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Estimating Gram-Charlier Expansions Under Positivity Constraints

Author

Listed:
  • Michael Rockinger

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eric Jondeau

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.

Suggested Citation

  • Michael Rockinger & Eric Jondeau, 1998. "Estimating Gram-Charlier Expansions Under Positivity Constraints," Working Papers hal-00601500, HAL.
    • Handle: RePEc:hal:wpaper:hal-00601500
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    Cited by:

    1. Kyriakos Chourdakis, 2002. "Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps," Working Papers 464, Queen Mary University of London, School of Economics and Finance.
    2. Kyriakos Chourdakis, 2002. "Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps," Working Papers 464, Queen Mary University of London, School of Economics and Finance.

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