Numericial Analysis Of Several Parallel Difference Methods For Nonlinear Leland Equation

Option pricing questions are central questions in financial markets,among them option pricing model with transaction costs(nonlinear Leland equation)is a famous financial mathematics basic modeling.It has an important position and function.Nonlinear Leland equation doesn't have accurate resolution solution,at physically in adopt more numericial method to solve.In view of Leland model,this paper gives Alternating Three Points Group Explicit(AGE-3)method.Theoretical analysis demonstrates that AGE-3 difference method of the model is unconditional stable.AGE-3 scheme has first accuracy in time and second accuracy in space.The numerical experiment shows that AGE-3 scheme can improve the calculation speed rapidly in contrast with implicit scheme and Alternating Segment Crank Nicolson(ASC-N)scheme,and save 99%of time.Thus the AGE-3 method can be used to solve the payment of dividend Black-Scholes equation effectively.For further raising the calculation accuracy of nonlinear Leland equation,this paper gives alternating group explicit iterative parallel calculating scheme.Theoretical analysis shows that AGEI-CN based on classical Crank-Nicolson(C-N)has second accuracy.The existence and uniqueness of solution and convergence of a class of AGEI schemes were given.Numerical experiments show that AGEI-CN scheme saves 69 percent of time with contrast to C-N and saves 36 percent of time with contrast to ASC-N.It shows that the AGEI-CN scheme can solve nonlinear Leland equation effectively.Finally,the numericial experiments compare and analyze AGE-3?ASC-N?AGEI-CN for solving nonlinear Leland equation.The answer shows,the calculation time of AGE-3 is less.But the calculation accuracy of AGE-3 is not good.The calculation accuracy of the AGEI-CN is better and the calculation time is less than ASC-N.In conclusion,the comprehensive calculation function of AGEI-CN is the superior.