Estimating Gram-Charlier Expansions with Positivity Constraints
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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|Date of creation:||1998|
|Contact details of provider:|| Postal: Banque de France 31 Rue Croix des Petits Champs LABOLOG - 49-1404 75049 PARIS|
Web page: http://www.banque-france.fr/
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