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Estimating Value at Risk and Expected Shortfall Using Expectiles

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  • James W. Taylor
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    Abstract

    Expectile models are derived using asymmetric least squares. A simple formula has been presented that relates the expectile to the expectation of exceedances beyond the expectile. We use this as the basis for estimating the expected shortfall. It has been proposed that the θ quantile be estimated by the expectile for which the proportion of observations below the expectile is θ. In this way, an expectile can be used to estimate value at risk. Using expectiles has the appeal of avoiding distributional assumptions. For univariate modeling, we introduce conditional autoregressive expectiles (CARE). Empirical results for the new approach are competitive with established benchmarks methods. Copyright , Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbn001
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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): 2 (Spring)
    Pages: 231-252

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    Handle: RePEc:oup:jfinec:v:6:y:2008:i:2:p:231-252

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    Cited by:
    1. Ngoc Mai Tran & Maria Osipenko & Wolfgang Karl Härdle, 2014. "Principal Component Analysis in an Asymmetric Norm," SFB 649 Discussion Papers SFB649DP2014-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Huang, Xiaolin & Shi, Lei & Suykens, Johan A.K., 2014. "Asymmetric least squares support vector machine classifiers," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 395-405.
    3. Jian Zhou & Randy Anderson, 2012. "Extreme Risk Measures for International REIT Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 45(1), pages 152-170, June.
    4. Omid Sabbaghi, 2011. "The behavior of green exchange-traded funds," Managerial Finance, Emerald Group Publishing, vol. 37(5), pages 426-441, May.
    5. Benjamin Hamidi & Bertrand Maillet & Jean-Luc Prigent, 2014. "A Dynamic AutoRegressive Expectile for Time-Invariant Portfolio Protection Strategies," Working Papers 2014-131, Department of Research, Ipag Business School.
    6. Zhijie Xiao & Roger Koenker, 2009. "Conditional Quantile Estimation for GARCH Models," Boston College Working Papers in Economics 725, Boston College Department of Economics.
    7. Mengmeng Guo & Lhan Zhou & Jianhua Z. Huang & Wolfgang Karl Härdle, 2013. "Functional Data Analysis of Generalized Quantile Regressions," SFB 649 Discussion Papers SFB649DP2013-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    9. Mengmeng Guo & Wolfgang Härdle, 2012. "Simultaneous confidence bands for expectile functions," AStA Advances in Statistical Analysis, Springer, vol. 96(4), pages 517-541, October.
    10. repec:hal:journl:halshs-00389773 is not listed on IDEAS
    11. repec:hal:journl:halshs-00336475 is not listed on IDEAS

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