Extreme Value Theory In Risk Measurement Applications,

The theory of extreme value(EVT) is a branch of order statistics, and its major research field includes the extreme value distribution and its characteristics, in particular the tail of the distribution of characteristics. In the field of natural sciences, finance and insurance, etc, extreme Value theory has been widely used. In the field of finance and insurance, the main application of extreme value theory is to measure extreme risk.In the financial risk measurement, VaR(Value at Risk) is paid wide attention in the financial field. More and more banks and other financial institutions have already adopted VaR as a prediction and an important index of preventing and controlling financial risks. This article first introduces present quite popular VaR risk measure method as well as the three kind of traditional computational methods of VaR in detail, and compares these three computational method from various aspects. Because there are a lot of flaw to use VaR to measure risk, for example, the dissatisfied uniform risk measure, this article also introduced uniform risk measure method ES. The ES method can better capture part distribution from finance data,which has made up the VaR f1aw.Traditional VaR model needs to suppose the distribution of the asset prices, and the traditional VaR model has not considered the financial data, especially the loss data, whose distributions have the characteristic of fat tail. The extreme value model needs to simulate the tailed distribution only, which reduces the error of the model made by the inaccurate hypothesis. It means that the extreme value model can reduce the modeling risk because it only needs to use the tailed distribution. Therefore, it can more precisely describe the reality to use the extreme value model to calculate the VaR.In the insurance risk measure, the ruin probability is an indicator of stability, which combines the premiums and claims of insurance. It is a useful risk management tool. This article describes another important theorem of extreme value theory, fat-tail distribution of equivalent-type theorem in detail. Using this theorem, we can calculate the ruin probability and related measurement more conveniently.This paper systematically expounded on the extreme value theory and the characteristics of extreme value distribution. It is also introduced to use extreme value theory to calculate value at risk in finance (VaR and ES estimation method). Then using the above methods we analyze the Shanghai Composite Index. And we also compare the results of traditional methods and the methods using extreme value theory. The empirical results show that it is more accurate to use extreme value theory to calculate the financial risk. In the process of empirical study, because the data are weak correlated, not completely independent, we use the extreme value index which is proposed by others. The empirical results show that this approach reduces the estimation error because of the problem that the correlation and volatility clustering phenomenon of the financial data can not meet the assumptions of the extreme value theory. In this paper we also introduce a method to use extreme value theory to calculate the initial surplus of the ruin probability. Under the certain assumption, an equivalent function is derived for heavy-tailed distribution. Finally using simulation we obtain the function relationship of the initial surplus and the ruin probability. The results show that the greater initial surplus, the smaller the probability of ruin probability. The conclusion is consistent with reality.