Measuring Systemic Risk With Time-Varying Factor Copula

The subprime crisis in 2007-2009 which originated in the United States has push US into great depression since 1930s. It was the most serious economic recession that hit the world financial system, including Iceland, Greece and other countries on the brink of national bankruptcy. The total financial sector writedowns from the US subprime crisis caused will reach $1,405 trillion, according to current statistics by IMF. The above phenomenon shows that it is necessary to analyze the financial risk from the perspective of overflow from extreme risk.Another lesson from subprime crisis is that the collapse of systemically important financial institutions will lead to "negative externalities". Its collapse would cause huge spillover effects of extreme risk to the entire financial system or the real economy because of its huge and widely associated with other agencies. Lehman Brothers collapsed triggered one after another collapse in the financial crisis and other financial institutions which caused the loss of systemic risk so that the "too big to fail" and "too important to fail", so it becomes a Wall Street consensus. The importance of the regulatory system of financial institutions have become one of the central issues of the post-crisis era financial regulation, and identify critical systemic importance of financial institutions and systemic risk measurement model is timely and accurately portray the financial institutions dependencies between assets returns.The root of the subprime crisis is the major US financial institutions overpriced CDO and other asset securitization products, which is grossly underestimated due to the overpricing of its assets to support the rear of each component dependencies between assets in the pool relationships. CDO Pricing model is called "formula that killed Wall Street." So the theorists and business community attach great importance to the financial dependence modeling. It is the hot and difficult problems of risk management, portfolio and asset pricing in current fields.The main challenges of the financial institutions systemic risk measurement is in complex interdependencies, time-varying dependence and high dimensional dependence. Complex dependence refers to financial institutions return on assets, such as between the tail dependence, nonlinear dependence and asymmetrical dependence. Time-Varying dependence refers to the relationship between the assets iss time-varying, and many studies show that the dependence in financial crisis was stronger than usual period. High dimensional dependence refers to It is necessary to analyze the dependence of large financial institutions when measuring systemic risk, and the key to model high dimension financial time series is high dimensional dependence.There are many methods to measure financial systemic risk, but these methods exist can not overcome three challenges, which is complex dependence, time-varying dependence, and high dimensional dependence. The first method is multivariate ARMA-GARCH, the typical model such as Acharya, Engle and Richardson use DCC-GARCH model to describe the relationship between the financial asset returns. This theory system is relatively mature, and the model is relatively simple, but the covariance matrix can only be used to describe the elliptical distribution, which can not describe the complex dependence, although it can also describe the time dependence relationship and the high dimensional dependence relationship. So it is insufficient to decrible the tail dependence^ the sharp rise and sharp fall phenomenon. The second method is time varying Copula method, which can overcome the disadvantages of the ARMA-GARCH simple linear dependence relationship effectively. The typical methods of Copula include Patton、Bartram、Rodriguez etc.. These time-varying Copula method can be directly used to model the dependence relationship among the financial institution’s asset returns. But at present, the majority of the system measurement based on the time varying Copula method is the two-dimensional. Because of the small number of candidates、the number of parameters and the complexity of computation, the second methods are still the major defects in the field of systematic risk measurement. That is, the time-varying Copula methods have the complexity and time-varying dependence except the high dimensional dependence.The third method is the factor Copula method in this paper. Factor technology has been widely used in the modeling of high dimensional dependence, such as the estimation of the super large covariance matrix、 multivariate financial time series factor technology for the high dimensional GARCH modeling and the formation factor GARCH model. This method assumes that the implicit variables used in the characterization of dependence relationships can be decomposed into the systematic factors that obey the skew t distribution and the special factors obey the t distribution. The advantage of this method is that it has three properties of the system risk measurement model, which describes the complex dependence, time-varying dependence and high dimensional dependence.In the paper, the third kinds of Copula methods are used to describe the stock returns of listed financial institutions in China. The tail contagious shows that systemic event will push systemic risk higher; MES has a decreasing tendency after the crisis, while capital shortfall has an evdent raising tendency because of the stable increasing of financial leverages. This study also shows that the major resource of possible capital shortfall is the bank industry, which means that the bank industry should be the key of financial stability supervision.