2019/12/14 by Lynn Boen, Boen, Lynn, Karel J. in ’t Hout +1
Economics, Econometrics and Finance · Mathematics · #Computational Engineering #Computational Finance (q-fin.CP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Stochastic processes and financial applications #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1912.06809
openalex publication_date 2019/12/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper deals with the efficient numerical solution of the two-dimensional\npartial integro-differential complementarity problem (PIDCP) that holds for the\nvalue of American-style options under the two-asset Merton jump-diffusion\nmodel. We consider the adaptation of various operator splitting schemes of both\nthe implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind\nthat have recently been studied for partial integro-differential equations\n(PIDEs) in [3]. Each of these schemes conveniently treats the nonlocal integral\npart in an explicit manner. Their adaptation to PIDCPs is achieved through a\ncombination with the Ikonen-Toivanen splitting technique [14] as well as with\nthe penalty method [32]. The convergence behaviour and relative performance of\nthe acquired eight operator splitting methods is investigated in extensive\nnumerical experiments for American put-on-the-min and put-on-the-average\noptions.\n