| For ordinary differential equation of the initial value problems，the numerical method can also beapplied to the partial differential equations. so we first introduce differential equation of the classicnumerical solution,the algorithm’s advantages and disadvantages can be attained by comparisons throughan example.The first chapter mainly introduced the development of the option pricing theory and the researchsituation in the domestic and foreign countries at present.At the same time,we showed the paper work Ihave done.In the second chapter we have systematically reasoned the common numerical methods such as Eulermethod, backward Euler method, trapezoidal method, improvement of the Euler method, the Adamsinserted formula and interpolation formula.In the third chapter, For the Black-Scholes option pricing mathematical model,the mixed differencescheme is adopted in order to discrete the numerical dates. By the numerical experiment,we have illustratedthat the trend of the option pricing coincides with the realistically financial world.Firstly, we transformed the Black-Scholes option pricing mathematical model equivalently.secondly tothe time variable we adopted the central difference scheme and to the spatial variable we adopted the fivepoints difference scheme and we get a stable mixed difference scheme by discrete the original Partialdifferential equation. At the same time,we have analysed the stability and convergence of the mixeddifference scheme by the Fourier method.At last,through the numerical test we have proved the feasibilityof the method and the method is more simple and easier compared with other methods. |
