The Jump Diffusion Model Parameter Estimation Method Of High-frequency Data

Outside interference sometimes impact financial markets, then generate abnormal fluctuations, such as the impact of the financial crisis on the securities market will lead to produce abnormal stock price volatility. In order to characterize this phenomenon, Morton introduced jump to characterize the abnormal price, based on the continuous diffusion model. At the same time, with the development of computer technology make it possible to obtain a high-frequency financial data. The high-frequency financial data have some features, which are common time-series data not available. And the features play an important role in grasping of the financial market microstructure. However, studies on the jump diffusion model based on high-frequency data are still relatively lacking. So this paper studies the jump diffusion model parameter estimation method of high-frequency data.In this paper, we propose a parameter estimation method point at high-frequency data jump diffusion model, which separations the jump process and the diffusion process first and then estimate the parameters separately. We first analyze the defect of computing the probability of failure to detect actual jump, which proposed in Lee-Mykland’s paper. Then constructed jump test statistic which obey t-distribution, and achieve a good result with the Monte Carlo simulation, that the probability of spurious detection and the probability of failure to detect actual jump are both control in a small range. We solve problem of Lee-Mykland’s paper with the new jump test statistic, and prove the statistic is better than Lee-Mykland’s method in some situations.Then this paper use the method of maximum likelihood estimation to estimate the parameters of the diffusion process and the jumping process respectively, and simulate test the method with Matlab programming. In test we first generation data set of jump diffusion process with the given parameter value, then estimate the parameters of the generated data, finally calculate the relative error of estimate value and the given value, thus examine the estimation method. Through simulation test we obtain a conclusion that each parameter estimates are controlled in a reasonable scope, and it is concluded that the method we proposed in paper is accurate and simple operation.At the end of the paper we select the three years (2012-2014) Hushen300index5minutes data to carry on the empirical analysis. First we preprocess the price data, then estimate the parameters with introduced method. Finally, we carry on comparative analysis the feature statistics between the data that the model simulated and the original data. The analysis shows that the Hushen300index nearly three years’data meet the normal jump diffusion model. At the same time, through the parameter estimation method proposed in this paper, it is concluded the concrete form of the jump diffusion model, which proves that the method has very good practicability to high frequency data.