Numerical Simulation Of European Call Option Pricing Model

Option pricing theory is one of the most basic and important research contents in modern finance,and it is also the cornerstone of financial economics theory.The option price has a dual nature,that is,it is both the cost of the option buyer and the income of the option seller,so option pricing will be the focus of this article.This article will analyze the European call option pricing model using numerical simulation.This article is devoted to the research of European call option model.Since this model is a complex nonlinear differential system,its exact solution is difficult to obtain.Therefore,choosing a stable high-precision numerical method has become an important research approach.However,there are few high-precision algorithms for European call option pricing models,and the analysis of the stability and convergence of these algorithms is even rarer.To this end,this article will propose two high-precision algorithms to solve the European call option pricing problem,and analyze the convergence and stability of the algorithms,and then use the new algorithm in the pricing of the underlying options.The following is the research content of this article:1.Firstly,the classical Black-Scholes equation is replaced with variables,the space first derivative term in the equation is eliminated,and then this article introduce the new variable so the equation is sorted to obtain an equivalent mathematical model.The compact difference method is used to discretize the equivalent model,and a compact finite difference scheme with high-order accuracy is obtained.Then this article analyze the stability and convergence of the scheme with the energy method in the linear case.Then,the convergence of the format was verified by a numerical example,and a numerical simulation was carried out for the European call option of SSE 50 ETFas an example.The applicability of the algorithm is demonstrated by comparing the error between the numerical result of the classic Black-Scholes model and the real data with the error between the numerical result of this algorithm and the real data.2.Secondly,another variable transformation is performed on the classic Black-Scholes equation to obtain another equivalent model,namely the standard parabolic partial differential equation,and then for the equivalence model,a fivepoint difference is used in the space direction,a forward difference and a backward difference are used in the time direction,then this article introduce parameters to establish a five-point finite difference scheme.At the same time,the Fourier analysis method is used to prove the stability and convergence of the scheme in the linear case.By comparing the error between the numerical result of the classic model and the real data with the error between the numerical result of this algorithm and the real data,it is found that this algorithm is also suitable for the prediction and simulation of European call option pricing data of SSE 50 ETF.