  This paper deals with the numerical solution of the two-dimensional
time-dependent Merton partial integro-differential equation (PIDE) for the
values of rainbow options under the two-asset Merton jump-diffusion model. Key
features of this well-known equation are a two-dimensional nonlocal integral
part and a mixed spatial derivative term. For its efficient and stable
numerical solution, we study seven recent and novel operator splitting schemes
of the implicit-explicit (IMEX) and the alternating direction implicit (ADI)
kind. Here the integral part is always conveniently treated in an explicit
fashion. The convergence behaviour and the relative performance of the seven
schemes are investigated in ample numerical experiments for both European
put-on-the-min and put-on-the-average options.
