A Research Of Asian Option Pricing Based On The Improved Finite Differences Method

Asian options has great advantages in risk management and control, it has become one of the most active options in financial markets, and in recent years the numerical study of Asian option pricing emerge in endlessly, more perfect. In Asian options numerical discrete method, finite difference method is a very good tool, using the method of finite difference method to the option price for discretization is becoming more and more popular. However, the traditional finite difference method for the grid structure, has its limitations. Radial basis function(RBF), on the other hand, is a useful tool for solving partial differential equations, very effective for dealing with diversity, not only high efficiency, and operation simple and convenient storage in the computer.The purpose of this article is using radial basis function(RBF) approximation method to describe the type of the option price, using finite difference method for discrete time derivative first, get a series of scattered data points, then use the radial basis function interpolation fitting of discrete data values. We through a series of variable substitution and put- call parity formula method, discussed about the arithmetic average fixed to finalize the price and the type of call option price at the beginning of the first order partial differential equations boundary value problem, and using radial basis function(RBF)approximation in the option price, and then puts forward the improved finite difference method based on radial basis function(RBF) approximation, and the rationality and superiority of this method is analyzed in theory. Finally, we validated by numerical analysis, this method is high precision, and has considerable stability.