Study Of Value At Risk Based On Extreme Value Theory

At present, as internationally tool of measuring financial risk. VaR describes themaximum possible loss in the future given a certain degree of confidence by the estimateddistribution of the assets. However, the normal distribution is very contrary to the sequence ofreturns on most financial assets practically with fat-tail, which means using VaR to measurerisk will lead to the tail extreme risk is probably underestimated because of the ignorance oftail events.Extreme Value Theory (EVT) is a method of modeling statistical, which is used tostudy rare events, but it will bring tremendous impact once it happens. It does not need toknow the overall distribution of the return series, but to concern the tail’s characteristics.Applying EVT to VaR model can solve the underestimate of tail risk due to the lack of normaldistribution assumption, and can estimate the financial extreme risk more accurately. Thispaper does the following works based on EVT:(1) Establish VaR method based on GARCH-EVT. Especially, when use peaks overthreshold model to calculate VaR, because of the correlation of financial series often happensby cluster, we import extreme index to eliminate the correlation nature.(2) According to the compound extreme value theory, the model is introduced to thearea of financial risk management and the model Variables have been given the financialmeans. First, define the number of threshold strings approximately obey Poisson distribution,fit the maximum threshold sequences to Generalized Pareto Distribution. Second, compoundthe number of cluster Variables and the maximum threshold in cluster, then it makes a newcompound extreme value theory, Poisson-gp distribution. Finally, use this method to makesempirical analysis on Shangzheng, HSI, KOSPI and U.S. Standard&Poor’s index. Resultsshow that compared to the other methods, use Poisson-gp threshold distribution model tostudy risk in financial is more reasonable.