Study On Volatility Of Financial High-Frequency Data Based On Market Microstructure Noises And Jumps

How to accurately measure the volatility of assets income has been one of the core research issues in the financial sector. Modern financial markets are of fast development with changing market conditions. People need to grasp the real-time information of the financial volatility to respond to market changes. In frequently trading financial markets, low-frequency data have erased too much useful information, which cannot fully reflect the real market situation. Under this circumstance research of the volatility of high-frequency financial data should be carried out.Volatility models of low-frequency data represented by ARCH and SV cannot meet the requirement of volatility modeling of high-frequency data. A new method to measure the volatility of high frequency data is needed. Andersen and Bollerslev (2000) made the pioneering work about it. They proposed a completely new method to measure the volatility of high-frequency financial data, namely Realized Volatility. Realized Volatility (RV) has no model and does not need complex estimation of parameters. RV has been widely used in the estimation of volatility of high-frequency data.High frequency data contain more information than low frequency data. With the increase of sampling frequency high frequency data will contain more and more information. However, with the increase of sampling frequency the impact of market microstructure noise on the volatility of high-frequency data will become more and more obvious. Additionally, return on assets will undergo jumping volatility in a short span of time under certain circumstances, which will also cause nonignorable influence on the estimation of volatility of return on assets. When market microstructure noises or jumps exist, RV is no longer a consistent estimator to the integral volatility and cannot accurately estimate the volatility of high frequency data.To eliminate the impact of market microstructure noises and jumps, various methods have been proposed to improve the RV so that better estimation of integral volatility can be achieved. However, most of the existing literatures have only studied how to reduce the impact of financial market microstructure noises on the volatility of high-frequency data, or only considered how to eliminate jump effects on high-frequency data. In practice, both financial market microstructure noises and jumps may exit simultaneously. Under such conditions, it is still a difficult task to estimate the volatility of high-frequency data.Having considered the condition that both financial market microstructure noises and jumps may exit simultaneously, this dissertation proposes a new estimator for the volatility of high-frequency data theoretically, discusses the theoretical features of the estimator, and carries out empirical test on the estimator by means of simulation data and real stock high-frequency data. This dissertation combines closely the theory of volatility of high-frequency data, analysis methods in financial econometrics, and empirical research and also combines the qualitative and quantitative methods. It has not only the theory research and construction, but also the empirical analysis and experience explanation. The specific content of this dissertation is as follows:The first chapter is an introduction section. This chapter mainly introduces the research background and the latest developments and issues to be addressed in financial econometrics based on high-frequency data. It puts forth the significance of the topic in this dissertation and main contents and innovation in this dissertation.The second chapter is about the research survey of volatility of high-frequency data. This chapter first analyzes the definition and statistic features of RV, further reviews the current research of the volatility estimator of high-frequency data under the condition of market microstructure noises and jumps respectively, and points out problems of current volatility estimators of high-frequency data and future research directions.Chapter three presents a new estimator - Modified Threshold Pre-averaging Realized Volatility (MTPRV). This chapter first presents a method to eliminate the impact of market microstructure noises on estimation of validate of high-frequency data - pre-averaging method and improved pre-averaging method. Such methods can well eliminate the effects of market microstructure noises on the estimation of volatility of high-frequency financial data. Although pre-averaging method can eliminate the effects of market microstructure noises on the estimation of volatility, it cannot handle the effects of jumps on the volatility. Then how to estimate the volatility of high-frequency data under the existence of both market microstructure noises and jumps? To this end, this chapter proposes a new estimator - Threshold Pre-averaging Realized Volatility (TPRV). This estimator combines the pre-averaging method and the threshold thinking method. The pre-averaging method is to reduce the impact of market microstructure noises and the threshold thinking method is to tackle the effects of jumps on estimation of volatility. But through the analysis of features of TPRV, it is found that this estimator is not the consistent estimator of IV. Thus TPRV should be modified and result is MTPRV. This chapter shows the limit theory of MTPRV, proves that MTPRV is the consistent estimator of IV, and presents the limit distribution of the estimator.Chapter four is mainly to use simulation data to verify features of MTPRV. Based respectively on constant volatility model and stochastic volatility model and under different sample sizes, simulation data with noises and jumps are generated in this chapter. And volatility of those data is estimated by MTPRV, through which features of MTPRV are analyzed. In this chapter, window width and selection method of threshold function in the estimator of MTPRV are given. Through simulation it is found that MTPRV can estimate IV effectively and that compared with other estimators of IV, estimation effect of MTPRV is optimal.Empirical analysis of volatility of high-frequency data in China's stock market is carried out in chapter five by means of MTPRV. Five-minute time-share data and tick-by-tick data of ultra-high frequency are randomly selected from five stocks as the study objects. Estimation of volatility of high-frequency data from the five stocks are conducted by means of MTPRV, and volatility caused by microstructure noises and jumps is abstracted from RV. In order to evaluate the MTPRV estimator, day, week, and month in RV are regressed by HAR-RV-CJ model. Regression results show that HAR-RV-CJ model based on MTPRV has a better fit than that based on other estimators of IV, which means that MTPRV method can better abstract microstructure noises and jumps from RV and can achieve better estimate of IV.Chapter six is about the risk measure based on MTPRV method. Value at Risk method is a mainstream financial risk management method, which has become the leading financial risk management method in the world's major corporations, banks and various financial institutions. VaR is calculated and tested based on MTPRV method and is compared with that of other estimators based on IV.Chapter seven is the conclusion and outlook of this dissertation. Research work of this dissertation is summarized in this chapter and future research directions and fields are pointed out.Innovation of this dissertation can be summarized as follows:(1) A new volatility estimator of high-frequency data is proposed, namely MTPRV.With the deepening research of the volatility of high frequency data, the impact of market microstructure noises and jumps on the estimation of volatility has become the unavoidable problem. Researchers have proposed many methods to eliminate market microstructure noises and jumps. However, these methods emphasized different aspects and only considered how to eliminate the market microstructure noises or jumps. While few literatures have studied how to estimate the volatility of high-frequency data under the condition of both market microstructure noises and jumps. A new volatility estimator of high-frequency data is proposed, namely MTPB. The estimator can not only smooth the impact of market microstructure noises on the volatility estimation of high-frequency data, but remove the volatility caused by jumps. Additionally, features of MTPRV are also discussed in this dissertation and MTPRV is proved to be the consistent estimator of IV which can achieve optimal convergence rate. Limit distribution of this estimator is also given in the dissertation.(2) MTPRV is tested to be of excellent feature through the simulation data and real China's stock high-frequency data.This dissertation uses a numerical approximation method and empirical data analysis to verify the applicability and good nature of MTPRV. Analysis of both the simulation data and the real data show that regarding the volatility estimation of high-frequency data, MTPRV is superior to the other estimators of IV To better smooth the effect of market microstructure noises on the volatility estimation, this research presents the selection of optimal window width in MTPRV, namely minimum MSE numerical approximation. To handle effects of jumps on volatility, conditions that threshold function should meet in MTPRV as well as the specific expression are presented in this dissertation.(3) MTPRV is applied to the estimation and test of VaR.MTPRV and non-parametric kernel density estimation method is combined in this dissertation, volatility of China's stock high-frequency data is estimated by MTPRV, distribution of financial returns on asset is obtained by kernel density estimation method, and VaR of China's stock high-frequency data is estimated and tested. Through the analysis of and comparison with other estimators based on IV in VaR, MTPRV can better estimate VaR and thus can undertake more effective risk management.