Spectral Solutions for Fractional Black-Scholes Equations

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Abdelkawy, MA (Author) Other; António Mendes Lopes (Author) FEUP

Journal

Title: Mathematical Problems in Engineering

Vol. 2022

Pages: 1-9

ISSN: 1024-123X

Publisher: Hindawi

Indexing

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Other information

Authenticus ID: P-00W-WQ6

DOI: 10.1155/2022/9365292

Abstract (EN): This paper presents a numerical method to solve accurately the fractional Black-Scholes model of pricing evolution. A fully spectral collocation technique for the two independent variables is derived. The shifted fractional Jacobi-Gauss-Radau and shifted fractional Jacobi-Gauss-Lobatto collocation techniques are utilized. Firstly, the independent variables are interpolated at the shifted fractional Jacobi nodes, and the solution of the model is approximated by means of a sequence of shifted fractional Jacobi orthogonal functions. Then, the residuals at the shifted fractional Jacobi quadrature locations are estimated. As a result, an algebraic system of equations is obtained that can be solved using any appropriate approach. The accuracy of the proposed method is demonstrated using two numerical examples. It is observed that the new technique is more accurate, efficient, and feasible than other approaches reported in the literature. Indeed, the results show the exponential convergence of the method, both for smooth and nonsmooth solutions.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9