An Efficient IMEX Compact Scheme for the Coupled Time Fractional Integro-Differential Equations Arising from Option Pricing with Jumps

When solving time fractional partial integro-differential equations (PIDEs) using standard finite difference methods, we have to invert the dense matrices arising from the discretization of the integral terms and this causes significant computational cost. In this paper, we develop an implicit-explicit (IMEX) compact finite difference scheme to raise computational efficiency when solving the coupled time fractional PIDEs arising in option pricing with jumps. First, we propose a new IMEX scheme for temporal discretization and compact finite difference scheme for spatial discretization. Then such high-order numerical scheme is proved to be unconditionally stable in the sense of the discrete \(L^2\) $L^2$ and \(L^\infty\) $L^{\infty }$ norms. Finally, ample numerical experiments are reported to test the convergence rates of the proposed numerical scheme, and show its feasibility and applicability for the option pricing problems.