THE EVALUATION OF MULTIASSET EUROPEAN AND AMERICAN OPTIONS VIA FOURIER HERMITE SERIES EXPANSIONS

We formulate European and American versions of a number of two-factor multiasset options (such as exchange options, quanto options and basket options) in a path integral framework via use of the Chapman-Kolmogorov equation. We show how to evaluate such options using Fourier-Hermite expansions developed in earlier work of the authors [see Chiarella, El-Hassan and Kucera (1999)], focusing in particular on how to handle the different boundary conditions associated with the different pay-off structures. The numerical results are compared for accuracy and speed with those obtained from lattice methods.