Financial Volatility Models And Their Application In Chinese Stock Markets

Avoiding financial risk is always the main subject of investment theories and practice. Since Markwitz put forward mean-variance model in 1952, research on financial risk and other related issues have begun to depend on mathematical methods and all kinds of mathematical models and theories have come into being, the most famous ones of which are Efficient Market Hypothesis (EMH), Portfolio Theory, Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), Option Pricing Equation and Capital Structure Theory and all of them except EMH and Capital Structure Theory are associated with volatility, which is the theory background of this dissertation. The empirical backgrounds of this dissertation are the volatility characters in financial markets. A large body of research suggests that volatility in financial market is time varying; that is to say, volatility is not constant but varying with time. In order to describe the time varying of volatility, two classes models?autoregressive conditional heteroskedasitic (ARCH) model and stochastic volatility (SV) model, were proposed. The main research objects of this dissertation are stochastic volatility modeling, estimating and their applications in Chinese stock markets. Based on reading document widely, we summarize the development of stochastic volatility modeling from viewpoint of how to unite discrete data and continuous models. After introducing the related notation and terminology, we discuss stochastic autoregressive volatility (SARV) model, which encompasses various representations of stochastic volatility model already available in the literature, where after we research the discrete time stochastic volatility modeling in detail, extensions of SV model are also given. The applications of the models are necessarily involved in their estimation; people have constructed many estimation methods of SV model, the simplest one is quasi-maximum likelihood (QML) estimation and it is inevitable to face with the optimization of the functions when using QML to estimate SV model. The likelihood of SV model can't be differentiated, so we must use free derivative methods to maximize it, but the results of the classical optimization methods highly depend on the choice of initial point and many problems often appear when implementing them. Therefore, we put forward a new method?TSGA-QML (quasi-maximum likelihood based on tabu search genetic algorithm), Monte Carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates. We also illustrate the method by analyzing daily returns of index, stocks and portfolios on Shanghai Stock Exchange and find that their volatility displays high persistence while traditional portfolio can't avoid the persistence. Persistence in volatility can be characterized by (near) unit root and long memory. We study the persistence from the former viewpoint in chapter 4; that is to say, we test for a unit root in volatility process. After presenting the usual unit root test methods, chapter 4 discusses unit root test for SV model and analyzes persistence in volatility for the daily stock returns on Shanghai Stock Exchange; we obtain that the unit root hypothesis are all rejected for the series we study, which suggests that they don't satisfy the definition of persistence in volatility of Li and Zhang (2000). Meanwhile, this dissertation considers persistence in volatility from viewpoint of long memory. In chapter 5, based on introducing the concepts, theories, models with respect to long memory, we research the statistical characters, volatility proxies, the relation with ARFIMA model and temporal aggregation of long memory stochastic volatility (LMSV) model, we also analyze the finite properties of QML estimators based on TSGA of LMSV model. Finally, empirical analysis on long memory of Shanghai Stock Exchange is conducted with the related theories and methods. In order to describe the relationship on volatility among different financial markets, chapter 6 extends univariate LMSV model to the multivariate one and gives its spectral-likelihood estimator, the test procedure for fractional cointegration is also developed under multivariate LMSV model. Finally, we apply the model and method to analyze daily returns of Shanghai Composite Index and Shenzhen Component Index and find their volatilities are fractional cointegrated. Chapter 7 provides a Bayesian detecting method for structural change in volatility and construct evident test with stock returns in Shanghai stock market, based on which we introduce structural change into SV model and LMSV model. Empirical evidence and Monte Carlo simulation confirm that the persistence parameter of SV model is very sensitive to structural change in volatility while memory parameter of LMSV model is also quite sensitive to it. In the end, this dissertation provides a selective summary of the most important developments in the field of financial econometrics in the past two decades, along with a discussion of promising avenues for future research. The contents of this dissertation are the components of National Natural Science Fund Persistence in Volatility of Multivariate Time Series and Its Applications in Financial System (No: 70171001).