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This paper deals with the efficient numerical solution of the two-dimensionalpartial integro-differential complementarity problem (PIDCP) that holds for thevalue of American-style options under the two-asset Merton jump-diffusionmodel. We consider the adaptation of various operator splitting schemes of boththe implicit-explicit (IMEX) and the alternating direction implicit (ADI) kindthat have recently been studied for partial integro-differential equations(PIDEs) in [3]. Each of these schemes conveniently treats the nonlocal integralpart in an explicit manner. Their adaptation to PIDCPs is achieved through acombination with the Ikonen-Toivanen splitting technique [14] as well as withthe penalty method [32]. The convergence behaviour and relative performance ofthe acquired eight operator splitting methods is investigated in extensivenumerical experiments for American put-on-the-min and put-on-the-averageoptions.

Operator splitting schemes for American options under the two-asset Merton jump-diffusion model