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

Ruifang Yan, Ying He and Qian Zuo

Chaos, Solitons & Fractals, 2021, vol. 151, issue C

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.

Keywords: Time-space fractional Black-Scholes (B-S) model; Mixed alternating segment Crank-Nicolson format (MASC-N); Unconditional stability; Convergence; Parallel calculation (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006342

DOI: 10.1016/j.chaos.2021.111280

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