Estimating Gram-Charlier Expansions Under Positivity Constraints

Michael Rockinger () and Eric Jondeau

Working Papers from HAL

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; GARCH model. (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (2)

Published in 1998

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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-00601500

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