2022/07/20 by Karel in ’t Hout, Hout, Karel in 't, Pieter Lamotte +1 · 1 citation
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2207.10060
openalex publication_date 2022/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the numerical solution of the two-dimensional time-dependent partial integro-differential equation (PIDE) that holds for the values of European-style options under the two-asset Kou jump-diffusion model. A main feature of this equation is the presence of a nonlocal double integral term. For its numerical evaluation, we extend a highly efficient algorithm derived by Toivanen (2008) in the case of the one-dimensional Kou integral. The acquired algorithm for the two-dimensional Kou integral has optimal computational cost: the number of basic arithmetic operations is directly proportional to the number of spatial grid points in the semidiscretization. For the effective discretization in time, we study seven contemporary operator splitting schemes of the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind. All these schemes allow for a convenient, explicit treatment of the integral term. We analyze their (von Neumann) stability. By ample numerical experiments for put-on-the-average option values, the actual convergence behavior as well as the mutual performance of the seven operator splitting schemes are investigated. Moreover, the Greeks Delta and Gamma are considered.