Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance

Malik Zaka Ullah, Abdullah Khamis Alzahrani, Hashim Mohammed Alshehri and Stanford Shateyi ()
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Malik Zaka Ullah: Mathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abdullah Khamis Alzahrani: Mathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Hashim Mohammed Alshehri: Mathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2023, vol. 11, issue 12, 1-12

Abstract: In this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the generalized multiquadric radial basis function (RBF). The time-fractional derivative is estimated by an L1-scheme but the spatial variable is discretized using fourth-order RBF-FD methodology. As a matter of fact, the PDE problem is transformed in the form of a linear set of algebraic equations. To support analytical discussions, numerical tests are furnished and reveal the efficacy of the presented solver.

Keywords: option pricing; fractional Black–Scholes; radial basis function (RBF); RBF-FD; numerical method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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