Several Parallel Difference Methods For Solving Time Fractional Black-Scholes Equations

Options are the core tools of financial risk management,efficient parallel differential method for studying fractional Black-Scholes equation has important theory and application value.Three kinds of parallel difference schemes are constructed in this paper for solving the time-fractional Black-Scholes equation:alternating segment explicit-implicit(ASE-I)scheme and alternating segment implicit-explicit(ASI-E)scheme.pure alternative segment explicit-implicit(PASE-I)scheme and pure alternative segment implicit-explicit(PASI-E)scheme?mixed alternative segment Crank-Nicolson(MASC-N)scheme.The theoretical analysis of stability and convergence of the difference scheme is given.Theoretical analysis and numerical experiments demonstrate the difference schemes in this paper are stable and convergence rates are spatially second-order and temporally 2-a order.The scheme has obvious parallel computing properties,computational efficiency is significantly higher than the serial scheme and the calculation time of PASE-I scheme is about 40%less than that of implicit scheme.Lastly,ASE-I scheme,PASE-I scheme and MASC-N scheme are compared from computational accuracy and computational efficiency.The results show that MASC-N parallel difference scheme has the highest accuracy and computational efficiency of PASE-I parallel difference scheme is highest,the computational performance of PASE-I method is optimal.