Semiparametric Extreme Value Model And Bayesian Method For Stock Market Risk

The risk of the securities market has always been concerned by the academic and practical departments.The risks and volatility of the securities market are closely related.The instability of the securities market volatility makes the financing,pricing and allocation functions of the securities market unable to fully play its role.Therefore,the research and analysis of the volatility of the securities market has important application value.The volatility of stock prices is the most direct interpretation of the volatility of the securities market,through which researchers can grasp the overall state of the market.In many fields of application,extreme theory has proven to be a very practical tool.The GPD distribution in extreme value theory can well fit the tail behavior in financial data.The tail parameters in the GPD distribution have a good explanation of risk to the securities market.This paper considers the estimation of the tail parameters in the extreme value theory.Based on the extreme value theory,a semi-parametric extreme model is constructed,that is,a non-parametric mixed Gamma distribution and a GPD distribution with parameters at the tail are used in the middle part.The global sample space is estimated by the Bayesian method for the position parameter u,shape parameter ? and scale parameter ? of the tail.The prior distribution of the semiparametric model imposes a limit on the parameter space,where the threshold obeys a normal distribution2(,)u uN ? ?,whereu? the distribution mean of the parameters may have a large impact on the result inference.The Bayesian inference of the posterior distribution of the semiparametric model is obtained by the Markov chain Monte Carlo algorithm.The parameters are modularized.Because there is no specific identifiable full conditional density,the parameter estimation of each block will be in accordance with Metropolis.This thesis is divided into four parts: The first part is the research background and significance of this thesis,and the related literatures on the application of extreme value theory in the limit of the limit and the estimation of the tail parameter of the extreme value theory are reviewed.The second part elaborates the basic theory of extreme value theory and the construction of nonparametric extreme value model.The third part and the fourth part are the core of the thesis,namely the construction of the semiparametric extremum model and the estimation of the tail parameters of the semiparametric extremum model by the MCMC method.The third part elaborates the construction of a semiparametric extremal model with a mixed Gamma distribution and a tail with a GPD distribution in the middle,and further a prior distribution selection and posterior distribution of the semiparametric extremum model,and the tail parameters.estimate.The fourth part elaborates the relationship between the distribution of the estimation results of the tail parameter of the semi-parametric extreme value model of China’s securities market and China’s price limit system.The Bayesian method is used to estimate the tail parameters of the semiparametric model.The empirical results show that most of the shape parameters ? of the tail are in a state less than 0,which means that the value of the falling index has a lower limit,and the phenomenon of “crunting” appears instead of the tail tail characteristic of peak thickness.The phenomenon of "crunting" just reflects the implementation of the ups and downs system in China’s stock market,which has a lower limit of negative yield.The tail scale parameter approximates a normal distribution,and the probability of extreme fluctuations is small.At present,China’s securities market still has great uncertainty.It can combine the volatility of the securities market with the market risk,especially the systemic risks in the financial market.China has gradually paid attention to China’s financial market since the subprime mortgage crisis in 2008.The prevention strategy of systemic risk,the ups and downs of the stock market in 2015 is further caused by the emphasis on systemic risks in the financial market.Combining mathematical theory with financial theory has an important impact on extreme value theory and the construction of a financial risk prevention system.