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


  • Jaschke, Stefan R.


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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    Value at Risk; Delta-Gamma-Normal; Cornish-Fisher expansion; Edgeworth series; Gram-Charlier series;

    JEL classification:

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

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