A Study On Financial Risk Measurement Based On Heavy Tail Distribution And GARCH Model

Along with the financial organ combination transaction property number increase sharply, the financial market presents the unprecedented undulation and the vulnerability. The market risk measure is the foundation of controlling and managing risk. As a measurement tool of financial risk, VaR has been recognized by financial field. In order to measure the risk accurately, the statistical characteristic of distribution must be described aboardly.Financial Asset price volatility, especially the large change for stock price such as rise and drop wildly, in view of probability distribution ,studies on occurrence laws for extreme returns is to explore the tail behavior of returns probability distribution. Financial practical analysis shows that not only has the asset returns fat tails, but also the volatility is clustered, i.e. large volatility is followed by large ones and small volatility is followed by small volatility. Extreme value theory and methods can deal with the tail behavior for returns series, and financial volatility models like GARCH model describe the returns volatility, this paper studies the tail behavior of returns from the returns volatility models, combining heavy tailed distribution with non-linear time series models, and discusses tail features for the marginal distribution by the time series characteristic. The paper makes Shangzheng index return datas as research objects, residuals series are obtained by fitting returns volatility models in order to compare the tails behavior of innovations and returns. Practical analysis shows that the modeling method is able to fit the returns tails better.Heavy-tailed distribution plays an important role in estimation of risk of financial asset return series. In Statistics of Extreme, the tail index is the basic parameter of extreme events. Such a parameter plays a relevant role in other extreme events'parameters, like high quantiles, namely VaR in financial risk. So exactness of VaR estimated depends strongly on exactness of the tail index estimated. The chapter 3 discusses estimate methods of the tail index in detail. The classical Hill estimator is a biased estimator, in many improved estimators, the maximum likelihood estimator in second-order regular condition not only is asymptotically unbiased and asymptotically normal, but also practical analysis shows that the simulation effect is well. This paper deduces least square estimator of tail index in common case(ρ< 0) and proves that the estimator is asymptotically unbiased and normal. Base on it, a new estimator of tail indexγwith a small asymptotic mean squared error in certain condition is introduced.