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基于移动克里金插值的无网格局部彼得罗夫-伽辽金（MLPG）方法对欧式期权的数值研究。

A numerical study of the European option by the MLPG method with moving kriging interpolation.

作者信息

Phaochoo P, Luadsong A, Aschariyaphotha N

机构信息

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-utid Road, Bangmod, Toongkru, Bangkok, 10140 Thailand.

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-utid Road, Bangmod, Toongkru, Bangkok, 10140 Thailand ; Ratchaburi Learning Park, King Mongkut's University of Technology Thonburi (KMUTT), Rang Bua, Chom Bueng, Ratchaburi 70150 Thailand.

出版信息

Springerplus. 2016 Mar 9;5:305. doi: 10.1186/s40064-016-1947-5. eCollection 2016.

DOI:10.1186/s40064-016-1947-5
PMID:27064892
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4783319/
Abstract

In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively. We show that the spectral radius of amplification matrix with the discrete operator is less than 1. This ensures that this numerical scheme is stable. Numerical experiments are performed with time varying volatility and the results are compared with the analytical and the numerical results of other methods.

摘要

本文将无网格局部彼得罗夫-伽辽金（MLPG）方法应用于求解金融问题中的广义布莱克-斯科尔斯方程。该方程是一个偏微分方程，用于描述布莱克-斯科尔斯模型下欧式看涨期权或欧式看跌期权的价格演变。分别采用θ加权法和MLPG对控制方程在时间变量和期权定价方面进行离散化。我们证明了离散算子的放大矩阵的谱半径小于1。这确保了该数值格式是稳定的。针对时变波动率进行了数值实验，并将结果与其他方法的解析结果和数值结果进行了比较。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/ac355a7c949a/40064_2016_1947_Fig9_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/c9bb74eb1302/40064_2016_1947_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/ac355a7c949a/40064_2016_1947_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/264796a52b5d/40064_2016_1947_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/3d964e053f61/40064_2016_1947_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/57105b63c049/40064_2016_1947_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/38c866d9b6c1/40064_2016_1947_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/d4955bbafb24/40064_2016_1947_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/491d22ec9559/40064_2016_1947_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/d884f2120ec1/40064_2016_1947_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/c9bb74eb1302/40064_2016_1947_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/511a/4783319/ac355a7c949a/40064_2016_1947_Fig9_HTML.jpg

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引用本文的文献

1
The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.基于移动克里金插值的无网格局部彼得罗夫-伽辽金方法求解时间分数阶纳维-斯托克斯方程
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