应用极值理论计算在险价值(VaR)——对恒生指数的实证分析

在险价值（Value-at-Risk,简称VaR）是度量市场风险的一种普遍使用的工具，可看作是市场风险度量的基石。本文应用统计学中的极值理论于VaR的计算，这是一种崭新的方法。传统的VaR计算方法都是考虑资产回报分布的全部，而极值理论只考虑分布的尾部，风险管理者注重的正是分布的尾部。通过一段长时间观察出的极值回报的极限分布独立于回报的初始分布，因此不必要假设一个回报的初始分布，这正是极值理论应用于VaR计算上的最大优势。相反，传统的方差－协方差方法假设回报服从正态分布，这低估了市场风险的价值。本文研究所用的数据是香港恒生指数，我们将用极值方法计算的结果与用方差－协方差方法计算的结果进行比较，发现极值方法要明显优于方差－协方差方法。

Calculating VaR with the Extreme Value Theory An Empirical Analysis of Hang Seng Index

Value-at-Risk(VaR) is a commonly used tool to measure market risk, and also the benchmark in risk management. This paper applies the extreme value theory on VaR calculation, which is a method emerging recently in risk management. Extreme value theory models the tail of the return distribution rather than the whole distribution. The limiting distribution of extreme returns observed over a long time-period is independent of the distribution of returns itself. So it is not necessary to assume a specific distribution for the returns, which is a great advantage of extreme value theory on VaR calculation. The data used in this paper are the Hang Seng Indices during January 1,1985 through December 31,1999.