Gram-Charlier Densities (Revised version)
University of Lausanne; Swiss Finance Institute
University of Lausanne - School of Economics and Business Administration (HEC-Lausanne); Centre for Economic Policy Research (CEPR); Swiss Finance Institute
Banque de France Working Paper No. 56
The Gram-Charlier expansion, where skewness and kurtosis directly appear as parameters, has become popular in Finance as a generalization of the normal density. We show how positivity constraints can be numerically implemented, thereby guaranteeing that the expansion defines a density. The constrained expansion can be referred to as a Gram-Charlier density. First, we apply our method to the estimation of risk neutral densities. Then, we assess the statistical properties of maximum-likelihood estimates of Gram-Charlier densities. Lastly, we apply the framework to the estimation of a GARCH model where the conditional density is a Gram-Charlier density.
Number of Pages in PDF File: 41
Keywords: Hermite expansions, Semi-nonparametric estimation, Risk-neutral density, GARCH model
JEL Classification: C40, C63, G13, F31working papers series
Date posted: January 5, 2011
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo2 in 0.360 seconds