We study the principal component analysis (PCA) based approach introduced by Reisinger & Wittum (2007) for the approximation of Bermudan basket option values via partial differential equations (PDEs). This highly efficient approximation approach requires the solution of only a limited number of low-dimensional PDEs complemented with optimal exercise conditions. It is demonstrated by ample numerical experiments that a common discretization of the pertinent PDE problems yields a second-order convergence behaviour in space and time, which is as desired. It is also found that this behaviour can be somewhat irregular, and insight into this phenomenon is obtained.

中文翻译：

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通过偏微分方程对百慕大一揽子期权进行数值估值

我们研究了 Reisinger & Wittum (2007) 引入的基于主成分分析 (PCA) 的方法，用于通过偏微分方程 (PDE) 逼近百慕大一揽子期权价值。这种高效的近似方法只需要解决有限数量的低维偏微分方程，并辅以最佳运动条件。大量数值实验证明，相关 PDE 问题的常见离散化会产生空间和时间上的二阶收敛行为，这是所期望的。还发现这种行为可能有些不规则，因此可以深入了解这种现象。