Dynamic Value-at-Risk Based On Extreme Value Theory

In recent years the market risk management has become increasingly important for a number of reasons:globalization,financial derivatives and high volatility in finance market.Value-at-Risk(VaR) is a popular method to compute finance risk and it takes the loss of investors as the risk simply.Traditionally,the VaR methods want to give a hypothesis of financial return data subjected to some distribution,which brings about the suspicion of validity of hypothesis.So traditional VaR methods have the risk of models.Extreme value theory(EVT) stemming from statistics has been used widely to analyse the financial risk quantitatively these years.The difference between EVT method and VaR method is that EVT method needn't give a hypothesis of financial return data subjected to some distribution and it takes the sample extreme values to simulates the distribution in tail only,which reduces the error of the model risk.Sample extreme values are the data that deviate the mean value much,which are some abnormal values with excess losses.After modeling the tail distribution,given some tail probability,EVT method can produce the risk value VaR.Because of the fat tail of the distribution,using the traditional VaR model will underestimate the risk,by contrast, using the EVT method could estimate the actual size of the risk even more.The EVT method gives a most useful conclusion that all the sample data have the same limit distribution and only have the difference parameter,which means the limit distribution of sample extreme values is independent with itself.So the EVT method can get the characteristic of extreme values by the sample data without assuming the total distribution.It can estimate the data outside the sample. Composite Stock Index of Shanghai Stock Exchange Centre is taken for example in this paper.In the analysis,we find the financial data not only have the character of fat tail but also have the character of conditional heteroskedasticity,which is that fluctuation ratio is not a constant but a variable.Conditional heteroskedasticity violates the hypothesis of sample independence.So introduce the GARCH family models to eliminate the conditional heteroskedasticity and get the i.i.d random variable.After that, the EVT method can give us the result of VaR.GARCH family models can forecast the variance of the return data and conditional variance not only depends on the latest information also it depends on the previous conditional variance.GARCH family models overcome the character of heteroskedasticity in the financial time series and offer the more effective sample data. For GARCH models take the conditional mean and variance to computer VaR,it is often called dynamic VaR method.In this paper,just take the GARCH models and EVT method to analyse the risk in the financial market.With the software of Eviews,analyse the Composite Stock Index of Shanghai Stock Exchange Centre.By comparing the model of based on the EVT dynamic VaR with the general model of dynamic VaR,The conclusion shows that the GARCH(1,1)-EVT model can save more capital investment as controlling the risk effectively and the result is much better in the higher confidence level.The GARCH(1,1)-EVT model is more stable at the 99th and higher quantile.In the comparision of GARCH family models,we fmd EGARCH(1,1)-EVT and GARCH (1,1)-M-EVT have better results than GARCH(1,1)-EVT for the upper tail VaR,in which GARCH(1,1)-M-EVT model is better than EGARCH(1,1)-EVT model. But for the lower tail VaR these three models almost have the same result.