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

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  • Naravadee Nualsaard
  • Anirut Luadsong
  • Nitima Aschariyaphotha

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.

Suggested Citation

  • Naravadee Nualsaard & Anirut Luadsong & Nitima Aschariyaphotha, 2020. "The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-17, May.
    • Handle: RePEc:hin:jnlamp:1942762
    DOI: 10.1155/2020/1942762
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