论文标题
在两个资产kou跳跃模型下的欧洲期权的有效数值估值
Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model
论文作者
论文摘要
本文涉及二维时间依赖性的局部差异方程（PIDE）的数值解，该方程（PIDE）符合二级分配KOU跳跃 - 跳转模型下欧洲风格期权的值。该方程的一个主要特征是存在非本地双积分项。对于其数值评估，我们扩展了Toivanen（2008）在一维kou积分的情况下得出的高效算法。二维KOU积分的获取算法具有最佳的计算成本：基本算术操作的数量与半差异中的空间网格点的数量成正比。对于时间上有效的离散化，我们研究了隐性解释（IMEX）的七个当代运算符分裂方案和隐式（ADI）类型的交替方向。所有这些方案允许对整体术语进行方便，明确的处理。我们分析了他们（冯·诺伊曼）的稳定性。通过针对平均值期权值的足够数值实验，研究了实际收敛行为以及七个操作员分裂方案的相互性能。此外，还考虑了希腊人三角洲和伽玛。
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.
