Estimating Gram-Charlier Expansions with Positivity Constraints
AbstractThe 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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Bibliographic InfoPaper provided by Banque de France in its series Working papers with number 56.
Length: 35 pages
Date of creation: 1998
Date of revision:
Hermite expansions ; Semi-nonparametric estimation ; Risk-neutral density ; GARCH model.;
Find related papers by 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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