Alternating segment explicit-implicit and implicit-explicit parallel difference method for the nonlinear Leland equation

The nonlinear Leland equation is a Black-Scholes option pricing model with transaction costs and the research of its numerical methods has theoretical significance and practical application value. This paper constructs a kind of difference scheme with intrinsic parallelism-alternating segment explicit-implicit (ASE-I) scheme and alternating segment implicit-explicit (ASI-E) scheme based on the improved Saul’yev asymmetric scheme, explicit-implicit (E-I) scheme, and implicit-explicit (I-E) scheme. Theoretical analysis demonstrates that this kind of scheme is unconditional stable parallel difference scheme. Numerical experiments show that the computational accuracy of this kind of scheme is very close to the classical Crank-Nicolson (C-N) scheme and the alternating segment Crank-Nicolson (ASC-N) scheme. But the computational time of this kind of scheme can save nearly 81% for the classical C-N scheme and save nearly 40% for the ASC-N scheme. Numerical experiments confirm the theoretical analysis, showing the higher efficiency of this kind of scheme given by this paper for solving a nonlinear Leland equation.