A User’s Guide to the Cornish Fisher Expansion

20 Pages Posted: 2 Feb 2012 Last revised: 8 Jun 2018

See all articles by Didier Maillard

Didier Maillard

Conservatoire National des Arts et Métiers (CNAM); Amundi Asset Management

Date Written: May 1, 2018


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.

Keywords: risk, value at risk, conditional value at risk, Variance, volatility, skewness, kurtosis, portfolio optimization, asset liability management, non Gaussian distribution

JEL Classification: C02, C51, G11, G32

Suggested Citation

Maillard, Didier, A User’s Guide to the Cornish Fisher Expansion (May 1, 2018). Available at SSRN: https://ssrn.com/abstract=1997178 or http://dx.doi.org/10.2139/ssrn.1997178

Didier Maillard (Contact Author)

Conservatoire National des Arts et Métiers (CNAM) ( email )

292, rue Saint-Martin
Paris cedex 03, 75141

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015

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