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Estimating Gram-Charlier Expansions Under Positivity Constraints

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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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Dates and versions

hal-00601500 , version 1 (17-06-2011)

Identifiers

  • HAL Id : hal-00601500 , version 1

Cite

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

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