Cubic Hermite Finite Element Method for Nonlinear Black-Scholes Equation Governing European Options

Authors

DOI:

https://doi.org/10.22481/intermaths.v2i2.9481

Keywords:

Nonlinear Black-Scholes, Finite Element Method, Crank-Nicolson, Hermite Polynomials

Abstract

A numerical algorithm for solving a generalized Black-Scholes partial differential equation, which arises in European option pricing considering transaction costs is developed. The Crank-Nicolson method is used to discretize in the temporal direction and the Hermite cubic interpolation method to discretize in the spatial direction. The efficiency and accuracy of the proposed method are tested numerically, and the results confirm the theoretical behaviour of the solutions, which is also found to be in good agreement with the exact solution.

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Author Biography

Teófilo Domingos Chihaluca, University of Beira Interior, Center of Mathematics and Applications, Covilhã, Portugal

Doutoramento em Matemática e Aplicações pela universidade da Beira Interior, Portugal. DEA (Doutoramento em Matemática Aplicada à Economia e a Gestão), ISEG, universidade de Lisboa, Portugal. Mestrado em Direcção Financeira e Auditoria, Universidade Politécnica de Madrid, Espanha. Mestrado em Gestão de Empresas, Instituto politécnico de Castelo Branco, Portugal. Licenciatura em Matemática, Universidade Agostinho Neto, Angola. Áreas de Investigação: Matemática Financeira, Equações Diferencias Parciais, Métodos Numéricos e Educação Matemática.

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Published

2021-12-28

How to Cite

Chihaluca, T. D. (2021). Cubic Hermite Finite Element Method for Nonlinear Black-Scholes Equation Governing European Options . INTERMATHS, 2(2), 23-38. https://doi.org/10.22481/intermaths.v2i2.9481

Issue

Vol. 2 No. 2 (2021)

Section

Artigos

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