带有马尔科夫区制转移的非对称ARCH模型及其VaR的估计

发布时间：2018-06-17 06:51

本文选题：ARCH模型 + 区制转移　；参考：《北京工业大学》2015年硕士论文

【摘要】：自从Engle(1982)首次提出自回归条件异方差模型(ARCH)以来,许多学者为描述金融资产收益率的波动聚集、尖峰厚尾、非对称等特点提出了各种ARCH的拓展模型。例如针对收益率受到未预期正向冲击和负向冲击会引起波动不对称的现象而提出的门限GARCH模型(TGARCH),针对收益率受到政策性的或者重大事件影响时会发生结构转移而提出的带有马尔科夫区制转移的ARCH模型(SWARCH)。考虑到这两种模型是从不同角度对ARCH模型的改进,因此将两者的特点结合描述收益率是有意义的。本文在传统ARCH模型基础上同时引入了非对称效应和Markov区制转移,深入研究了非对称的SWARCH模型,简称为ASWARCH模型。并讨论了模型的参数估计,给出了资产收益率条件均值和条件方差的预测表达式。我们还利用ASWARCH模型研究了风险价值(VaR)的计算。VaR在度量金融风险方面方法简便,经过量化结果易于分析,因此受到风险管理者的广泛关注。VaR的估计不仅依赖收益率的分布而且受尾部极端值的影响很大,本文进一步利用极值理论中的超阈值峰值法(POT)模拟尾部分布,提高了VaR估计的准确性。最后我们对上证综合指数进行了实证分析,结果表明:第一,上证指数收益率确实存在明显的波动聚集现象和结构转移;第二,ASWARCH模型相对于常方差模型、ARCH模型、GARCH模型、TGARCH模型和SWARCH模型能更好的描述上证指数收益率及其波动情况;第三,结合极值理论估计的VaR在高置信度下预测结果更好。
[Abstract]:Since Engle first proposed the autoregressive conditional heteroscedasticity model (ARCH), many scholars have proposed a variety of arch extension models to describe the characteristics of volatility aggregation, peak and thick tail, asymmetry and so on. For example, the threshold GARCH model proposed in which the rate of return is subject to unexpected positive shocks and negative shocks will lead to asymmetric fluctuations, for example, when the rate of return is affected by policy or major events, the structural shift will occur. The arch model with Markov region system transfer is presented in this paper. Considering that the two models improve arch model from different angles, it is meaningful to combine the characteristics of the two models to describe the rate of return. Based on the traditional arch model, the asymmetric effect and Markov region transition are introduced, and the asymmetric SWARCH model, called ASWARCH model, is studied in detail. The parameter estimation of the model is discussed, and the predicative expressions of the conditional mean and conditional variance of the asset return rate are given. We also use ASWARCH model to study the calculation of VaR. VaR is simple and convenient to measure financial risk, and the quantitative results are easy to analyze. Therefore, the estimation of .VaR not only depends on the distribution of return rate but also is greatly affected by the extreme value of tail. In this paper, the tail distribution is simulated by the method of over-threshold peak value (POT) in extreme value theory. The accuracy of VaR estimation is improved. Finally, we make an empirical analysis of the Shanghai Composite Index. The results show that: first, the return rate of the Shanghai Stock Exchange Index does exist obvious volatility aggregation phenomenon and structural transfer; The second ASWARCH model can better describe the return rate of Shanghai stock market index and its fluctuation than the GARCH model and the SWARCH model compared with the constant variance model and the GARCH model. Thirdly, the VaR estimated by the extreme value theory is better than that of the GARCH model and the SWARCH model under the high confidence level.
【学位授予单位】：北京工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

【相似文献】