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.

翻译：本文研究双资产Kou跳扩散模型下欧式期权价值满足的二维时间依赖偏积分微分方程（PIDE）的数值解法。该方程的主要特征在于包含非局部二重积分项。为进行数值求解，我们将Toivanen（2008）针对一维Kou积分提出的高效算法扩展至二维情形。所获得的二维Kou积分算法具有最优计算成本：基本算术运算次数与半离散化中空间网格点数成正比。在时间方向的有效离散方面，我们研究了七种当代算子分裂格式，包括隐式-显式（IMEX）类和交替方向隐式（ADI）类。所有格式均允许对积分项进行便捷的显式处理。我们分析了这些格式的（冯·诺依曼）稳定性。通过针对平均价看跌期权价值的大量数值实验，考察了七种算子分裂格式的实际收敛行为及相互性能表现。此外，还考虑了希腊字母Delta和Gamma的计算。