基于MCMC方法的SV模型的贝叶斯估计及实证分析
发布时间：2018-10-08 20:07
【摘要】：随机波动率模型自建立以来,在金融时间序列波动率建模中得到了广泛的应用,但是由于SV模型波动率的潜藏性,使得传统的似然函数极其复杂,这导致SV模型在最大似然估计方面面临着一定的困难.而Bayes方法结合了参数的先验信息和后验分布,在SV模型的参数估计方面具有一定的优势,基于MCMC方法的Bayes估计在实际应用中具有较好的精确度.因此,本文通过Bayes方法来研究SV模型的参数估计问题,并且利用MCMC方法进行了计算和实证分析.根据参数的估计的结果,得出在刻画中国银行和交通银行的收益率序列时,厚尾SV模型的模拟效果要优于标准SV模型.本文主要研究SV模型的参数估计方法,其中是将标准SV模型和厚尾SV模型进行对比研究,主要内容如下:1.论文介绍了金融市场的波动率,波动率在金融时间序列中表现出的特征以及相应的预备知识.2.论文对标准SV模型和厚尾SV模型进行了详细的结构分析,得到SV模型的似然函数表现形式.3.论文在SV模型的参数估计中使用的是MCMC方法,该方法结合了贝叶斯估计方法,在抽样过程中使用的是Gibbs抽样方法.在贝叶斯估计法中,推导了后验分布的理论公式.并且将后验分布理论公式运用到SV模型中,推导出了标准SV模型和厚尾SV模型的每个待估参数的后验分布函数.4.论文在实证分析中,使用Win Bugs软件得到参数估计的结果,根据模型对数据的拟合效果,以及模型DIC值的比较,通过得到的结果对比分析了标准SV模型和厚尾SV模型的模拟效果,得到厚尾SV模型的拟合效果更优.
[Abstract]:Since the establishment of stochastic volatility model, it has been widely used in financial time series volatility modeling. However, because of the latent volatility of SV model, the traditional likelihood function is extremely complex. This leads to some difficulties in maximum likelihood estimation for SV model. The Bayes method combines the prior information and the posterior distribution of the parameters, so it has some advantages in the parameter estimation of the SV model. The Bayes estimation based on the MCMC method has good accuracy in practical application. Therefore, the Bayes method is used to study the parameter estimation of SV model, and the MCMC method is used to calculate and analyze the model. According to the result of parameter estimation, it is concluded that the simulation effect of the thick tail SV model is better than that of the standard SV model in describing the return sequence of Bank of China and Bank of Communications. In this paper, we mainly study the parameter estimation method of SV model, in which the standard SV model and the thick-tailed SV model are compared. The main contents are as follows: 1. This paper introduces the volatility of financial market, the characteristics of volatility in financial time series and the corresponding preparatory knowledge. In this paper, the standard SV model and the thick-tailed SV model are analyzed in detail, and the expression form of likelihood function of SV model is obtained. In this paper, the MCMC method is used in the parameter estimation of SV model, which combines Bayesian estimation method and Gibbs sampling method in the sampling process. In Bayesian estimation, the theoretical formula of posterior distribution is derived. The posterior distribution function of the standard SV model and the thick-tailed SV model is derived by applying the posterior distribution formula to the SV model. In the empirical analysis, the results of parameter estimation are obtained by using Win Bugs software. According to the fitting effect of the model and the comparison of the DIC value of the model, the simulation results of the standard SV model and the thick-tailed SV model are compared and analyzed. The fitting effect of SV model with thick tail is better.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8
本文编号：2258098
[Abstract]:Since the establishment of stochastic volatility model, it has been widely used in financial time series volatility modeling. However, because of the latent volatility of SV model, the traditional likelihood function is extremely complex. This leads to some difficulties in maximum likelihood estimation for SV model. The Bayes method combines the prior information and the posterior distribution of the parameters, so it has some advantages in the parameter estimation of the SV model. The Bayes estimation based on the MCMC method has good accuracy in practical application. Therefore, the Bayes method is used to study the parameter estimation of SV model, and the MCMC method is used to calculate and analyze the model. According to the result of parameter estimation, it is concluded that the simulation effect of the thick tail SV model is better than that of the standard SV model in describing the return sequence of Bank of China and Bank of Communications. In this paper, we mainly study the parameter estimation method of SV model, in which the standard SV model and the thick-tailed SV model are compared. The main contents are as follows: 1. This paper introduces the volatility of financial market, the characteristics of volatility in financial time series and the corresponding preparatory knowledge. In this paper, the standard SV model and the thick-tailed SV model are analyzed in detail, and the expression form of likelihood function of SV model is obtained. In this paper, the MCMC method is used in the parameter estimation of SV model, which combines Bayesian estimation method and Gibbs sampling method in the sampling process. In Bayesian estimation, the theoretical formula of posterior distribution is derived. The posterior distribution function of the standard SV model and the thick-tailed SV model is derived by applying the posterior distribution formula to the SV model. In the empirical analysis, the results of parameter estimation are obtained by using Win Bugs software. According to the fitting effect of the model and the comparison of the DIC value of the model, the simulation results of the standard SV model and the thick-tailed SV model are compared and analyzed. The fitting effect of SV model with thick tail is better.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8
【参考文献】
相关期刊论文 前7条
1 周孝华;张保帅;;基于SV-GED模型的极值风险度量研究[J];管理工程学报;2014年01期
2 朱慧明;李素芳;虞克明;曾慧芳;林静;;基于Gibbs抽样的贝叶斯金融随机波动模型分析[J];湖南大学学报(自然科学版);2008年12期
3 刘乐平;张美英;李姣娇;;基于WinBUGS软件的贝叶斯计量经济学[J];东华理工学院学报(社会科学版);2007年02期
4 李付军;;SV-GED模型在中国股市的VaR与ES度量及分析[J];系统工程理论方法应用;2006年01期
5 余素红,张世英;SV和GARCH模型拟合优度比较的似然比检验[J];系统工程学报;2004年06期
6 余素红,张世英,宋军;基于GARCH模型和SV模型的VaR比较[J];管理科学学报;2004年05期
7 余素红,张世英;SV与GARCH模型对金融时间序列刻画能力的比较研究[J];系统工程;2002年05期
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