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

Naravadee Nualsaard, Anirut Luadsong and Nitima Aschariyaphotha

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

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.

Date: 2020
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https://doi.org/10.1155/2020/1942762

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:1942762

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