关键词: 高维波动率网络模型, 互信息, 已实现波动率, 金融风险管理

Abstract: Volatility is crucial in financial risk management research. This paper proposes a high-dimensional volatility network model for the stock market based on complex network theory and data mining technology. Firstly, the theory of mutual information is utilized to measure the correlation of stock price fluctuations. Secondly, we design the network topological indicators such as the degree centralization, average distance and power law distribution for different periods of the stock market. With these indicators, the Prim algorithm and the Newman-Girvan algorithm are used to construct the highdimensional volatility network models and stratify the correlation of the volatility respectively. Compared with the conventional models, our new model can overcome the difficulties of high dimensional settings, explore the relationship among different financial market entities, and reflect the risk features and network topology of financial markets based on just a few hypotheses. The empirical results demonstrate that in contrast to Pearson correlation coefficient, the mutual information is a better measure for the nonlinear correlations of stock price volatility. The market volatility and price volatility correlation move in opposite directions, and the portfolio decentralization effect is more obvious in the period of high market volatility. The effects of industry agglomeration are significant. There exist a small number of key nodes and central nodes in the network, and the risk quickly spreads to the entire market through these nodes. The network stratification further shows the characteristics of risk transmission between layers and corresponding industrial characteristics. The high-dimensional volatility network model provides a novel tool for exploring the risk features in stock market and managing financial risks.

Key words: High-Dimensional Volatility Network Model, Mutual Information, Realized Volatility, Financial Risk Management