More on Cornish Fisher: Distribution Density and Boundary Conditions

Abstract

The Cornish Fisher expansion is a mean to transforming a Gaussian distribution into a non-Gaussian distribution, the skewness and the kurtosis of which can be controlled if the transformation is properly implemented.

This paper displays the characteristics of the density of the transformed distribution, which may be obtained analytically by reversing the Cornish-Fisher transformation.

It also studies what happens when nearing the borders of the domain of validity for the transformation.

Keywords: Risk, variance, volatility, skewness, kurtosis, non Gaussian distribution Risk, variance, volatility, skewness, kurtosis, non Gaussian distribution

JEL Classification: C02, C51, G11, G32