Parameter Estimation And Option Pricing Of Jump Diffusion Model

The study of the problem of the jump diffusion model is one of the hotspots of current financial market research.In this paper,the parameter estimation and option pricing problems with lognormal jump model and stochastic volatility model with jump are studied.Firstly,the theoretical content of the parameter estimation method is given in this paper.The basic theory of LM jump recognition and the basic theory of maximum likelihood of parameters are also given.The LM jump identification method for jump diffusion model with normal jump is established.The properties of statistics and their corresponding estimators are proved.Secondly,the theoretical knowledge of the LM jump recognition method proposed in this paper is applied to two jump diffusion models,and its process is derived and proved in detail.Firstly,the parameter estimation of the jump part is given by the method of jump recognition,and the parameter estimation result of the diffusion part is estimated by the method of maximum likelihood through the discretization of the model.Then the paper discusses the put and call formulas of American options and European options by discretizing the log-normal jump diffusion model.Finally,the effectiveness of the parameter estimation method proposed in this paper is discussed by simulation,and the empirical analysis of the data of China's financial market and the US financial market is conducted for the Shanghai Composite Index and the S&P500 from January 4,2016 to December 30,2016.The data establishes two models,which compare the data of the two models and the two financial markets vertically and horizontally.The empirical analysis of option pricing is made by applying the results of parameter estimation to option pricing.