A User’s Guide to the Cornish Fisher Expansion

Abstract

Using the Cornish Fisher expansion is a relatively easy and parsimonious way of dealing with non-normality in asset price or return distributions, in such fields as insurance asset liability management or portfolio optimization with assets such as derivatives. It also allows to implement portfolio optimization with a risk measure more sophisticated than variance, such as Value-at-Risk or Conditional Value-at-Risk The use of Cornish Fisher expansion should avoid two pitfalls: (i) exiting the domain of validity of the formula; (ii) confusing the skewness and kurtosis parameters of the formula with the actual skewness and kurtosis of the distribution.This paper provides guidelines for a proper use of the Cornish Fisher expansion.