A Multinomial Theorem for Hermite Polynomials and Financial Applications

• 作者: Francois Buet-Golfouse
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: HERMITE POLYNOMIALS Multi-Factor Model HILBERT Space Mehler FORMULA
• 年，卷（期）: 2015,（6）
• 页码范围: 1017-1030
• 页数: 14页
• 分类号: O1

摘要

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.