The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method

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Author list: Nualsaard, Naravadee; Luadsong, Anirut; Aschariyaphotha, Nitima;

Publisher: Hindawi

Publication year: 2020

Journal: Advances in Mathematical Physics (1687-9120)

Volume number: 2020

ISSN: 1687-9120

eISSN: 1687-9139

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085583222&doi=10.1155%2f2020%2f1942762&partnerID=40&md5=b85784156377326dcf643c2512f9bbf0

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo's sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution. © 2020 Naravadee Nualsaard et al.

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