  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.
