Application Of The Beck Model To Evaluation Of VaR In Stock Markets

As the core of China's securities market,the stock market has the most widespread investors participating in,and involves the most wide-ranging interests.At present,in the case of sharp drop,stock market's volatility and systemic risks increased greatly.So for business circles and financial institutions,risk management is more important than before.The key link of risk management is an estimation of risk,only accurately calculating the size and probability of uncertainty,financial participants and regulators can set up the position of bargaining,adjust the portfolio's assets structure,and control the uncertainty at a level which can be endured and preset.As one method of the mainstream of current risk measure,the VaR method has been widely used at home and abroad.The VaR is only one idea of risk measure,and it has many ways to calculate.If the method is choosed improperly,it also will give investors a wrong guide to decide.This paper uses the Beck model to calculate the stock market's Value-at-Risk(VaR).The Beck model gives a dynamical foundation of Tsallis statistics,and the Tsallis statistics is based on the principle of maximum entropy.It is showed by the analysis that the theory is suitable for the securities business,and many studies at home and abroad have used the entropy of Shannon information to analyze the portfolio in securities business.This paper use the Tsallis entropy to compute VaR.Our study reveals that the Beck model elucidates the properties of stock market returns and is applicable to practical use of the VaR estimation.Volatility is one of the most important features of financial market,and directly related to the market's uncertainty,so it influences corporate and individual behavior of investment.Usually variance is used to describe and measure volatility,the traditional econometrics models often assume that the variance is unchanged,but the real stock market is not the case.The paper chooses daily legarithm data of hangseng index return as samples of the research,and finds that the volatility fluctuation of the real stock market is well-consistent with the two assumptions of the Beck model.They are that the return's volatility fluctuates at a much larger time scale than itself,besides it obeys inverse Gamma distribution. Slow fluctuation in this paper is commentated that the return's volatility has long time memory compared with the return in econometrics method. We adopts the auto-correlation function to prove the volatility's long time memory.Based on the formal analysis,the return obeys q-Gaussian distribution of Tsallis statistics and converges into a Gaussian distribution in the limit of qâ†'l.Our purpose of studying VaR for q-Gaussian distribution is to enable the VaR evaluation in consideration of the tail risk,which is neglected by the variance-covariance method.Finally,this paper testifies a linear equation,namely a linear relationship between VaR values of Gaussian distribution and that of q-Gaussian distribution.