2015/11/16 by Xun Li, Ping Lin, Li, Xun +5
Economics, Econometrics and Finance · Engineering · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1511.04950
openalex publication_date 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article presents a finite element method (FEM) for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled by an exponential Levy process. We provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-based solution. Then we discuss the localization of the infinite domain problem to a finite domain and analyze its error. We tackle the localized problem by an explicit-implicit time-discretization of the PIDE, where the space-discretization is done through a standard continuous finite element method. Error estimates are given for the fully discretized localized problem where two assets are assumed to have uncorrelated jumps. Numerical experiments for the polynomial option and a few other two-asset options shed light on good performance of our proposed method.