An Error Analysis of a Finite Element Method with IMEX-Time Semidiscretizations for Some Partial Integro-differential Inequalities Arising in the Pricing of American Options

Abstract

The aim of this article is to develop and analyze a finite element method, combined with implicit-explicit (IMEX) time semidiscretizations, for pricing American options under Merton's and Kou's jump-diffusion models. Under realistic regularity assumptions on the data, some error estimates are established. The theoretical findings and the efficiency of the proposed methods are demonstrated by several numerical experiments.