Pre-average Nonparametric Estimation Of Noise Jump-diffusion Process And Its Application

With the rapid development of computer information technology,the application of big data is becoming wider and wider.In accordance with the financial industry,high frequency transaction has gradually become the mainstream of transaction strategy,and the high frequency transaction data generated by transaction has also become the focus of financial mathematics and econometrics research.Compared with traditional low-frequency financial transaction data,high-frequency transaction data can usually store market information other than transaction price.However,due to the imperfection of foreign exchange market rules,there are differences between the observed and theoretical values of high-frequency financial data.These gaps are often referred to as microstructure noise.Therefore,the models and methods based on traditional low-frequency data are no longer fully applicable.In the field of modern financial mathematics,jump diffusion model plays a very important role in asset evaluation.The accuracy of the model mainly depends on two main parameters:drift coefficient and diffusion coefficient.Therefore,the estimation of these two parameters is the key problem of modeling.This paper studies a nonparametric estimation method using high-frequency financial data to improve the jump diffusion model.This paper first describes the high-frequency financial data with microstructure noise,and then constructs a nonparametric jump diffusion process to estimate the drift and diffusion coefficient in the model.Data denoising can not only maintain the rich market information in RF data,but also reduce the noise error of nonparametric model estimation.Aiming at the two main problems of nonparametric estimation,considering the non-negativity of asset price and the volatility of real financial market,that is,the abstract target probability density function is bounded support,the asymmetric gamma kernel function is selected.Solving the boundary effect of kernel density estimation in boundary band estimation;The window width is h=hssn-2/5,which hs is an adjustable constant.On this basis,the NW estimation and local linear estimation after noise suppression are proposed,and the existing nonparametric estimation methods are improved.To verify the performance of the improved estimation method in limited samples,the Monte Carlo simulation method is used to verify the effectiveness and robustness of the method.The finite sampling performance of nonparametric drift coefficient and diffusion coefficient estimation is studied and evaluated from the aspects of simulation estimation diagram,estimation deviation and error,QQ diagram and error analysis.The results show that the local and NW linear nonparametric estimation constructed by asymmetric gamma kernel has strong robustness to the high-frequency data processed by pre mean denoising method,and has certain advantages over the nonparametric estimation without denoising.When comparing different estimators,the sample performance of local linear estimator is better than that of NW estimator,with small estimation error and high estimation accuracy.Eventually,the non-parametric estimation method proposed in this thesis is used for the empirical investigation of the stock price fluctuation process.Taking into account the high frequency data from the Shanghai 500 Index from 25.April 2021 to 25.December 2021 as a research object,the jump diffusion process is constructed with the sample frequency of 1 min and 164 trading days.The improved non-parametric estimation method is used to estimate the drift and diffusion coefficient.The error results show that the non-parametric leap diffusion process,constructed after noise reduction,is better suited to describe the process of stock price fluctuation.It further enriches the idea of noise reduction of high frequency data and the non-parametric estimation method of the jump diffusion process.