Numerical Analysis Of Explicit-Implicit Alternating Parallel Diffference Methods For Several Option Pricing Models

The Black-Scholes model is the core of option pricing theory.Its numerical solution can promote the reasonable pricing of financial derivatives and the healthy development of financial market,which has the practical significance.In this paper,we construct a class of parallel numerical methods considering both short-time and high-precision for single-asset option pricing model(the payment of dividend Black-Scholes model and the nonlinear Leland option pricing model with transaction fee)and the multi-asset quanto options pricing model.For the payment of dividend Black-Scholes model,we construct the pure alternative segment explicit-implicit and implicit-explicit parallel difference schemes.Theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are second-order convergence in both space and time.Their overall accuracy is better than that of the existing alternating segment explicit-implicit and the implicit-explicit parallel difference methods.In calculation time,our schemes are reduce by 89.93%compared with classics Crank-Nicolson scheme.For solving nonlinear Leland equation of payment transaction fee,this paper offers a class of parallel difference numerical methods which are pure alternative segment explicit-implicit and implicit-explicit parallel difference methods.PASE-I and PASI-E schemes are unconditionally stable and second-order convergence in both space and time.The numerical experiments verify that the calculation accuracy of numerical methods in this paper are better than that of the existing alternating segment Crank-Nicolson parallel difference scheme,alternating segment explicit-implicit and implicit-explicit difference schemes.Compared with classical Crank-Nicolson scheme,the speedup of PASE-I format is 9.89.For the multi-asset quanto options pricing model,based on the explicit-implicit difference numerical method,combing the idea of alternating band Crank-Nicolson difference scheme.Then we can get pure alternating band explicit-implicit and alternating band implicit-explicit schemes.The theory analysis and numerical experiments show that the PABdE-I and PABdI-E schemes are unconditionally stable and second-order accuracy in space and time,which are superior to the existing ABdC-N scheme.In addition,compared with the C-N scheme,the computing time of PABdE-I and ABdC-N schemes are reduced by 93.56%and 83.61%respectively.In conclusion,we can get the explicit implicit parallel difference method is high-efficient when solving single asset pricing model and multi asset quanto option pricing model.