Gram-Charlier Processes and Applications to Option Pricing

Abstract EN

A Gram-Charlier distribution has a density that is a polynomial times a normal density.

For option pricing this retains the tractability of the normal distribution while allowing nonzero skewness and excess kurtosis.

Properties of the Gram-Charlier distributions are derived, leading to the definition of a process with independent Gram-Charlier increments, as well as formulas for option prices and their sensitivities.

A procedure for simulating Gram-Charlier distributions and processes is given.

Numerical illustrations show the effect of skewness and kurtosis on option prices.