Gram–Charlier densities
Eric Jondeau and Michael Rockinger*
Journal of Economic Dynamics and Control, 2001, 25(10), 1457-1483.
Abstract
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.
Keywords: Hermite expansion; Semi-nonparametric estimation; Risk-neutral density;
GARCH model
JEL classification: C40; C63; G13; F31.
* HEC Lausanne