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Journal of Probability and Statistics
Volume 2017, Article ID 8690491, 19 pages
https://doi.org/10.1155/2017/8690491
Research Article

Gram-Charlier Processes and Applications to Option Pricing

1Faculty of Business Administration, University of Macau, Macau
2Montreal, QC, Canada

Correspondence should be addressed to Daniel Dufresne; ua.ude.bleminu@enserfud

Received 17 August 2016; Accepted 1 November 2016; Published 8 February 2017

Academic Editor: Aera Thavaneswaran

Copyright © 2017 Jean-Pierre Chateau and Daniel Dufresne. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.