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Estimating Gram-Charlier Expansions with Positivity Constraints

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  • Jondeau, E.
  • Rockinger, M.

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

  • Jondeau, E. & Rockinger, M., 1999. "Estimating Gram-Charlier Expansions with Positivity Constraints," Working papers 56, Banque de France.
    • Handle: RePEc:bfr:banfra:56
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    Cited by:

    1. Jacques Pézier, 2011. "Rationalization of Investment Preference Criteria," ICMA Centre Discussion Papers in Finance icma-dp2011-12, Henley Business School, University of Reading.

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    More about this item

    Keywords

    Hermite expansions ; Semi-nonparametric estimation ; Risk-neutral density ; GARCH model.;
    All these keywords.

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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