The Hidden Martingale Restriction in Gram-Charlier Option Prices

Abstract

A hidden martingale restriction is developed for option pricing models based on Gram-Charlier expansions of the normal density function. The restriction is hidden behind a reduction in parameter space for the Gram-Charlier expansion coefficients. The resulting restriction is invisible in the option price.

Keywords: Option prices, martingale restriction, skewness, kurtosis, Gram-Charlier density expansions

JEL Classification: C14, G12, G13