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Estimating Gram-Charlier Expansions Under Positivity Constraints

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.
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Contributor : Antoine Haldemann Connect in order to contact the contributor
Submitted on : Friday, June 17, 2011 - 9:19:31 PM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM


  • HAL Id : hal-00601500, version 1



Michael Rockinger, Eric Jondeau. Estimating Gram-Charlier Expansions Under Positivity Constraints. 1998. ⟨hal-00601500⟩



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