Applications Of Extreme Value Theory To Measurement And Modeling Of Risk

In recent years, among various methods of financial risk measurement, VaR (Valueat Risk) receives the attention of the financial world most. More and more banks andother financial institutions have already adopted VaR as a prediction and animportant index of preventing and controlling financial risks.The models used for calculating VaR of this paper are mainly the traditional VaRmodel and the extreme value model: the former is based on the assumption that theassets income obays normal distribution; the latter is a kind of application of extremevalue theory in calculating VaR.There are two main differences between the two methods in calculating VaR:First, the traditional VaR model needs to suppose the whole distribution of the assetsincome, while the extreme value model need to simulate the distribution in tail only,which reduces the error of the model which dues to the inaccurate hypothesis, that isto say it can reduce the modeling risk; Second, the traditional VaR model has notconsidered the financial data, especially the loss data, whose distribution have thecharacteristic of fat tail, while the extreme value model considers this point, and setmain attention on the tail of the distribution, therefore using the extreme value modelto calculate the VaR corresponds to the reality even more. Precisely, because of thefat tail of the distribution, using the traditional VaR model will underestimate the risk,by contrast, using the extreme value method could estimate the actual size of the riskeven more.In the section of demonstration, Composite Stock Index of Shanghai StockExchange Centre is taken for example. The article applies EVT to compute value atrisk and gives the estimation value of VaR and ES.Then,the estimation results arecompared to those conventional methods.The conclusion shows that the EVTmethods have good veracity in estimating financial risk.In this paper,Extreme ValueIndex is introduced, to some extent,estimate errors that caused by unfitting thehypothesis of extreme value theory for the finance data series' autocorrelation andthe fluctuated clustering are overcome.