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On the Way to Recovery: A Nonparametric Bias Free Estimation of Recovery Rate Densities

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  • Olivier RENAULT

    (Standard and Poor’s Risk Solutions)

  • Olivier SCAILLET

    (HEC-University of Geneva and FAME)

Abstract

In this paper we analyse recovery rates on defaulted bonds using the Standard and Poor’s/PMD database for the years 1981-1999. Due to the specific nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametrically using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.

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Bibliographic Info

Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp83.

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Date of creation: May 2003
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Handle: RePEc:fam:rpseri:rp83

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Keywords: default; recovery; kernel estimation; credit risk;

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References

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  1. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
  2. Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(02), pages 390-412, April.
  4. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 471-480, September.
  5. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, December.
  6. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
  7. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
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Citations

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Cited by:
  1. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
  2. Radovan Chalupka & Juraj Kopecsni, 2008. "Modelling Bank Loan LGD of Corporate and SME Segments: A Case Study," Working Papers IES 2008/27, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Nov 2008.
  3. Han, Chulwoo & Jang, Youngmin, 2013. "Effects of debt collection practices on loss given default," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 21-31.
  4. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2012. "Bayesian Approaches to Non-parametric Estimation of Densities on the Unit Interval," Monash Econometrics and Business Statistics Working Papers 3/12, Monash University, Department of Econometrics and Business Statistics.
  5. 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.
  6. Max Bruche & Carlos Gonzalez-Aguado, 2006. "Recovery rates, default probabilities and the credit cycle," LSE Research Online Documents on Economics 24524, London School of Economics and Political Science, LSE Library.
  7. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
  8. J. Samuel Baixauli & Susana Alvarez, 2010. "The Role of Market-Implied Severity Modeling for Credit VaR," Annals of Economics and Finance, Society for AEF, vol. 11(2), pages 337-353, November.
  9. J. Baixauli & Susana Alvarez, 2012. "Implied Severity Density Estimation: An Extended Semiparametric Method to Compute Credit Value at Risk," Computational Economics, Society for Computational Economics, vol. 40(2), pages 115-129, August.
  10. Matthias Hagmann & Olivier Scaillet, 2004. "Local Multiplicative Bias Correction For Asymmetric Kernel Density Estimators," Royal Economic Society Annual Conference 2004 25, Royal Economic Society.
  11. Calabrese, Raffaella & Zenga, Michele, 2010. "Bank loan recovery rates: Measuring and nonparametric density estimation," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 903-911, May.
  12. Choroś-Tomczyk, Barbara & Härdle, Wolfgang Karl & Okhrin, Ostap, 2013. "Valuation of collateralized debt obligations with hierarchical Archimedean copulae," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 42-62.
  13. David Wozabal & Ronald Hochreiter, 2009. "A Coupled Markov Chain Approach to Credit Risk Modeling," Papers 0911.3802, arXiv.org, revised Jan 2014.
  14. Hibbeln, Martin & Gürtler, Marc, 2011. "Pitfalls in modeling loss given default of bank loans," Working Papers IF35V1, Technische Universität Braunschweig, Institute of Finance.
  15. Raffaella Calabrese, 2012. "Modelling Downturn Loss Given Default," Working Papers 201226, Geary Institute, University College Dublin.
  16. Jankowitsch, Rainer & Pichler, Stefan & Schwaiger, Walter S.A., 2007. "Modelling the economic value of credit rating systems," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 181-198, January.

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