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Sensitivity Analysis of Distortion Risk Measures

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  • Christian Gourieroux

    (Crest)

  • Wei Liu

    (Crest)

Abstract

This paper provides a uni¯ed statistical framework for the analysis of distortion riskmeasures (DRM) and of their sensitivities with respect to parameters representing riskaversion and/or pessimism. We derive the general formula for calculating the functionalasymptotic distribution of the nonparametric estimator of the functional distortion riskmeasures. Closed form expressions are provided for special examples such as VaR, Tail-VaR and Proportional Hazard distortion risk measure. Moreover, we analyze the linkbetween Value-at-Risk and Tail-VaR and characterize the underlying distributions underwhich the two risk measures are linearly related through their risk levels. We apply theresults to currency portfolios and observe that this linearity relationship between Value-at-Risk and Tail-VaR is a surprisingly common phenomenon for the portfolios considered.

Suggested Citation

  • Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers 2006-33, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2006-33
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    References listed on IDEAS

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    Cited by:

    1. Christian Gourieroux & Wei Liu, 2006. "Efficient Portfolio Analysis Using Distortion Risk Measures," Working Papers 2006-17, Center for Research in Economics and Statistics.
    2. Wozabal, Nancy, 2009. "Uniform limit theorems for functions of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1450-1455, June.
    3. John Cotter & Kevin Dowd, 2010. "Estimating financial risk measures for futures positions: A nonparametric approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(7), pages 689-703, July.
    4. Cotter, John & Dowd, Kevin, 2007. "Evaluating the Precision of Estimators of Quantile-Based Risk Measures," MPRA Paper 3504, University Library of Munich, Germany.
    5. Debora Daniela Escobar & Georg Ch. Pflug, 2020. "The distortion principle for insurance pricing: properties, identification and robustness," Annals of Operations Research, Springer, vol. 292(2), pages 771-794, September.
    6. Daniela Escobar & Georg Pflug, 2018. "The distortion principle for insurance pricing: properties, identification and robustness," Papers 1809.06592, arXiv.org.
    7. Peter W. Glynn & Yijie Peng & Michael C. Fu & Jian-Qiang Hu, 2021. "Computing Sensitivities for Distortion Risk Measures," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1520-1532, October.

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