Analysis of global stock index data during crisis period via complex network approach

Abstract

Considerable research has been done on the complex stock market, however, there is very little systematic work on the impact of crisis on global stock markets. For filling in these gaps, we propose a complex network method, which analyzes the effects of the 2008 global financial crisis on global main stock index from 2005 to 2010. Firstly, we construct three weighted networks. The physics-derived technique of minimum spanning tree is utilized to investigate the networks of three stages. Regional clustering is found in each network. Secondly, we construct three average threshold networks and find the small-world property in the network before and during the crisis. Finally, the dynamical change of the network community structure is deeply analyzed with different threshold. The result indicates that for large thresholds, the network before and after the crisis has a significant community structure. Though this analysis, it would be helpful to investors for making decisions regarding their portfolios or to regulators for monitoring the key nodes to ensure the overall stability of the global stock market.

Fig 1. Volatility of the global representative stock index: 2005–2010.

The volatility of the global representative stock index from the year 2005 to 2010. They are FTSE Europe Pioneer 300 Index, Shanghai Composite Index, FTSE Straits Times Index, S & P 500 index, European Stoxx 600 index and Dow Jones Industrial Average index.

Fig 2. Correlation coefficient matrix before the crisis.

This is the correlation coefficient matrix before the crisis. This is corresponding to data in S3 File. The vertical axis and the horizontal axis all represent the 38 stock indexes. The redder the color of the block area, the greater the correlation coefficient. The bluer the color of the block area is, the smaller the correlation coefficient is.

Fig 3. Correlation coefficient matrix during the crisis.

This is the correlation coefficient matrix during the crisis. This is corresponding to data in S3 File. The vertical axis and the horizontal axis all represent the 38 stock indexes. The redder the color of the block area, the greater the correlation coefficient. The bluer the color of the block area is, the smaller the correlation coefficient is.

Fig 4. Correlation coefficient matrix after the crisis.

This is the correlation coefficient matrix after the crisis. This is corresponding to data in S3 File. The vertical axis and the horizontal axis all represent the 38 stock indexes. The redder the color of the block area, the greater the correlation coefficient. The bluer the color of the block area is, the smaller the correlation coefficient is.

Fig 5. Minimum spanning tree of network before the crisis.

The network before the crisis is divided into three areas of aggregation. They are American stock market, Asia Pacific& Australia stock market and European stock market. The lighter the color of the node is, the greater the degree of the node is. In addition, the thicker the edge is, the greater the weight is in the figure.

Fig 6. Minimum spanning tree of network during the crisis.

The network during the crisis is divided into three areas of aggregation. They are American stock market, Asia Pacific& Australia stock market and European stock market. The lighter the color of the node is, the greater the degree of the node is. In addition, the thicker the edge is, the greater the weight is in the figure.

Fig 7. Minimum spanning tree of network after the crisis.

The network after the crisis is divided into three areas of aggregation. They are American stock market, Asia Pacific& Australia stock market and European stock market. The lighter the color of the node is, the greater the degree of the node is. In addition, the thicker the edge is, the greater the weight is in the figure.

Fig 8. The influence of the threshold on the modularity Q.

This is the modularity variation curve of the network in three different periods under different threshold conditions. The values greater than about 0.3 appear to indicate significant community structure.

Fig 9. Hierarchical clustering structure before the crisis.

This is the hierarchical clustering structure before the crisis. The horizontal axis represents the stock index, while the vertical axis represents the distance between these indices. The network could be divided into four communities whose member is shown in purple, red, green and black line.

Fig 10. Hierarchical clustering structure after the crisis.

This is the hierarchical clustering structure after the crisis. The horizontal axis represents the stock index, while the vertical axis represents the distance between these indices. The network could be divided into four communities whose member is shown in purple, red, green and black line.