摘要 近年來，重大的金融危機事件層出不窮，使得風險管理的概念越來越受重視，而風險值(VaR)能將風險量化，更成為管理市場風險的利器。本篇研究我們利用極值理論(Extreme Value Theory)來求算風險值，可以以一長期的觀點來衡量風險，如五年或是十年內所發生的重大損失事件，或是進行壓力測試時，極值理論下的風險值可以提供管理者一些情境的資訊，使其能了解最糟的情形為何。 因為我們通常不知道財務資料實際的分配為何，而且一般的財務資料通常具有厚尾的現象，極值理論不用假設資料的分配為何，而專注在資料尾部的變化情形，可以減少模型誤設的風險，也注重單一重大的事件風險。 所以本篇研究我們利用極值理論的區段最大化模型計算風險值，與其他三種方法：歷史模擬法，一般常態分配和GARCH(1,1)模型下的風險值比較，對於風險態度上較為保守的投資人而言，發現在較低信賴水準如90％和95％，利用常態分配假設的風險值會較適宜，而在較高信賴水準如99％以上，則利用極值理論所計算出的風險值才不會低估風險，造成重大的損失。 Abstract Value at Risk and Extreme Value Theory: An Empirical Study on Taiwan Stock and Exchange Markets. In recent years, there are more and more significant financial markets crises. Many practitioners and researchers pay a lot of attention to the risk management. As a result, value at risk (VaR) has become a widely used measure of market risks in risk management. This article presents an application of extreme value theory to compute the VaR. VaR based on extreme values can give us the long term view of risk management. We can focus on rare events, such as a 5-year or 10-year loss. Besides, this kind of information may be interesting to risk managers who wish to perform stress testing and get a feeling for the scale of worst case. As we do not know the exact distribution of returns and the security returns tend to be fat-tailed, the normal distribution or any given distribution may be badly fitted. The extreme value method does not assume a particular model for returns but lets the data speak for themselves when fitting the distribution tails. Thus, the model risk is reduced. Moreover, the method explicitly takes the risk of extreme events into account. In this article we use the block maximum method to compute VaR and compared the results with the classical methods, such as historical distribution method, normal distribution method and the conditional GARCH(1,1) process method. The value of the probability of an extreme return not exceeding the VaR ranges from 90% to 99%. To sum up, we can use the normal or GARCH(1,1) method to compute the VaR for lower probability values such as 90% or 95%. If we are interested in the VaR for higher probability values, higher than the 99% for instance, we can use the extreme value approach to estimate it.
