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A difference method with parallel nature for solving time-space fractional Black-Schole model

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  • Yan, Ruifang
  • He, Ying
  • Zuo, Qian

Abstract

The fractional Black-Scholes (B-S) model can better describe the change process of asset prices, so the research of its numerical solution has important theoretical significance and practical value. For the time-space fractional B-S model, a kind of difference format with parallel nature is proposed: based on the alternating segment Crank-Nicolson format, the Saul’yev asymmetric format at the inner boundary is replaced with an explicit format and an implicit format. A mixed alternating segment Crank-Nicolson (MASC-N) difference format is obtained. Theoretical analysis shows that the existence, uniqueness, unconditional stability, and convergence of the MASC-N scheme. Numerical experiments verify the theoretical analysis, and show that the format of this paper is better than the existing alternating segment pure explicit-implicit (PASE-I) difference format.

Suggested Citation

  • Yan, Ruifang & He, Ying & Zuo, Qian, 2021. "A difference method with parallel nature for solving time-space fractional Black-Schole model," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006342
    DOI: 10.1016/j.chaos.2021.111280
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    References listed on IDEAS

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    1. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    2. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
    3. Jumarie, Guy, 2008. "Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 271-287, February.
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    1. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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