Research On Nonlinear Dynamics Of The Nonlinear Option Pricing Model

As the main body of the option market,option pricing has been concerned by many scientists.It has been a long process from the proposal of the option to the Black-Scholes model,which is a revolutionary option pricing model.In 1973,Black and Scholes proposed the Black-Scholes model by using the Ito’s lemma on the basis of the Wiener process,and then they revised and improved it to enhance its effectiveness.Because of the importance of this model,many scholars at home and abroad have studied it by using a variety of mathematical methods.But in the face of the financial crisis,this model seems to have shown its limits.In 2010,Australian researcher Ivancevic proposed to use the nonlinear Schr(?)dinger equation to fit the Black-Scholes model,that is,the nonlinear option pricing model.In view of the important application of the nonlinear option pricing model in finance,this thesis makes a detailed study of this model.The specific content of this thesis is as follows:Firstly,this thesis introduces the background and the significance.By consulting the books and literatures on option pricing,the main content and the frame of this thesis is determined.The definition and classification of option and the factors that affect the price of option are introduced in detail,so as to have a more intuitive understanding of the financial derivative products.Secondly,this thesis deduces the Black-Scholes option pricing model using the Ito’s lemma from the Wiener process equation.Some equivalent forms of the model are also introduced.In the face of the financial crisis,people find that the BlackScholes model has its limitations,so the nonlinear option pricing model is introduced,which is brought in by Ivancevic to fit the Black-Scholes option pricing model.Then,the bright soliton solution and the dark soliton solution of the nonlinear option pricing model are obtained by using the tanh function expansion method and the trial function method respectively.Some other solutions of the nonlinear option pricing model are introduced briefly.According to the given analytical solutions,the thesis also gives some dynamics analysis of the exact solutions.Finally,considering the factors influencing the price of options,the nonlinear option pricing model with perturbation is introduced,and the direct perturbation method is used to solve this model.On this basis,a simple dynamic analysis of the perturbation solution is performed and the prospect of the full thesis are given.