一种q-高斯分布的VaR计算方法

A Method of Calculating VaR of q-Gaussian Distribution

准确地描述资产收益率分布是进行风险度量的基础.利用q-高斯分布刻画股票的收益率,运用泰勒级数给出一种新的基于q-高斯分布的VaR计算公式.实证分析结果表明,运用q-高斯分布拟合上证综合指数的收益率比用正态分布样本平均误差减少了22.40%;在置信水平分别为0.05和0.01下,正态分布计算的VaR要比q-高斯分布计算的分别低估16.00%和30.88%;而且低估风险的程度随置信水平的减小而增加.说明q-高斯分布能够准确地刻画资产收益率分布的"尖峰厚尾"现象,用该分布进行VaR风险度量可以有效地克服风险被低估情况的发生.

Accurately describing the distribution of return on assets is the basis of risk measurement.Using the q-Gauss distribution to characterize stock returns,a new VaR formula based on the q-Gauss distribution was given by using Taylor series.Empirical analysis results showed that the return of Shanghai Composite Index fitted by q-Gauss distribution was 22.40%less than the average error of normal distribution sample.Under the confidence level 0.05 and 0.01,the VaR calculated by normal distribution was underestimated by 16.00%and 30.88%respectively.Moreover,the degree of underestimating risk increased with the decrease of confidence levels.So,qGaussian distribution can accurately describe the peak and fat tail of returns,and overcome more effectively underestimating risk.