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The Cornish-Fisher-Expansion in the context of Delta - Gamma - Normal approximations

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  • Jaschke, Stefan R.

Abstract

Qualitative and quantitative properties of the Cornish-Fisher-Expansion in the context of Delta-Gamma-Normal approaches to the computation of Value at Risk are presented. Some qualitative deficiencies of the Cornish-Fisher-Expansion - the monotonicity of the distribution function as well as convergence are not guaranteed - make it seem unattractive. In many practical situations, however, its actual accuracy is more than sufficient and the Cornish-Fisher-approximation can be computed faster (and simpler) than other methods like numerical Fourier inversion. This paper tries to provide a balanced view on when and when not to use Cornish-Fisher in this context.

Suggested Citation

  • Jaschke, Stefan R., 2001. "The Cornish-Fisher-Expansion in the context of Delta - Gamma - Normal approximations," SFB 373 Discussion Papers 2001,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200154
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    Citations

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    Cited by:

    1. Steven E. Pav, 2015. "Safety Third: Roy's Criterion and Higher Order Moments," Papers 1506.04227, arXiv.org.
    2. Steven E. Pav, 2015. "Inference on the Sharpe ratio via the upsilon distribution," Papers 1505.00829, arXiv.org, revised Aug 2021.
    3. Peter J. Barry & Bruce J. Sherrick & Jianmei Zhao, 2009. "Integration of VaR and expected utility under departures from normality," Agricultural Economics, International Association of Agricultural Economists, vol. 40(6), pages 691-699, November.
    4. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Didier Maillard, 2019. "Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR," Annals of Operations Research, Springer, vol. 281(1), pages 423-453, October.
    5. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy, 2022. "Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion," Annals of Operations Research, Springer, vol. 313(2), pages 691-712, June.

    More about this item

    Keywords

    Value at Risk; Delta-Gamma-Normal; Cornish-Fisher expansion; Edgeworth series; Gram-Charlier series;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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