A Local Radial Basis Function Method for High-Dimensional American Option Pricing Problems
A Local Radial Basis Function Method for High-Dimensional American Option Pricing Problems
复制标题
求解高维美式期权定价问题的局部径向基函数法
DOI：
10.3846/mma.2018.008
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发表时间：
2018
影响因子：
1.8
通讯作者：
F. Soleymani
中科院分区：
文献类型：
--
作者：
R. Company;V. Egorova;L. Jódar;F. Soleymani
本文将局部Wendland径向基函数(RBF)应用于求解含时多维期权定价的非线性偏微分方程组。首先，基于扩散矩阵的LDLT分解，通过改变空间变量来去除偏微分方程的交叉导数项。在此基础上，提出了一种改进的形状参数算法，并讨论了多资产期权的定价问题。事实上，包含三个和四个资产的多个实验表明，所提出的方法的结果与文献很好地吻合，并且只要仔细选择形状参数，可以得到更精确的结果。
In this work, we apply the local Wendland radial basis function (RBF) for solving the time-dependent multi dimensional option pricing nonlinear PDEs. Firstly, cross derivative terms of the PDE are removed with a change of spatial variables based in LDLT factorization of the di_usion matrix. Then, it is discussed that the valuation of a multi-asset option up to 4D can be computed using a modified shape parameter algorithm. In fact, several experiments containing of three and four assets are worked out showing that the results of the presented method are in good agreement with the literature and could be much more accurate once the shape parameter is chosen carefully.