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On the way to recovery: A nonparametric bias free estimation of recovery rate densities

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  • Renault, Olivier
  • Scaillet, Olivier

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

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 28 (2004)
Issue (Month): 12 (December)
Pages: 2915-2931

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Handle: RePEc:eee:jbfina:v:28:y:2004:i:12:p:2915-2931

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References

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  1. Hardle, W., 1992. "Applied Nonparametric Methods," Discussion Paper 1992-6, Tilburg University, Center for Economic Research.
  2. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, April.
  3. 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.
  4. 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.
  5. 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.
  6. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  7. 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).
  8. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
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Citations

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Cited by:
  1. Matthias HAGMANN & Olivier SCAILLET, 2003. "Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators," FAME Research Paper Series rp91, International Center for Financial Asset Management and Engineering.
  2. 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.
  3. Carlos González-Aguado & Max Bruche, 2006. "Recovery Rates, Default Probabilities and the Credit Cycle," FMG Discussion Papers dp572, Financial Markets Group.
  4. Hibbeln, Martin & Gürtler, Marc, 2011. "Pitfalls in modeling loss given default of bank loans," Working Papers IF35V1, Technische Universität Braunschweig, Institute of Finance.
  5. Wozabal, David & Hochreiter, Ronald, 2012. "A coupled Markov chain approach to credit risk modeling," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 403-415.
  6. 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.
  7. Raffaella Calabrese, 2012. "Modelling Downturn Loss Given Default," Working Papers 201226, Geary Institute, University College Dublin.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Schläfer, Timo & Uhrig-Homburg, Marliese, 2014. "Is recovery risk priced?," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 257-270.
  13. 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.
  14. 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.
  15. Muhammad Hanif, 2011. "Reweighted Nadaraya-Watson estimator of scalar diffusion models by using asymmetric kernels," Far East Journal of Psychology and Business, Far East Research Centre, vol. 4(5), pages 53-69, July.
  16. 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.
  17. 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.
  18. 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.

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