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Mesgarani, Hamid, Ahanj, Sara, Esmaeelzade Aghdam, Yones. (1401). A novel local meshless scheme based on the radial basis function for pricing multi-asset options. سامانه مدیریت نشریات علمی, 10(3), 716-725. doi: 10.22034/cmde.2021.44790.1891
Hamid Mesgarani; Sara Ahanj; Yones Esmaeelzade Aghdam. "A novel local meshless scheme based on the radial basis function for pricing multi-asset options". سامانه مدیریت نشریات علمی, 10, 3, 1401, 716-725. doi: 10.22034/cmde.2021.44790.1891
Mesgarani, Hamid, Ahanj, Sara, Esmaeelzade Aghdam, Yones. (1401). 'A novel local meshless scheme based on the radial basis function for pricing multi-asset options', سامانه مدیریت نشریات علمی, 10(3), pp. 716-725. doi: 10.22034/cmde.2021.44790.1891
Mesgarani, Hamid, Ahanj, Sara, Esmaeelzade Aghdam, Yones. A novel local meshless scheme based on the radial basis function for pricing multi-asset options. سامانه مدیریت نشریات علمی, 1401; 10(3): 716-725. doi: 10.22034/cmde.2021.44790.1891

A novel local meshless scheme based on the radial basis function for pricing multi-asset options

Computational Methods for Differential Equations
مقاله 11، دوره 10، شماره 3، مهر 2022، صفحه 716-725    اصل مقاله (687.21 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44790.1891
نویسندگان
Hamid Mesgarani؛ Sara Ahanj؛ Yones Esmaeelzade Aghdam*
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, Iran.
چکیده
A novel local meshless scheme based on the radial basis function (RBF) is introduced in this article for price multi-asset options of even European and American types based on the Black-Scholes model. The proposed approach is obtained by using operator splitting and repeating the schemes of Richardson extrapolation in the time direction and coupling the RBF technology with a finite-difference (FD) method that leads to extremely sparse matrices in the spatial direction. Therefore, it is free of the ill-conditioned difficulties that are typical of the standard RBF approximation. We have used a strong iterative idea named the stabilized Bi-conjugate gradient process (BiCGSTAB) to solve highly sparse systems raised by the new approach. Moreover, based on a review performed in the current study, the presented scheme is unconditionally stable in the case of independent assets when spatial discretization nodes are equispaced. As seen in numerical experiments, it has a low computational cost and generates higher accuracy. Finally, the proposed local RBF scheme is very versatile so that it can be used easily for solving numerous models and obstacles not just in the finance sector, as well as in other fields of engineering and science.
کلیدواژه‌ها
Pseudo-differential operators؛ Separation-Preserving operators؛ Adjoints
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