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

  • Renault, Olivier
  • Scaillet, Olivier

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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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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  1. HÄRDLE, Wolfgang, 1992. "Applied nonparametric methods," CORE Discussion Papers 1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  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. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
  6. O. Scaillet, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels," THEMA Working Papers 2001-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  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.
  8. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
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