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 – neither the monotonicity of the distribution function nor convergence are 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 more simply) than other methods, such as numerical Fourier inversion. This paper attempts to provide a balanced view on when and when not to use the Cornish–Fisher expansion in this context.