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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. 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.
    3. 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.
    4. Steven E. Pav, 2015. "Inference on the Sharpe ratio via the upsilon distribution," Papers 1505.00829, arXiv.org, revised Aug 2021.
    5. 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.

    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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