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Title: Numerical analysis of the European and American options with the SPH method

Authors: Abdelmjid Qadi El Idrissi; Boujemaa Achchab; Abdellahi Cheikh Maloum

Addresses: Hassan I University, National School of Applied Sciences Berrechid, Morocco ' Hassan I University, National School of Applied Sciences Berrechid, Morocco ' Hassan I University, National School of Applied Sciences Berrechid, Morocco

Abstract: In this paper, we propose a numerical method to solve the European and the American options by using the SPH method. Because its robustness and efficacy, this numerical method has been widely applied in the computation of partial differential equations particularly in fluid dynamic. To model these financial options, we use the Black Scholes equation. It is a mathematical model consisting of a set of partial differential equation supplemented by some boundary conditions. We evaluate the accuracy of our numerical method by giving some comparisons between the analytic solution and the numerical simulation.

Keywords: Black Scholes equation; European option; American option; SPH method.

DOI: 10.1504/IJMMNO.2020.104322

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.1, pp.28 - 48

Received: 12 Dec 2018
Accepted: 18 Mar 2019

Published online: 26 Dec 2019 *

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