| In order to help financial market participants who hold the concept of index investment to deeply understand the regular patterns of volatility spillover of daily log returns of A shares'main sector indices and to give them references for carrying out risk measurement of sector indices investment, by using the time-varying correlation bivariate GARCH(1,1) model based on Cholesky decomposition, we conduct a comprehensive and detailed study of the characteristics of volatility spillover among daily log return rates of the four A shares'main sector indices: the coal and oil, the banking, the real estate, and the power, and furthermore, we use the established volatility models to calculate the daily VaR of a financial position which contains a certain amount of two sector indices respectively.In accordance with the different contents, this paper is divided into five sections: chapter one is the introduction, chapter two is the review of domestic and overseas literature on multivariate volatility study, chapter three is the statement about the basic theories , models and methods, chapter four is about the empirical study of multivariate volatility spillover, chapter five is the conclusions.In chapter one, firstly, the introduction gives the background to the thesis, and points out that this study has great significance because of the rise of the concept of index investment, the research results of multivariate GARCH models, and the important role in the decision-making of optimal asset allocation and in the investment risk measurement. Secondly, this section also tells the framework of the empirical study, and states the objects, methods and purposes of this research.In chapter two, the domestic and overseas literature review part mainly gives a detailed report on the three kinds of foreign literature related to multivariate volatility study: the foundation-laid literature, the knowledge-integrated and model-improved literature, and the latest representative literature, and briefly introduces several domestic representative dissertations on this subject, to help readers to understand the history, the research status and the development direction of the multivariate volatility study. The development trend of the multivariate volatility study is summarized from the aspect of the theoretical method and the aspect of the application at last.In chapter three, the paper is about the basic theories, models and methods. This section firstly makes clear the basic concepts involved in the empirical process: asset logarithm return rate and its mean and volatility equation are defined, weakly stationary, cross-correlation matrices and the sample cross-correlation matrices are explained; secondly, the time-varying correlation multivariate GARCH modeling method based on Cholesky decomposition, and the principle of multivariate portmanteau tests are also introduced; thirdly, detailed definition of VaR under a probabilistic framework and the VaR calculation method under Risk-Metrics are stated.In chapter four, the section of the empirical study of sector indices'multivariate volatility has three components:In the component of sector indices description, firstly, related to the sector indices, the base period, the calculation formula, the sample space, the rules of the adjustment of the constituent stocks, and the index correction method and the situations needing to amend the index are explained, and the specific circumstances of the four indices involved are detailed; secondly, the data-processing means in the empirical process are introduced, the statistics list, the trend charts and the return rate charts of the sector indices are given, and about the smooth features, it is pointed out that there is an obvious phenomenon of volatility clustering in the index return rate series, and that volatility does not diverge to infinity.In the component of the empirical research of multivariate volatility spillover, the four indices are divided into six groups. Then firstly, a comprehensive use of the scatter charts, the calculation of cross-correlation matrices, ACF and cross correlation function charts, and the Ljung-Box statistics is made to detailedly describe the correlation among the series, and it is pointed out that the correlation does exist; secondly, the time-varying correlation bivariate GARCH(1,1) models of series in the six groups based on Cholesky decomposition are obtained by programming, and the test results of each model are detailedly explained; finally, based on the previous study, the state of volatility spillover between series of each group is comprehensively analysed from the aspect of volatilities correlation, the aspect of the characteristics of volatility trend fitted by the respective model, and the aspect of the characteristics of the relationship between series'volatility and time-varying correlation, and many meaningful conclusions are drawn.In the component of the empirical research of the VaR of the sector index investment, the previously established volatility models are applied to calculating the VaR of a financial position containing a number of assets, the daily VaR of the financial position is computed, which contains 100,000 yuan RMB assets of the coal and oil sector index and the banking sector index respectively, and it is compared with the results obtained by the other two models.In the section of the conclusion, first of all, the correlation among volatilities of the four daily log returns of A shares'main sector indices are illustrated, especially it is pointed out that the daily log return rate of the coal and oil sector index does not depend on the daily log return rates of the banking, real estate, and power indices, but besides mainly relying on their own in the past and the shock term of returns, the volatilities of daily log return rates of the banking, real estate, and power indices do also rely partly on volatility and the shock term of the daily log return rate of the coal and oil sector index.; secondly, the specific volatility trends of series of each group are described, and the time when the volatility trends change significantly and the rules of volatility synchronous changes in series of every group are also pointed out; Thirdly, it is showed that show that the correlation coefficient between two return series increases when the returns increases, and this is not in agreement with the empirical study of relationships between international stock market indices, and this means that Chinese stock market has its own characteristics which are different from the foreign mature markets and that it is incorrect to mechanically imitate the foreign experience while investing in the A shares market; finally the VaR calculating methods under Risk-Metrics by using the previously established time-varying multivariate volatility models are summarized.The novelty of this paper lies in the following fact: first of all, the four daily log return series of A shares'main sector indices , which are the coal and oil, banking, real estate, and power sector indices, are divided into six groups on combination principle, and the time-varying correlation bivariate GARCH(1,1) models of each group of the series based on Cholesky decomposition are built respectively, so the state of volatility spillover among the four series is comprehensively and detailedly analysed; and secondly, using the previously established time-varying multivariate volatility models, the daily VaR under Risk-Metrics of the long position containing two indices is calculated, and the result is compared with the daily VaRs obtained by the univariate GARCH model and the constant-correlation bivariate GARCH model, so a example for reference is established for market participants who are carrying out risk measurement of sector indices investment. In addition, there are many other meaningful places about this subject worth exploring, for example, to manage to find more effective programming methods to obtain more accurate models, to look for more simple and practical methods to build trivariate and four-variate volatility models based on Cholesky decomposition. |
