Local Linear Estimation Of Stochastic Volatility Model

With the deepening of reform and opening up and the rapid trend of economic globalization,China's financial market has also developed rapidly,At the same time,the novel coronavirus pneumonia is rebounding,and there are risks and opportunities in the financial market as the world pattern evolves.It is difficult for investors to balance market risks and returns,subjective factors lead to the aggravation of financial market fluctuations.Therefore,a scientific and sy stematic study of volatility is conducive to the realization of the goal of 'taking the lead in the crisis and opening a new situation in the changing situation',which is of great practical significance for investors to make decisions and avoid risks.This paper selects the stochastic volatility model.The innovation of this paper is to study the drift coefficient and diffusion coefficient of SV model at the same time,and use two-step estimation method to calculate the local linear estimator and NW estimator of parameters,and compare the quality of the two estimation methods.Two-step estimation method of stochastic volatility model:in the first step,the nonparametric kernel estimation method is used to estimate the unobservable instantaneous volatility process based on the observable state variables Xt.In the second step,the potential instantaneous volatility process is replaced by the volatility process estimated in the first step.The local linear estimation method and the NW estimation method are used to estimate the drift coefficient ?(·)and the diffusion coefficient ?2(·)of the stochastic volatility model respectively,and then the estimation effects of the two estimators are compared.In this paper,Monte Carlo method is used to simulate.Firstly,the estimation effect of the first step instantaneous volatility kernel estimator is tested.It is found that the selected kernel estimator has a better effect.Then,taking the estimated volatility as the sample data,the drift coefficient and diffusion coefficient of the stochastic volatility model are calculated.The local linear estimator and the NW estimator are compared and analyzed,which can be seen from the graph.From the graph,it can be found that the local linear estimator has a better fitting effect on the real value,which can automatically adapt to the boundary and effectively avoid the‘boundary effect'.Quantitatively,the statistical properties of local linear estimators are better,because the MSE,RMSE and MAE of local linear estimators of drift coefficient and diffusion coefficient are smaller than those of corresponding NW estimators.Finally,this paper selects the daily closing price data of CSI 300 index and SSE 50 index under 5-minute high-frequency data from January 1,2019 to December 31,2020 for empirical research.By studying the return,volatility and statistical properties of the two indexes,this paper analyzes the characteristics of volatility and verifies that the local linear estimation method is better from the qualitative and quantitative perspectives.