New Methods Of Finite Difference Parallel Computing For Solving Several Option Pricing Models

The research of efficient numerical method for option pricing models has important scientific significance and application value.For the payment of dividend option pricing model(linear Black-Scholes equation),this paper puts forward grouping explicit method:three points group explicit(GE-3)difference scheme and alternating group explicit(AGE-3)three difference scheme.Theoretical analysis and numerical experiment demonstrate that GE-3 scheme is conditional stable and AGE-3 scheme is unconditional stable and convergent,that the computational time of AGE-3 scheme is 1/2 of improved Saul'yev asymmetric scheme,which confirms AGE-3 scheme given by this paper can be used to solve linear Black-Scholes equation effectively.Basing on the thought of explicit-implicit alternating method,this paper constructs alternating segment explicit-implicit(ASE-I)difference scheme and alternating segment implicit-explicit(ASI-E)difference scheme with intrinsic parallelism for solving the option pricing models with transaction costs(nonlinear Leland equation).Theoretical analysis and numerical experiment show that this kind of scheme is unconditional stable parallel difference scheme and the computational accuracy of this kind of scheme is very close to the classical Crank-Nicolson(C-N)scheme.But the computational time of this kind of scheme can save nearly 81% for the classical C-N scheme,showing the higher efficiency of this kind of scheme given by this paper for solving the nonlinear Leland equation.In order to improve the computational accuracy of difference scheme for solving nonlinear Leland equation,this paper constructs improved alternating segment Crank-Nicolson(IASC-N)parallel difference scheme.Theoretical analysis and numerical experiment confirm that IASC-N scheme is unconditionally stable and has second order in time and space.Lastly,for solving nonlinear Leland equation,numerical experiment compares IASC-N scheme,ASE-I scheme,and alternating segment Crank-Nicolson(ASC-N)scheme,obtaining that the computational accuracy of IASC-N parallel difference scheme is best.The computational time of ASE-I parallel difference scheme is shortest.Comprehensive consideration,the performance of IASC-N scheme is optimal which shows IASC-N scheme has good practical application value.