Spectral Solutions for Fractional Black-Scholes Equations

• Tipo: Artigo em Revista Científica Internacional
• Data: 2022

Autores

Abdelkawy, MA (Autor) Outra; António Mendes Lopes (Autor) FEUP

Revista

Título: Mathematical Problems in Engineering

Vol. 2022

Páginas: 1-9

ISSN: 1024-123X

Editora: Hindawi

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 9