In this paper, a fast and efficient numerical method which relies on the far field truncation technique, the finite element discretization, and the projection contraction method (PCM) is proposed for pricing American multi-asset options. It is well known that American multi-asset option satisfies a linear complementarity problem (LCP), which is a multi-dimensional variable coefficient parabolic model on an unbounded domain. First, we transform it into a constant coefficient parabolic LCP on a bounded domain by some skillful transformations and far-field boundary estimate. Then, the variational inequality (VI) corresponding to the truncated LCP is obtained. Further, it is discretized by the finite element method and the implicit difference method in spatial and temporal directions, respectively. Based on the symmetric positive definiteness of the full-discrete matrix, the discretized VI is solved by the PCM. Finally, numerical simulations are provided to verify the efficiency of the proposed method.

中文翻译：

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一种评估美国多资产期权的有效数值方法

本文提出了一种基于远场截断技术，有限元离散化和投影收缩法（PCM）的快速有效的数值方法，用于对美国多资产期权进行定价。众所周知，美国的多资产期权满足线性互补问题（LCP），它是无界域上的多维可变系数抛物线模型。首先，通过一些熟练的变换和远场边界估计，将其转换为有界域上的常数系数抛物线LCP。然后，获得对应于截短的LCP的变分不等式（VI）。此外，它分别通过有限元法和隐式差分法在空间和时间方向上离散化。基于全离散矩阵的对称正定性，通过PCM求解离散VI。最后，通过数值模拟验证了所提方法的有效性。