High Precision Difference Method Of Option Pricing Model

In 1973,Black-Scholes equation was established by Black and Scholes for the first time,which created a new field of option pricing.Then by continuous improving and promotion,this equation was widely applied to financial transactions,which greatly promoted the development of the derivative financial market.Considering that the analytical solution of the option pricing model is too complex,and that it may even do not exist in some boundary value conditions,we use numerical method to get its numerical solution.With the development of computer technology and algorithm,numerical solution out of reasonable algorithm,which is much easier to run,is almost the exact analytical solution.So it is of great significance to work out option pricing solution using numerical method.Compact finite difference method,one type of finite difference,has the characteristics of high precision,requiring less template node,but simpler operation and so on.It has become a focus in recent years.In this paper,three point four order compact difference scheme is obtained by analyzing Taylor.And format error is analyzed theoretically using the method of Fourier.And the constant coefficient convection-diffusion equation is obtained through the coordinate transformation of the option pricing model.We use the compact difference scheme and MacCormack method to discrete space and time,and then we obtain reasonable numerical results by MATLAB software.But as a result of the unsmoothness of the strike price function,some small error in the actual calculation may appear under the uniform grid of fourth order difference scheme.So we adopt the stretching transfer to encrypt the grid near the strike price,and fourth-order finite difference scheme is used to discrete the model.Thus we get the finite difference scheme of fourth order accuracy to solve option model.The numerical results fully show the advantage of this method.