VaR Estimation Of Heavy-tailed Distributions

VaR is the standard method to manage financial risk at present. Because of its simplicity and practicability,most of the banks,nonfinancial companies have adopted this method to manage their market risk soon after it was invented.Although the concept of VaR is simple, its measurement is a statistical problem with challenge .Recently, there were many papers about the VaR method written by oversea scholars. Nowadays, it is also an important and urgent task to investigate definition and computing method of VaR in China.Usually it has three kinds of major computing technologies-Historical Simulation Approach , Monte Carlo Simulation Approach , Analyse Approach ,and every kind of VaR computing technology has its weak points. More and more researchers put forward using extreme-value-theory to measure market risk , Because extreme-value-distribution need not to put any hypothesis on the whole distribution of return but only fitting the tail of distribution, which is fitted to measure risk,so it can avoid risk of model and computer rightly the VaR of extreme event.There the character of " heavy-tailed " exists in financial time series. The subject of this article is finding a new way to estimate VaR. The theory of extreme value and other knowledge will be used in this article. One new probability density will be established by parametric-non- parametric approach, and the high quantile of the heavy-tailed function will be evaluated under the hypothesis of its hail is regular varying function.