Contrast Estimation Of The Vasicek Integrated Diffusion Process

Since Black and Scholes proposed the famous Black-Scholes option pricing formula in 1973,the importance of stochastic diffusion process in the field of financial mathematics and financial statistics has become increasingly prominent,and the statistical inference of diffusion process has gradually become the focus of scholars.However,in general,the diffusion model is difficult to deal with non-stationary data,and most of the data in the financial field are non-stationary.In order to solve this problem,Nicolau(2007)first systematically proposed the concept of integrated diffusion process.The integrated diffusion process overcomes the shortcoming of non-differentiability of Brownian motion,and can establish a mathematical model that can be both integral and differential.It has a wide range of applications in the analysis and processing of non-stationary data.Based on the contrast function proposed by Gloter(2006),we give the parameter contrst es-timators of the drift coefficient μ(x)and the diffusion coefficient σ~2(x)of the Vasicek integrated diffusion process,and derive the mean-square error of the parameter estimation of the drift coeffi-cient,so as to obtain the optimal sampling interval of the parameter estimation.In the numerical simulation,we investigate the fitting effect of the estimated value under different sampling intervals and different sample sizes.The results show that the optimal sampling interval can obtain better estimation results,even if the sample size is small.In the empirical analysis,we select the daily closing price data of the Shanghai Composite Index,the GEM Index and the Bank of China stock to establish the Vasicek integrated diffusion model,and we obtain the predicted value and confidence interval of the closing price data.The coverage of the confidence interval is 95.1%,and the results show that the model can effectively fit the actual data.