Finite Difference Parallel Computing Of 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 Black-Scholes equation of the dividend-paying option pricing model, a class of parallel difference scheme:the alternating segment explicit-implicit (ASE-I) scheme and alternating implicit-explicit (ASI-E) scheme is given in this paper. The theoretical analysis shows that these two schemes are unconditionally stable, convergent and are first order accurate in time, second order in space. What’s more, the ASE-I scheme and ASI-E scheme also have the parallel property and can improve calculation efficiency greatly. The numerical experiments show that the calculation time of the ASE-I (ASI-E) scheme is only1/2and1/5of that of the explicit-implicit (implicit-explicit) scheme and Crank-Nicolson scheme, respectively. Thus the ASE-I scheme and ASI-E scheme given by this paper are effective and feasible in solving the dividend-paying option pricing model.For solving the two-dimensional Black-Scholes equation of the quanto options pricing model, a class of improved ADI difference scheme:the ADI scheme based on the Douglas-Rachford splitting form (D-R ADI), the ADI scheme based on the Craig-Sneyd splitting form (C-S ADI) and the compact ADI scheme based on the Douglas-Rachford splitting form are constructed in this paper. The basic idea of these improved ADI schemes is to split the original two-dimensional equation into two one-dimensional equations. Then calculate these equations by semi-implicit difference scheme or compact difference scheme. The theoretical analysis shows that these improved ADI schemes are unconditionally stable, convergent and has higher calculation accuracy.As the ADI scheme is easy to realize parallelization, these improved ADI schemes D-R ADI scheme, C-S ADI scheme and compact ADI scheme can improve the calculation efficiency and reduce the calculation time greatly. The numerical experiments show that the calculation time of the D-R ADI scheme, C-S ADI scheme and compact ADI scheme is only1/2,3/4and4/5of that of the serial Crank-Nicolson scheme, respectively. Thus the improved ADI schemes given by this paper can be used to solve the quanto options pricing model rapidly and validly.