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(Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution

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  • Christian Gourieroux

    (Crest)

  • Alain Monfort

    (Crest)

Abstract

In this paper, we explain why a nonparametric approach based on a betakernel [Renault, Scaillet (2004)] will lead to significant bias when appliedto recovery rate distributions. This is due to a specific feature of thesedistributions, which admit strictly positive weights at 100 % correspondingto full recovery (and also at 0 % corresponding to total loss). Moreover, fordistributions without point mass at 0% and 100%, the beta kernel approachfeatures significant bias in finite sample. In large sample the method isconsistent, but other competing approaches presented in the paper providemore accurate results.

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  • Christian Gourieroux & Alain Monfort, 2006. "(Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution," Working Papers 2006-31, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2006-31
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    Cited by:

    1. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    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. J. Baixauli & Susana Alvarez, 2012. "Implied Severity Density Estimation: An Extended Semiparametric Method to Compute Credit Value at Risk," Computational Economics, Springer;Society for Computational Economics, vol. 40(2), pages 115-129, August.
    4. Bessa, Ricardo J. & Miranda, V. & Botterud, A. & Zhou, Z. & Wang, J., 2012. "Time-adaptive quantile-copula for wind power probabilistic forecasting," Renewable Energy, Elsevier, vol. 40(1), pages 29-39.
    5. 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.
    6. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    7. 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.
    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. Gospodinov, Nikolay & Hirukawa, Masayuki, 2012. "Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 595-609.
    10. 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.

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