The Parameter Estimation And Empirical Study Of The Double Uniform Jump Diffusion Model

The parameter estimation and empirical research on the jump diffusion model of stock price is an application of mathematical finance theory and software calculation method in practice.In this paper,on the basis of previous studies,some research has been made in terms of parameter estimation and empirical studies involving double uniform jump diffusion model.It has some practical significance to expand the theory of the asset price change,and to seek the risk characteristics of derivatives.According to the traditional continuous time finance model cannot describe the "jump"phenomenon and "asymmetric leptokurtic features" appeared in the actual financial market,we put forward jump diffusion model to study the asset price motion.Firstly,in the order of the time course and a major breakthrough of jump diffusion model theory study,direction and research progress in recent years on the jump diffusion model and main results are reviewed,summarized several typical jump diffusion model and parameter estimation methods,describe the research progress and results of the jump diffusion model.Then,based on the analysis of all kinds of existing models,the object of this paper,double uniform jump diffusion model is established.Assuming the jump amplitude obeys the double uniform distribution,the double uniform jump diffusion model of the underlying asset price is established.Based on the theory and recognition algorithm of LM jump recognition method,combined with the probability distribution of each part of the model,a parameter estimation combination method based on LM jump recognition is proposed.At the same time,the jumping point data repair algorithm is proposed,and the parameter estimation theory of each part of the model is given.And then,we carry on the simulation analysis.Finally,an empirical study,using empirical analysis of uniform double jump diffusion model in Shanghai stock market price index since 2000,given the specific jump point,calculate the bilateral jump parameters are estimated using the data.The simulated data by Monte Carlo simulation method of this model,by comparing with the real data,make the jump diffusion model Q-Q,check the fitting effect.The empirical results illustrate the validity of the model and the estimation method we established.The work of this paper is innovative and effective.