Operator splitting schemes for American options under the two-asset Merton jump-diffusion model
Abstract
This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind that have recently been studied for partial integro-differential equations (PIDEs) in [3]. Each of these schemes conveniently treats the nonlocal integral part in an explicit manner. Their adaptation to PIDCPs is achieved through a combination with the Ikonen-Toivanen splitting technique [14] as well as with the penalty method [32]. The convergence behaviour and relative performance of the acquired eight operator splitting methods is investigated in extensive numerical experiments for American put-on-the-min and put-on-the-average options.
Keywords
Cite
@article{arxiv.1912.06809,
title = {Operator splitting schemes for American options under the two-asset Merton jump-diffusion model},
author = {Lynn Boen and Karel J. in 't Hout},
journal= {arXiv preprint arXiv:1912.06809},
year = {2019}
}