Study Of Parameter Estimation And Prediction Of Volatility In Financial Market

Volatility represents the uncertainty of asset price change. It plays an important role in asset pricing, portfolio, risk management and asset allocation. Following the coming period of economic and financial globalization, we further deepen the reform and opening up in China. Market transactions are more active, while investing and financing are more free and frequent as well. How to forecast the reasonable volatility and estimate the parameter of volatility model have become a hot topic in academe and industry in the past thirty years. The start of Chinese financial market was late, and it exhibited certain patterns like high risk and high volatile. Com-paring with the well-studied volatility abroad, our domestic research still has a long way to go. The current topic, which is the study of parameter estimation and prediction of volatility in fi-nancial market, has crucial theoretical and practical significance for it reveals the patterns and mechanism of volatility, and also helps risk diversification and reasonable asset allocationThe stylized facts of volatility in financial market that we have found include fat tail, lever-age effect, co-movements in volatility, long memory and volatility clustering. The features differ from each other for different market and countries. Taking into account the comprehen-sive features of volatility, we study the three types of volatility models which are stochastic volatility, realized volatility and multivariate GARCH models. The estimation of the unknown parameters is stated in this thesis in the framework of continuous time, and the prediction of realized volatility and historical volatility is studied as well in this thesis. We also give some empirical results about the features of volatility and the prediction in U.S.stock market, Chinese stock market and RMB exchange market respectively. The main results and innovations in this thesis are listed as follows:First, this thesis obtains the parameter estimation of long-memory stochastic volatility in continuous time and their asymptotic properties as well.Since the volatility exhibits long memory in continuous time, we usually use the fraction-al Brownian motion as the driving source in volatility process. As the volatility process can not be observed directly nor the fractional Brownian motion presents Markov property, we fin-ish the work in two ways. Firstly, we give both the parameter estimators for drift and diffusion through variogram method using discrete observations when the Hurst parameter is known. Fur- thermore, we prove the consistency and the asymptotic normality of the variogram estimators. Numerical examples are also presented to illustrate the performance of this method. Secondly, a two-steps estimation procedure that could estimate all Hurst index, diffusion coefficient and drift parameter in volatility process is presented in this thesis. The consistency as well as the central limit theorems are also provided by applying Malliavin calculus. We apply our method to Chinese stock market and find that there exists long memory in Chinese stock market.Second, this thesis performs the out-of-sample prediction under the assumption of market microstructure noise.The high-frequency observations of transaction price arise one problem, i.e., the presence of market microstructure noise. Using all the high-frequency data leads to the biased estimation of integrated volatility, whereas the two-time scale realized volatility is a good way to correct it. This thesis adopts seven different time scales and applies them to five volatility models for Monte-Carlo simulation. Each sample path covers 100 days or 200 days, and each interval be-tween two observations is 1 second. We propose autoregressive models, including AR(1) model, AR(p)model,ARIMA(p,d,q) model, MIDAS model and HAR model for the 1-step,3-steps and 5-steps forward prediction. With different loss functions, the forecasting results show that the two-time scale realized volatility is a good estimation of integrated volatility. Autoregressive models are reasonable in prediction and HAR model performs the best prediction accuracy a-mong them. Moreover, the empirical work about high-frequency Dow Jones industrial average index indicates the long memory, non-structure change and intraday effect in U.S. stock mar-ket. We also test the simulation results in empirical work. The empirical results consist with our simulation results and HAR model performs the best in prediction through 1000 bootstraps simulation and SPA test.Third, with the help of independent components analysis, this thesis forecasts multivariate time series.In order to overcome the curse of dimensionality and the heavy training burden, we conduct FastICA algorithm to extract the independent components, which makes it possible to forecast the multivariate RMB exchange rate. This thesis presents two parts of this work. Firstly, the complete multivariate volatility forecasting model is put forward by combining the transfor-mation matrix and GARCH models for independent components. Considering the asymmetric property and fat tail of volatility, we make further extensions including IC-GJRGARCH model, IC-IGARCH model, generalized error distribution, student-t distribution and dimensionality re-duction. Secondly, as a front system, independent components analysis is designed to integrate a BP network. Then we perform the forward prediction by identifying the optimal lag periods and activation function. Empirical test based on RMB exchange market indicates there exists co-movement, asymmetric and fat tail in volatility. Empirical forecasting results which adapt the RMB exchange rate data show that ICA reduces the number of unknown parameter and the computational burden. It has good prediction accuracy.