Estimating Gram-Charlier Expansions with Positivity Constraints

Eric Jondeau and Michael Rockinger ()

Working papers from Banque de France

Abstract: The Gram-Charlier expansion, where skewness and kurtosi 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 expansions; Semi-nonparametric estimation; Risk-neutral density; GARCH model. (search for similar items in EconPapers)
JEL-codes: C40 C63 F31 G13 (search for similar items in EconPapers)
Pages: 35 pages
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:bfr:banfra:56

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