基于极值理论估计外汇在险价值VaR

Estimating the VaR of Exchange Rates Using Extreme Value Theory

采用极值理论POT模型对欧元兑美元等4种外汇对数收益序列的VaR进行了估计。为了比较阈值选取对估计结果的影响,变化选取不同汇率的阈值分位点,则超限点数也相应地变化。使用估计的GPD分布参数,分别构造上界和下界的分布函数,从而计算出VaR的95%置信区间。极值理论作为测量极端市场条件下市场风险的一种方法,具有超越样本数据的估计能力,并可以准确地描述分布尾部的分位数。结果表明:外汇对数收益分布左右尾具有不对称性,而且都有一定程度的胖尾现象,但是均存在二阶矩,分布具有有限方差。

An evaluation of the logarithm gains of the Euro against 4 foreign currencies including the U.S. dollar is made, using the POT model of the Extreme Theory. In order to compare the impact of the threshold value selection on the estimated consequence, we change the threshold quantile of different exchange rates, then a corresponding change of the number of the extreme points will be shown. GPD distribution with estimated parameters, upper and lower bounds of the distribution function are constructed to calculate the VaR of the 95 % confidence intervals. Analysis on the distributional characteristics of several exchange rates is delivered based on the computational results. Results show that the left and right tails in the distribution of the logarithm gains of foreign exchanges are asymmetric, both having a fat tail to some degree, and a secondary moment. The distribution presents finite variance.