Gram-Charlier Processes and Applications to Option Pricing

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. © 2017 jean-pierre chateau and daniel dufresne.