Research On Global Stock Market Linkage And Systematic Financial Risk Based On Topological Structures

In recent years,the process of global economic integration is accelerating,and the homogeneity and linkage of financial markets,especially stock markets,are strengthening.Since the 21st century,there have been many major financial turmoil in the world,including the financial risks caused by the US subprime mortgage crisis in2007-2008,the European debt crisis in 2010-2011,and the stock market crash in2015-2016,all of which were caused by risks within the financial system.COVID-19which broke out at the end of 2019,is a risk from outside the system and has a great impact on the international financial market.Michelle Walker,the proponent of“Grey Rhino”,said that the COVID-19 pneumonia epidemic is a recurring“grey rhinoceros”,which is a high probability risk event that is often prompted but not fully valued.COVID-19’s outbreak scope and scale are larger than SARS.And compared with the financial crisis in 2008,it has a faster and deeper impact on the market,which is still spreading today.The financial crisis will bring devastating damage to the economy and society.Therefore,it is of great practical significance to study the linkage of stock market and systematic financial risks.This paper mainly studies the linkage of global stock markets during several financial crises or risks since 2001,and focuses on COVID-19 period.First of all,this paper introduces the research background and significance,combs the relevant literatures at home and abroad from three aspects:the early warning research of systemic financial risks or financial crises based on traditional methods,the research of stock market linkage and systemic financial risks based on complex networks,and the application of topological data analysis in the financial field.And it relates and analyzes the research methods,thinking and innovations.Secondly,it introduces the basic theory of stock market linkage and systemic financial risk,as well as the theoretical basis and methods of topological data analysis and complex network.Thirdly,45 countries/districts are selected globally,and one index is extracted from each country/district.Based on the daily logarithmic return rate,the correlation coefficient and distance between every two indices are calculated by sliding window method.Fourthly,based on persistent homology,the complex of the distance between45 stock indices is constructed under the sliding window.And the topological data analysis is carried out by persistent landscapes,showing the daily changes of the complex,and their L~p-norm.Then,a key date detection system based on persistent landscapes is established,and the robustness of the system is verified by constructing subgroups.Finally,based on the key date detected,threshold networks and minimum spanning trees are constructed respectively,and the related topological features are displayed and compared with those of the complex network before the key date and the validity of the key date detection system is verified.According to the empirical results,this paper makes conclusions as follows.Firstly,among the above financial turmoil events have triggered systemic financial risks in global stock markets.According to the comprehensive topological measures,these systemic financial risks by the severity of them from high to low are respectively in 2020,2008,2011 and 2015 according to years.Secondly,before and after the financial crisis,the correlation among global stock indices became closer.The connection among stock indices from late February to March in 2020 was also obviously closer than ever before,when COVID-19 was spreading all over the world.Thirdly,different stock markets usually have different contact forms.During the crisis transition period,the indices became“closely connected”from“normal connected”among the developed countries.The emerging countries are more affected by crises.Their indices have fewer connections with other indices in the normal period.But when a crisis came,they became to track fast the indices of the developed countries,and thus they have closer contact with other stock markets.Fourthly,there is obvious geographical agglomeration phenomenon among global main stock indices.Stock indices belonging to the same region have strong linkage.Stock indices in European countries have closer and more stable connections than those in other regions,and they are the bridge of stock indices in all countries in the world.By studying the risk transmission mechanism,the important nodes of the system are found,which is of great help to study the linkage of the stock market and provides guidance for preventing and defusing systemic financial risks.