An Application Of Extreme Value Theory For Measuring Risk

Extreme value theory is a branch of order statistics, widely used in the field of natural science, finance, insurance, etc. The research object is the tail characteristics of the asset earning rate distribution. Extreme value theory is mainly used for risk measurement in the field of financial and insurance. There are two main extreme value theory model:(1) the BMM model based on generalized extreme value distribution, and (2) the POT model based on the generalized pareto distribution.In recent years, the Value at Risk(VaR) have been more and more popular in risk management. But VaR is not necessarily sub-additive meaning that VaR is not a coherent risk measure. To solve this problem, other scholars introduced the Expected Shortfall ES (Expected Shortfall) instead of VaR. ES is a coherent risk measurement tool, which makes up the defect of the VaR, but also retains the advantages of VaR.This paper introduces the definition of VaR and three kinds of traditional calculation methods of VaR, which is normal distribution method, the historical simulation method and Monte Carlo simulation method, and makes a comparison of three methods. What's more, this article clearly points out the traditional VaR methods have two significant disadvantages and the corresponding improving methods.In this paper, the empirical part uses four Chinese important stock market index to take researches. We show an underestimation of the risk of loss for the VaR calculated in variance-covariance method compared with POT mothod. Improved Monte Carlo simulation method is accurate for extreme events but show an overestimation in non-extreme situation. Take volatility clustring and autocorrelation into consideration by introducing GJR-GARCH model in the above three methods. The results shows the effects are all improved.