Making Cornish–Fisher Distributions Fit

59 Pages Posted: 1 Oct 2016

See all articles by John D. Lamb

John D. Lamb

University of Aberdeen - Business School

Maura Monville

Varian Medical Systems Finland Oy

Kai-Hong Tee

Loughborough University - School of Business and Economics

Date Written: September 30, 2016

Abstract

The truncated Cornish–Fisher inverse expansion is well known. It is used, for example, to approximate value-at-risk and conditional value-at-risk. It is known that this expansion gives a distribution for limited skewness and kurtosis and that the distribution may be a poor fit. drawing on Maillard (2012) we show how to find a unique corrected Cornish–Fisher distribution efficiently for a wide range of skewness and kurtosis. We show it has a unimodal density and a quantile function that is twice continuously differentiable as a function of mean, variance, skewness and kurtosis. We show how to obtain random variates efficiently and how to test goodness-of-fit. We apply the Cornish–Fisher distribution to fit hedge-fund returns and estimate conditional value-at risk. Finally, we investigate various generalisations of the Cornish–Fisher distributions and show they do not have the same desirable properties.

Keywords: Conditional value-at-risk, Goodness-of-fit, Kurtosis, Random variates, Skewness

Suggested Citation

Lamb, John D. and Monville, Maura and Tee, Kai-Hong, Making Cornish–Fisher Distributions Fit (September 30, 2016). Available at SSRN: https://ssrn.com/abstract=2845873 or http://dx.doi.org/10.2139/ssrn.2845873

John D. Lamb (Contact Author)

University of Aberdeen - Business School ( email )

Edward Wright Building
Dunbar Street
Aberdeen, Scotland AB24 3QY
United Kingdom

Maura Monville

Varian Medical Systems Finland Oy ( email )

Paciuksenkatu 21
Helsinki, CA 00270
Finland

Kai-Hong Tee

Loughborough University - School of Business and Economics ( email )

Epinal Way
Leics LE11 3TU
Leicestershire
United Kingdom

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