论文标题
基于紧凑的有限差异方案和赫米特插值来解决美国选择的多移民迭代算法
Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options
论文作者
论文摘要
我们提出了一种多移民迭代算法，用于求解一个耦合的自由边界问题系统，以定价美国与政权转换的选项。该算法基于我们最近开发的紧凑型有限差异方案以及Hermite插值，用于求解由资产选项和Delta，Gamma和速度敏感性组成的耦合部分微分方程。在该算法中，我们首先使用高斯 - 塞德尔方法将其更顺畅，然后基于修改周期（M-Cycle）实施多机策略来求解我们的离散方程。使用牛顿插值分隔的差异（作为基础）的HERMITE插值用于估计方程组中的耦合资产，三角洲，伽玛和速度选项。用两种制度示例进行数值实验，并与其他现有方法进行验证以验证最佳策略。结果表明，该算法提供了一种快速有效的工具，用于用政权开关定价美国将选项定价。
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme coupled with Hermite interpolation for solving the coupled partial differential equations consisting of the asset option and the delta, gamma, and speed sensitivities. In the algorithm, we first use the Gauss-Seidel method as a smoother and then implement a multigrid strategy based on modified cycle (M-cycle) for solving our discretized equations. Hermite interpolation with Newton interpolatory divided difference (as the basis) is used in estimating the coupled asset, delta, gamma, and speed options in the set of equations. A numerical experiment is performed with the two- and four- regime examples and compared with other existing methods to validate the optimal strategy. Results show that this algorithm provides a fast and efficient tool for pricing American put options with regime-switching.
