Research On The Risk Of Chinese Stock Market Based On Extreme Value Theory

In this paper,we discuss the risk measurement of single stock market from the univariate extreme value theory as well as the extreme correlation between two markets from the multivariate extreme value theory.In the first part,we give the risk measurement of single stock market based on uni-variate extreme value theory.Firstly,we obtain Value at Risk(VaR)and Conditional Tail Expection(CTE)of a sequence of independent identical distribution random variablee by BMM method and POT model,Secondly,we discuss the risk measure of stationary random sequence based on relatively weak condition.Under a condition of D(un),we cal-culate the risk measure which is comprised of VaR and CTE by introducing the extremal index as well as improving the BMM method and POT model.In empirical research,we take the sequence of Shanghai Stock Index within ten years as our training sample while the next period of 10 months of the sequence of Shanghai Stock Index is selected as our test sample for testing the risk measurement according to the feature of the sequence itself.The result shows that,most of the financial sequences do not satisfy the condition of independent identical distribution(i·i·d),thus they need to be improved by intro-ducing the extreme index.Compared with the extreme value model under the condition of i·i·d,the extremal index makes It more accurate when estimating the VaR.The object of the second part is the measurement of the eorrelation of the extreme loss in two markets from three points of views,Firstly,we discuss the definition of consistency and some correlation coefficient,and give the the integral transformation expression betwem Copula function and specific correlation coefficient.Secondly,we get the bivariate extreme value Copula function based on Pickands fuaction.Furthermore,we obtain the reverse solution of correlation function between Extreme Copula and Pickands function.After exploring the relationship with the Tail dependence eoefficient(TDC),we get the expression of various TDC of Extreme Copula related to Pickands function.Finally,we put up with a nonparametric method which is gived by the likelihood function according to the definition of TDC.In empirical research,we take the Extreme Loss within ten years from Shanghai Stock Index and Shenzhen Stock Index as our target.By fitting various type of Copula,we select the best suitable Gopula model and calculate the common correlation coefficient and TDC according to the three methods mentioned above.The resultsshow that,there exists obvious eorrelation between the Extreme Loss of stock markets of Shanghai and Shenzhen.