The Research Of Chinese Fund Market Based On Extreme Value Theory And Copula Function Of Portfolio VaR

Recently,with the daily volatility of financial market and some financial catastrophic events happened one by one, which put a challenge for risk management, we have been long for some more appropriate models to deal with such events. Because the conventional method to measure is based on normal distribution assumption which has been proved to underestimate risk, in order to measure the risk more accurate, more and more researchers put forward using extreme-value-theory to measure market risk which has been used in engineering field widely. Because extreme-value-distribution need not to put any hypothesis on the whole distribution of return but only by data themselves, fitting the tail of distribution, which is fitted to measure risk.Based on the study of extreme-value-theory by forefathers,we will discuss how to use extreme-value-theory to estimate financial risk precisely faced by Chinese fund market. At the same time, it's more practical to study the portfolio case. Portfolio can disperse risk on a scale for the correlation amount risk factors. The assumptions of traditional portfolio risk VaR measurement models may underestimate or overestimate VaR. Through Copula theory, a multiVaRiate distribution with all kinds of marginal distribution coupled by a suitable Copula functions can be built. Copula function not only describes the correlation of VaRiables, but also the dependence structure of VaRiables, which makes Copula function a strong dynamic model to describe financial series distribution.Based on portfolio theory of Markowitz, we want to concider the influence on VaR by dependence when we use VaR to measure risk. If market data has Guassian distribution, we can prove the smaller linear correlation is, the smaller VaR of portfolio is. However, masses of market data hasn't Gaussian distribution, and it is fat-tailed. We focus on finding the influence on VaR by linear correlation and tail dependence in this paper. The result indicates the tail dependence has an important influence on VaR of portfolio. Therefore, we must consider the dependence completely when we use VaR to measure risk.