The Edgeworth and Gram-Charlier Densities

This paper is the first to define the Edgeworth density and comprehensively compare it to the Gram–Charlier density in the context of option pricing. The two densities allow additional cumulants to the normal distribution; although similar, they are not the same when truncated. Many academics have misidentified the two. This paper clearly distinguishes the two, presents the derivation of both, and develops a general option pricing model which can be used for both densities with an arbitrary number of additional cumulants. The option pricing formula for each density is also calibrated and compared to more typical models with the most advanced being the affine jump-diffusion model (stochastic volatility with double jumps).