Finally, a Chi-square test of the Gaussian kernel density estimation proves that it can fit the curve of recovery rates of loans and bonds. So using the kernel density distribution to precisely delineate the bimodal recovery rates of bonds is optimal in credit risk management.

Suggested Citation

  • Rongda Chen & Ze Wang, 2013. "Curve Fitting of the Corporate Recovery Rates: The Comparison of Beta Distribution Estimation and Kernel Density Estimation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-9, July.
    • Handle: RePEc:plo:pone00:0068238
    DOI: 10.1371/journal.pone.0068238
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0068238
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0068238&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0068238?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. Daniel Rösch & Harald Scheule, 2006. "A Multi-Factor Approach for Systematic Default and Recovery Risk," Springer Books, in: Bernd Engelmann & Robert Rauhmeier (ed.), The Basel II Risk Parameters, chapter 0, pages 105-125, Springer.
    2. Jon Frye, 2000. "Depressing recoveries," Emerging Issues, Federal Reserve Bank of Chicago, issue Oct.
    3. repec:uts:ppaper:v:15:y:2005:i:3:p:63-75 is not listed on IDEAS
    4. Düllmann, Klaus & Trapp, Monika, 2004. "Systematic Risk in Recovery Rates: An Empirical Analysis of US Corporate Credit Exposures," Discussion Paper Series 2: Banking and Financial Studies 2004,02, Deutsche Bundesbank.
    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. Can Yilmaz Altinigne & Harun Ozkan & Veli Can Kupeli & Zehra Cataltepe, 2019. "An Empirical Study on Arrival Rates of Limit Orders and Order Cancellation Rates in Borsa Istanbul," Papers 1909.08308, arXiv.org.
    2. 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.
    3. Pawel Siarka, 2021. "Modeling Recoveries of US Leading Banks Based on Publicly Disclosed Data," Mathematics, MDPI, vol. 9(2), pages 1-14, January.
    4. Castellano, Rosella & Corallo, Vincenzo & Morelli, Giacomo, 2022. "Structural estimation of counterparty credit risk under recovery risk," Journal of Banking & Finance, Elsevier, vol. 140(C).

    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. Pavel V. Shevchenko & Xiaolin Luo, 2011. "Dependent default and recovery: MCMC study of downturn LGD credit risk model," Papers 1112.5766, arXiv.org.
    2. Yao, Xiao & Crook, Jonathan & Andreeva, Galina, 2017. "Is it obligor or instrument that explains recovery rate: Evidence from US corporate bond," Journal of Financial Stability, Elsevier, vol. 28(C), pages 1-15.
    3. 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.
    4. Jean-David Fermanian, 2020. "On the Dependence between Default Risk and Recovery Rates in Structural Models," Annals of Economics and Statistics, GENES, issue 140, pages 45-82.
    5. Maria Stefanova, 2012. "Recovery Risiko in der Kreditportfoliomodellierung," Springer Books, Springer, number 978-3-8349-4226-5, November.
    6. Gürtler, Marc & Heithecker, Dirk, 2004. "Modellkonsistente Bestimmung des LGD im IRB-Ansatz von Basel II," Working Papers FW08V3, Technische Universität Braunschweig, Institute of Finance.
    7. Michael Jacobs, 2012. "An empirical study of the returns on defaulted debt," Applied Financial Economics, Taylor & Francis Journals, vol. 22(7), pages 563-579, April.
    8. Li, Hui, 2010. "Downturn LGD: A Spot Recovery Approach," MPRA Paper 20010, University Library of Munich, Germany.
    9. González, Marta Ramos & Ureña, Antonio Partal & Fernández-Aguado, Pilar Gómez, 2018. "Proposal on ELBE and LGD in-default: tackling capital requirements after the financial crisis," Working Paper Series 2165, European Central Bank.
    10. Schläfer, Timo & Uhrig-Homburg, Marliese, 2014. "Is recovery risk priced?," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 257-270.
    11. Xiaolin Luo & Pavel V. Shevchenko, 2010. "Markov chain Monte Carlo estimation of default and recovery: dependent via the latent systematic factor," Papers 1011.2827, arXiv.org, revised Oct 2014.
    12. Li, Hui, 2010. "Downturn LGD: A Spot Recovery Approach," MPRA Paper 71986, University Library of Munich, Germany, revised 30 Apr 2013.
    13. Stefano Caselli & Stefano Gatti & Francesca Querci, 2008. "The Sensitivity of the Loss Given Default Rate to Systematic Risk: New Empirical Evidence on Bank Loans," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 1-34, August.
    14. 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.
    15. Palmroos, Peter, 2009. "Effects of unobserved defaults on correlation between probability of default and loss given on mortgage loans," Research Discussion Papers 3/2009, Bank of Finland.
    16. Helmut Elsinger & Alfred Lehar & Martin Summer, 2006. "Risk Assessment for Banking Systems," Management Science, INFORMS, vol. 52(9), pages 1301-1314, September.
    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. Linda Allen & Anthony Saunders, 2004. "Incorporating Systemic Influences Into Risk Measurements: A Survey of the Literature," Journal of Financial Services Research, Springer;Western Finance Association, vol. 26(2), pages 161-191, October.
    19. Tomas Konecny & Jakub Seidler & Aelta Belyaeva & Konstantin Belyaev, 2017. "The Time Dimension of the Links Between Loss Given Default and the Macroeconomy," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 67(6), pages 462-491, October.
    20. Mora, Nada, 2015. "Creditor recovery: The macroeconomic dependence of industry equilibrium," Journal of Financial Stability, Elsevier, vol. 18(C), pages 172-186.

    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:plo:pone00:0068238. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.