基于Pearson Ⅳ分布的VaR与CVaR估计

VaR and CVaR Estimation Using Pearson Ⅳ Distribution

基于GARCH模型,用Pearson Ⅳ分布拟合标准残差,给出一种更为精确的VaR和CVaR计算方法。重点研究在Norm-GARCH、t-GARCH与GED-GARCH模型下,用原分布和Pearson Ⅳ分布计算VaR的比较,结果表明,用Pearson Ⅳ分布计算VaR都能得到比原分布更小的失败率,且在三种模型之下用Pear-son Ⅳ分布计算VaR结果很接近,都能通过检验,所以选择最简单的Norm-GARCH模型就可以;基于此,研究在Norm-GARCH模型下,用正态分布和Pearson Ⅳ分布计算CVaR,并与VaR进行比较,结果表明,用Pearson Ⅳ分布计算VaR和CVaR的失败率都远远小于由正态分布所得到的失败率,特别在VaR估计失效的交易日里,用Pearson Ⅳ分布得到的CVaR均值与实际损失均值非常接近。因此,Pearson Ⅳ分布能很好地刻画金融数据的特征,相对其他分布而言是一个很好的选择。

Basing on GARCH model, a novel VaR and CVaR estimation method with more accuracy is developed by employing Pearson IV distribution. This paper is mainly concerned on the comparison between VaR estimation through Pearson IV distributions and through original distributions under norm-GARCH, t-GARCH and GED-GARCH models. The results show that the failure frequency of VaR estimation through Pearson IV distribution is smaller than that through original distributions. Also, the estimated VaR through Pearson IV distribution basing on various GARCH models are similar and effective. Thus, the easiest Norm-GARCH model is effective enough. Furthermore, we use normal distribution and Pearson IV distribution to calculate CVaR, and compare it to VaR under nonrrGARCH model. The results show the failure frequencies of VaR and CVaR through Pearson IV distribution are both smaller than those ＂through the normal distribution. Especially when the VaR estimation fails, the mean of CVaR estimated through Pearson IV distribution is very close to the mean of real loss. Therefore, Pearson IV distribution can capture the features of financial data very well and is a better choice than other distributions.