Open AccessCubic Hermite Finite Element Method for Nonlinear Black-Scholes Equation Governing European Options
Author(s) -
Teófilo Domingos Chihaluca
Publication year - 2021
Publication title -
intermaths
Language(s) - English
Resource type - Journals
ISSN - 2675-8318
DOI - 10.22481/intermaths.v2i2.9481
Subject(s) - discretization , hermite polynomials , partial differential equation , mathematics , finite element method , hermite interpolation , crank–nicolson method , black–scholes model , interpolation (computer graphics) , nonlinear system , mathematical analysis , physics , econometrics , classical mechanics , motion (physics) , volatility (finance) , quantum mechanics , thermodynamics
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.