Research On New Methods Of Finite Difference Parallel Computing For Solving Two Option Pricing Models

The option occupies an important position in the modern financial trading market. It has theoretical significance and application value to research numerical methods for different option pricing models. This paper mainly studies on the finite difference parallel computing methods of solving two option pricing models:single-asset option pricing model and multi-asset options pricing model.For solving the one-dimensional B-S (Black-Scholes) equation of the dividend-paying option pricing model, this paper gives the group explicit (GE) difference scheme and the alternating group explicit (AGE) difference scheme. Theoretical analysis and numerical experiment demonstrate that GE difference scheme is conditional stable and AGE difference scheme is unconditional stable. The numerical experiment shows that AGE difference scheme can improve the calculation speed rapidly, the calculation time of AGE difference scheme and GE difference scheme is 1/2 of the improved Saul’ yev asymmetric difference scheme, which confirms the parallel computation method of GE finite difference AGE finite difference given by this paper can be used to solve the payment of dividend option pricing model of the single asset effectively.This paper gives a kind of alternating direction implicit method based on the modified Peaceman-Rachford (MP-R ADI) difference method for solving the quanto options pricing model (two-dimensional B-S equation). Theoretical analysis demonstr-ates that MP-R ADI difference scheme has several advantages such as:parallel property, unconditional stability and a better accuracy than alternating direction implicit method based on the Douglas-Rachfordalternating direction implicit (D-R ADI) parallel difference method. Numerical experiment results show that MP-R ADI has improved the computational efficiency of the model greatly, the calculation time of MP-R ADI difference scheme is about 1/2 of the Crank-Nicolson (C-N) scheme, which confirms the MP-R ADI difference scheme can be used to solve the quanto options pricing problems effectively.