Crisis Spreading Model of the Shareholding Networks of Listed Companies and Their Main Holders and Their Controllability

Bankruptcy of listed companies or shareholders delisting usually causes the crisis spreading in stock markets. Based on the systematic analysis of the epidemic diseases and rumors spreading on the complex networks, the SIR model is introduced to research the crisis spreading in shareholding networks of listed companies and their main holders on the basis of the data about ownership structure in Chinese Stock Markets. The characteristics of shareholding networks are studied, and the parameters for the SIR model are obtained by empirical approach. Then, the numerical computation method is successfully used to analyze the crisis spreading in the networks when the networks meet random failures or intentional attacks. We find the networks have good robustness against the random failures. However, the crisis will spread at a high speed and cause catastrophic damage if there are some failures or attacks on hub vertices in the networks. Under this condition, the networks show obvious vulnerability. Last but not least, the controllability of the networks under the condition of intentional attacks and random failures is studied. The results show that if the network is controlled globally, it is more reliable to allow a politically good new or an appropriate exciting economical policy to play the role in orienting markets under the control of public opinions as the crisis occurs. However, under normal circumstances, controlling a small part of driver vertices representing listed companies, applying appropriate control strategies, and using its characteristics of high efficiency of sending information can effectively control the stock market. Our research provides a new reference to further exploration about the transmission mechanism of the crisis based SIR model and further research on the controllability of crisis spreading in financial markets.