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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.

Suggested Citation

  • Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(1), pages 87-107, Winter.
  • Handle: RePEc:oup:jfinec:v:6:y:2008:i:1:p:87-107
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbm019
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    Cited by:

    1. Cotter, John & Dowd, Kevin, 2007. "Evaluating the Precision of Estimators of Quantile-Based Risk Measures," MPRA Paper 3504, University Library of Munich, Germany.
    2. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org.
    3. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    4. Li, Leon, 2017. "Testing and comparing the performance of dynamic variance and correlation models in value-at-risk estimation," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 116-135.
    5. Saša ŽIKOVIÆ & Randall K. FILER, 2013. "Ranking of VaR and ES Models: Performance in Developed and Emerging Markets," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(4), pages 327-359, August.
    6. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    8. Oliver Linton & Dajing Shang & Yang Yan, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers CWP25/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Vijverberg, Chu-Ping C. & Vijverberg, Wim P.M. & Taşpınar, Süleyman, 2016. "Linking Tukey’s legacy to financial risk measurement," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 595-615.
    10. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
    11. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    12. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    13. Wang, Chuan-Sheng & Zhao, Zhibiao, 2016. "Conditional Value-at-Risk: Semiparametric estimation and inference," Journal of Econometrics, Elsevier, vol. 195(1), pages 86-103.
    14. Timo Dimitriadis & Sebastian Bayer, 2017. "A Joint Quantile and Expected Shortfall Regression Framework," Papers 1704.02213, arXiv.org, revised Aug 2017.
    15. Henryk Zähle, 2011. "Rates of almost sure convergence of plug-in estimates for distortion risk measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 267-285, September.
    16. Sasa Zikovic & Randall Filer, 2009. "Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets," CESifo Working Paper Series 2820, CESifo Group Munich.
    17. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    18. 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, vol. 25(C), pages 188-201.
    19. Christophe Hurlin & Gregoire Iseli & Christophe Pérignon & Stanley Yeung, 2014. "The Counterparty Risk Exposure of ETF Investors," Working Papers halshs-01023807, HAL.
    20. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2013. "Pair Copula Construction based Expected Shortfall estimation," Economics Bulletin, AccessEcon, vol. 33(2), pages 1067-1072.
    21. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.

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