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

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.