基于高维波动率网络模型的股票市场风险特征研究

Research on Stock Market Risk Features Based on High-Dimensional Volatility Network Model

波动率是金融风险管理研究的重要内容之一.本文基于复杂网络理论和数据挖掘技术提出股票市场的高维波动率网络模型.首先运用互信息度量不同股票价格波动之间的相关关系,其次对股票市场不同周期下的波动情况建立度的中心势、平均距离、幂律分布等网络拓扑指标,再次根据这些指标利用Prim算法构建出高维波动率网络模型,最后运用Newman-Girvan算法对股票价格波动率的相关性进行分层研究.高维波动率网络模型突破了传统波动率模型关于变量维数的限制,能够在依赖少量假设的基础上,挖掘出多个金融市场主体间的相互关系,反映金融市场的风险特征及网络拓扑性质.实证结果发现:与常用的Pearson相关系数法相比,在互信息框架下,股价波动的非线性相关关系得到了更好的度量;股票市场的整体波动性与个股波动率相关性变化趋势相反,市场处在高波动时期资产组合分散化效果较好;网络中存在少量度数大的关键节点和中心节点,风险通过这些节点可以迅速传递到整个市场;股票市场的运行具有明显的行业聚集现象;网络分层研究进一步直观的展现了风险在层与层之间的传递规律和与之对应的行业特征.高维波动率网络模型为挖掘股票市场的风险特征与管理金融风险提供了一个新的工具.

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.