Extreme Value Theory And Its Applications, Value At Risk

The theory of extreme value (EVT) is a branch of order statistics,which traditionally can be used as a tool forecasting tsunami,earthquake and flood. Recently it has been applied to financial risk management.Because EVT mainly studies extreme value and models the tail of distribution financial return,it can effectively forecasts and guards against the financial risk on the condition of lacking of sample data. More and more people recognize the great potentials of EVT dealing with the risk of extreme event. Especially EVT can be used in application to value at risk due to modeling the tail of distribution.Value at risk is a tool which be widely used in application to financial risk management and regarded as extreme quantile method. Traditional VaR methods want to give a hypothesis of financial return data subjected to some distribution,which brings about the suspicion of validity of hypothesis. However EVT educes the tail of distribution instead of the hypothesis. So it can avoid risk of model and computer rightly the VaR of extreme event.This article presents the theory of extreme value and character of tail of distribution and gives the example of VaR with index of Shanghai stock market by EVT,then compares the VaR result of different computation methods and concludes that traditional VaR method is static state model and VaR with EVT is dynamic conservative model and has the ability of forecasting risk out of sample comparing tohistorical simulation method.