Application of the improved fast Gauss transform to option pricing under jump-diffusion processes

Takayuki Sakuma and Yuji Yamada

Abstract

ABSTRACT

Efficient kernel summation is an active research topic in machine learning and computational physics. Fast multipole methods (FMMs) in particular are known as efficient computational methods in these fields, but they have not gained much attention in computational finance. In this paper,we apply the improved fast Gauss transform (IFGT), a version of an FMM, to the computation of European-type option prices under Merton's jump-diffusion model. IFGT is applied to computing the nonlocal integral terms in partial integrodifferential equations, and our results indicate that IFGT is useful for the fast computation of option pricing under this model.