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

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