Numerical Simulation And Empirical Analysis Of The European Option Pricing Model Based On A Radial Functio

The development of economic globalization is promoting the integration of the world economy and finance,so the financial industry has developed rapidly,and option,as an important financial derivative tool,has attracted more and more attention.How to grasp the price change of option is the basis of market transaction,so the theory of option pricing arises at the historic moment.Black-Scholes pricing model,an important milestone of modern finance,has been widely used in financial transactions and greatly promoted the rapid development of global financial derivatives market.With the rapid progress of the financial industry,a variety of option pricing models have been derived on the basis of Black-Scholes model.However,most analytical solutions of these options pricing models are not easy to obtain,so it is of great significance to study their numerical solutions.The purpose of this paper is to study of European option pricing model.Usually the study of numerical algorithm of the European option is by means of finite difference method and finite element method to the numerical method of grid subdivision.This paper puts forward a kind of meshless method,radial basis function quasi-interpolation method,respectively,for the classic Black-Scholes equation and jump-numerical diffusion equation.The specific numerical algorithm is applied to SSE 50 ETF options for empirical research.When estimating the parameters of the model,the classical methods of statistical analysis,conditional heteroscedasticity model and normal sample outlier test method are used to carry out corresponding statistical analysis,and the main content is summarized as follows:One is to solve the classical Black-Scholes.Based on the idea of line method,the derivative is approximated by radial basis function method in the spatial direction,and the Crank-Nicolson scheme is used in the time direction to obtain a numerical scheme with high accuracy and fast calculation,whose convergence is also analyzed.A numerical example is given to verify the effectiveness of the proposed algorithm.Finally,a case study is carried out with the help of SSE 50 ETF option data,in which the estimation of volatility is characterized by GARCH model,and the obtained parameters are substituted into the algorithm and compared with the actual market data to verify the practical applicability of the algorithm.Second,the jump-diffusion model is solved.This part aims to apply radial basis function quasi-interpolation method to solve jump-diffusion model and make empirical analysis.The radial basis function quasi-interpolation method and Crank-Nicolson method are used to discrete the spatial and temporal directions respectively,and the integral terms were estimated by using the fourth order Simpson formula.In the empirical analysis,the normal sample outlier method is used to estimate the jump parameters.This part can not only verify the effectiveness of radial basis function quasi-interpolation method again,but also achieve the theoretical expected effect.It shows that the improved jump-diffusion model has better simulation results than the classical Black-Scholes model.