Owen, A., Bryers, J. and Buet-Golfouse, F. (2015) Hermite Polynomial Approximations in Credit Risk Modelling with PD-LGD Correlation. Journal of Credit Risk, Accepted Paper.

has been cited by the following article:

• TITLE: A Multinomial Theorem for Hermite Polynomials and Financial Applications

  AUTHORS: Francois Buet-Golfouse

  KEYWORDS: Hermite Polynomials, Multi-Factor Model, Hilbert Space, Mehler Formula

  JOURNAL NAME: Applied Mathematics, Vol.6 No.6, June 5, 2015

  ABSTRACT: 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.