Application Of Copula Theory In Financial Dependence Risk

With the development of economic globalization and financial integration,various financial markets and financial industries present a diversified and complex structure,which makes their relations closer and more complicated.It is of theoretical and practical significance for scientific market risk assessment and accurate financial decision-making to accurately characterize the risk dependence structure and correlation among financial variables.At present,the mature Copula theory can well describe risk dependence of financial variables.Therefore,from part to whole,this paper uses Copula model to study risk dependence among 14 representative financial institutions,four sub-sectors of China's finance and the stock markets of five major economic powers in the world.Firstly,the relevant preliminary knowledge of this paper is sorted out,including the basic theory of Copula and hidden markov model.The definition and properties of Copula function are introduced,common Copula function,estimation method and tail risk measure are elaborated,and optimal Copula selection method is summarized,the hidden markov model is also introduced.Secondly,14 representative institutions in banking and insurance industry are selected,the marginal distribution is fitted by parameter estimation and non-parametric estimation respectively,and the distribution function with better fitting is selected.Hierarchical Archimedean Copula model is constructed for uniform variables,and optimal Copula function is selected according to the PP graph,so as to obtain hierarchical structure and dependent strength between industries.The conclusions are as follows: Firstly,insurance industry,large commercial banks and joint-stock commercial banks are clustered separately and have obvious hierarchical dependence structure.Secondly,the dependence of insurance industry is higher than that of banking,the dependence of large commercial banks is generally higher than that of joint-stock commercial banks.Thirdly,the correlation between ICBC and CCB is the highest among large commercial banks,and their relationship with Bank of Communications is the weakest;Industrial Bank and Shanghai Pudong Development Bank have the highest dependence among joint-stock commercial Banks and the weakest dependence with China Citic Bank.Ping An Insurance and China Pacific Insurance have the highest dependence in insurance industry,and they are relatively weak with life insurance.Generally speaking,insurance industries and banking are highly dependent and closely connected.When financial extreme events occur,banking and insurance are vulnerable to the impact of each other's risks.Thirdly,based on mixed Copula model,Hidden Markov Model(HMM)is introduced to construct dynamic mixed Copula model.The transformed uniform variables are brought into three kinds of single Copula,mixed Copula and HMM mixed Copula model to obtain dependence and dynamic transformation path among the four sub-industries of finance,and tail risks among the four sub-industries are analyzed by using HMM mixed Copula model.The results show that HMM mixed Copula model can better present dynamic dependence state and dynamic transition path between financial industries.In the high dependency state,financial sub-industries have stronger dependence and the probability of risk contagion is larger,from the perspective of dependence and contagion,it may lead to macro or systemic risks.In the high state,the tail risk of financial sub-industries is larger than low state,the tail dependence between banking and insurance is the strongest in both states,while the tail risk between trust industry and other three industries is relatively weak.Finally,the non-parametric kernel density estimation is used to fit the marginal distribution,and Hierarchical Archimedean Copula model is nested in the Hidden Markov framework to construct a high-dimensional HMM Hierarchical Copula model,and to analyze hierarchical structure and dynamic risk dependence of the world's five major stock markets during and after the crisis.The results show that five countries' stock markets have tail risks,and the two-stage hierarchical structure is the same,but the intensity is different.They forms 4 layers fully Nested Archimedean Copula structure,layered step by step,in which the British and German stock markets are at the first level,the U.S stock market is located in the second level,and Japan's stock market is located in the third level,China's stock market is located in the fourth level,and the degree of dependence decreases with the increase of the level,that is,the risk dependence between the British and German stock markets are the strongest,followed by American stock market and Japan's stock market,and the correlation between China's stock market and them is the smallest.Compared with the two stages,the correlation between the stock markets is strong,although the risk-dependent intensity between stock markets after the crisis is lower than that in the crisis period,it still maintained a high level.