Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model

This paper concerns the numerical solution of the two-dimensional time-dependent partial integro-differential equation that holds for the values of European-style options under the two-asset Kou jump-diffusion model. A main feature of this equation is the presence of a nonlocal double integral term. For its numerical evaluation, we extend a highly efficient algorithm derived by Toivanen in the case of the one-dimensional Kou integral. The acquired algorithm for the two-dimensional Kou integral has an optimal computational cost: the number of basic arithmetic operations is directly proportional to the number of spatial grid points in the semidiscretization. For effective discretization in time, we study seven contemporary implicit-explicit and alternating-direction implicit operator splitting schemes. All these schemes allow for a convenient, explicit treatment of the integral term. We analyze their (von Neumann) stability. Through ample numerical experiments for put-on-the-average option values, we investigate the actual convergence behavior as well as the relative performance of the seven operator splitting schemes. In addition, we consider the Greeks Delta and Gamma.