In this paper we consider the numerical solution of the two-dimensional time-dependent partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Kou jump-diffusion model. Following the method of lines (MOL), we derive an efficient numerical method for the pertinent PIDCP. Here, for the discretization of the nonlocal double integral term, an extension is employed of the fast algorithm by Toivanen (2008) in the case of the one-asset Kou jump-diffusion model. For the temporal discretization, we study a useful family of second-order diagonally implicit Runge-Kutta (DIRK) methods. Their adaptation to the semidiscrete two-dimensional Kou PIDCP is obtained by means of an effective iteration introduced by d'Halluin, Forsyth & Labahn (2004) and d'Halluin, Forsyth & Vetzal (2005). Ample numerical experiments are presented showing that the proposed numerical method achieves a favourable, second-order convergence behaviour to the American two-asset option value as well as to its Greeks Delta and Gamma.

翻译：本文研究二维时变偏积分-微分互补问题（PIDCP）的数值解法，该问题描述了双资产Kou跳跃扩散模型下美式期权的价值。采用直线法（MOL）框架，我们推导出适用于该PIDCP的高效数值方法。针对非局部二重积分项的离散化，本文扩展了Toivanen（2008）在单资产Kou跳跃扩散模型中提出的快速算法。在时间离散方面，我们研究了一类实用的二阶对角隐式龙格-库塔（DIRK）方法。通过采用d'Halluin、Forsyth & Labahn（2004）以及d'Halluin、Forsyth & Vetzal（2005）提出的有效迭代技术，实现了这些方法对半离散二维Kou PIDCP的适配。大量数值实验表明，所提出的数值方法对双资产美式期权价值及其Delta和Gamma希腊字母均能实现良好的二阶收敛特性。