%0 Journal Article
%T A Multinomial Theorem for Hermite Polynomials and Financial Applications
%A Francois Buet-Golfouse
%J Applied Mathematics
%P 1017-1030
%@ 2152-7393
%D 2015
%I Scientific Research Publishing
%R 10.4236/am.2015.66094
%X Different aspects of mathematical finance benefit from the use Hermite polynomials, and this is particularly the case where risk drivers have a Gaussian distribution. They support quick analytical methods which are computationally less cumbersome than a full-fledged Monte Carlo framework, both for pricing and risk management purposes. In this paper, we review key properties of Hermite polynomials before moving on to a multinomial expansion formula for Hermite polynomials, which is proved using basic methods and corrects a formulation that appeared before in the financial literature. We then use it to give a trivial proof of the Mehler formula. Finally, we apply it to no arbitrage pricing in a multi-factor model and determine the empirical futures price law of any linear combination of the underlying factors.
%K Hermite Polynomials
%K Multi-Factor Model
%K Hilbert Space
%K Mehler Formula
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=56933