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Nonparametric Estimation of Expected Shortfall

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  • Song Xi Chen

Abstract

The expected shortfall is an increasingly popular risk measure in financial risk management and it possesses the desired sub-additivity property, which is lacking for the value at risk (VaR). We consider two nonparametric expected shortfall estimators for dependent financial losses. One is a sample average of excessive losses larger than a VaR. The other is a kernel smoothed version of the first estimator (Scaillet, 2004 Mathematical Finance), hoping that more accurate estimation can be achieved by smoothing. Our analysis reveals that the extra kernel smoothing does not produce more accurate estimation of the shortfall. This is different from the estimation of the VaR where smoothing has been shown to produce reduction in both the variance and the mean square error of estimation. Therefore, the simpler ES estimator based on the sample average of excessive losses is attractive for the shortfall estimation. Copyright 2007 The Authors, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 6 (2008)
Issue (Month): 1 (Winter)
Pages: 87-107

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Handle: RePEc:oup:jfinec:v:6:y:2008:i:1:p:87-107

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Cited by:
  1. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, Elsevier, vol. 147(1), pages 120-130, November.
  2. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, Elsevier, vol. 34(1), pages 267-279, January.
  3. Sasa Zikovic & Randall Filer, 2012. "Ranking of VaR and ES Models: Performance in Developed and Emerging Markets," CESifo Working Paper Series, CESifo Group Munich 3980, CESifo Group Munich.
  4. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2013. "Pair Copula Construction based Expected Shortfall estimation," Economics Bulletin, AccessEcon, vol. 33(2), pages 1067-1072.
  5. Yang Yan & Dajing Shang & Oliver Linton, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP25/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. John Cotter & Kevin Dowd, 2011. "Evaluating the Precision of Estimators of Quantile-Based Risk Measures," Working Papers, Geary Institute, University College Dublin 200743, Geary Institute, University College Dublin.
  7. Sasa Zikovic & Randall Filer, 2009. "Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets," CESifo Working Paper Series, CESifo Group Munich 2820, CESifo Group Munich.
  8. Christophe Hurlin & Gregoire Iseli & Christophe Pérignon & Stanley Yeung, 2014. "The Collateral Risk of ETFs," Working Papers, HAL halshs-01023807, HAL.
  9. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers, arXiv.org math/0411034, arXiv.org.
  10. Henryk Zähle, 2011. "Rates of almost sure convergence of plug-in estimates for distortion risk measures," Metrika, Springer, Springer, vol. 74(2), pages 267-285, September.
  11. Bai, Zhidong & Phoon, Kok Fai & Wang, Keyan & Wong, Wing-Keung, 2013. "The performance of commodity trading advisors: A mean-variance-ratio test approach," The North American Journal of Economics and Finance, Elsevier, Elsevier, vol. 25(C), pages 188-201.
  12. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 101(10), pages 2452-2463, November.
  13. Francq, Christian & Zakoian, Jean-Michel, 2012. "Risk-parameter estimation in volatility models," MPRA Paper 41713, University Library of Munich, Germany.

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