A New Stable Local Radial Basis Function Approach for Option Pricing

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• 作者：A. Golbabai ; E. Mohebianfar
• 关键词：Local meshless method ; Radial basis function ; Black–Scholes equation ; Unconditional stability
• 刊名：Computational Economics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：49
• 期：2
• 页码：271-288
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Economic Theory/Quantitative Economics/Mathematical Methods; Computer Appl. in Social and Behavioral Sciences; Operation Research/Decision Theory; Behavioral/Experimental Economics; Math Applications
• 出版者：Springer US
• ISSN：1572-9974
• 卷排序：49

文摘

In this paper, we develop a new local meshless approach based on radial basis functions (RBFs) to solve the Black–Scholes equation. The global RBF approximations derived from conventional global collocation method usually lead to ill-conditioned matrices. The new scheme employs the idea of the finite difference method to localize them. It removes the difficulty of ill-conditioning of the original method. The new proposed approach is unconditionally stable as it is shown by Von-Neumann stability analysis. As well as it is fast and it produces accurate results as shown in numerical experiments.