基于HMM的VaR风险度量及其实证分析

VaR risk measurement based on HMM and its empirical analysis

文章基于隐马尔科夫模型(HMM)提出了度量金融资产风险价值(VaR)的HMM-ARMA-GARCH模型。首先对金融资产收益率序列建立正常状态和异常状态的隐马尔科夫模型,使用期望最大化算法估算出模型中的未知参数,再利用Viterbi算法估算出收益率序列所对应的隐状态序列,根据隐状态序列把收益率序列数据分成正常状态类序列和异常状态类序列2个大类,对2个状态类序列分别建立ARMA-GARCH模型来估算VaR。最后利用该模型和传统的ARMA-GARCH模型对上证企债指数进行了实证分析,采用Ku-piec失败频率检验法对VaR的准确性进行检验。实证结果表明,该模型的VaR计算方法具有较好的估计效果,能够有效地降低GARCH模型高估波动持续性的现象。

The HMM-ARMA-GARCH model to measure the financial assets value at risk（VaR） is presented based on the hidden Markov model（HMM）. First, the hidden Markov models of the financial asset return sequence under normal and abnormal states are set up. The expectation maximization algorithm is used to estimate the unknown parameters of the model. Then, the Viterbi algorithm is used to estimate the corresponding hidden state sequence of the return sequence. According to the hidden state sequence, the return sequence is classified into two categories, i.e. the normal state sequence and the abnormal state sequence. And the ARMA-GARCH model is established to estimate VaR for each state sequence respectively. Finally, the Shanghai enterprise debt index sequence is analyzed by using the presented model and the traditional ARMA-GARCH model respectively. The accuracy of the VaR is tested by the Kupiec failure frequency method. The results show that the presented model has a good esfimate effect, and reduce effectively the problem of overestimating the fluctuation persistence by the GARCH model.