金融资产动态相关性方法及应用研究
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摘要
在许多金融计量问题中,例如衍生产品定价、风险管理、套期保值和最优投资组合选择等,模拟和预测二阶矩的相关性和各个市场收益之间波动性的动态相关关系有很重要的意义。目前研究动态相关关系的角度有三类,第一类是利用多维时间序列的角度进行研究,第二类是利用多维随机过程进行研究,第三类是利用Copula理论研究随机变量之间的相关程度。本文主要从多维时间序列的角度对相关性分析进行理论方法的研究和实证分析。
论文第一章对本文的选题意义、方法的创新和缺陷进行了总结。论文的第二章回顾了多维时间序列相关性模型的发展历程以及估计方法和诊断检验,并对各种模型的优缺点和适用性进行了比较评述。论文的第三章和第四章运用各种多维时间序列进行预测分析和风险分析,实证结果表明,同其他模型相比,用ADCC模型拟合中国股指收益率的方差协方差矩阵效果较好,这个结果可以为资产配置决策、风险管理提供理论性的指导。
论文的第五章提出了一种处理高维金融时间序列的新方法一基于Cholesky分解方法的SCC(序列条件相关)方法,并进行理论研究和实证分析。近年来出现了大量多维GARCH模型来模拟资产组合的波动性及相关性,但是在估计多维GARCH模型中仍存在着不尽如人意的地方,资产数量过多困扰着估计时的最优化问题,即使随着模型的逐渐改善,参数估计仍然十分困难,因此许多文献都停留在二维或三维GARCH模型的估计,很难推广到高维GARCH模型。本文提出了一种处理高维相关矩阵的估计方法—SCC方法,此方法非常灵活,可以把高维相关矩阵的估计问题转化为二维相关矩阵的估计,并且允许二维相关矩阵的估计采用各种灵活的二维GARCH模型或其他新的方法进行分别估计,然后再组合为一个高维相关矩阵。这种新方法未来的发展不仅仅局限于和二维GARCH模型相结合,它也可以与任何描述二维动态相关性的最新理论,譬如动态的Copula理论相结合,从而更好地解决高维动态相关性的问题,是一种理论的突破。
论文的最后一章对全文进行了总结,并提出了今后所做的工作,和未来关于动态相关性发展的方向。
总之,论文研究了动态相关性的预测以及在风险上的应用,同时针对金融资产高维相关性目前存在的估计上的困难,提出了一种基于Cholesky分解方法的SCC方法,并给出了理论证明和完善。
Modeling the temporal dependence in the second order moments and forecasting future volatility have key relevance in many financial econometric issues such as risk evaluation, derivatives pricing, and optimal portfolio choice. We review different specifications of dynamic correlation. They differ in various aspects. We distinguish three approaches for constructing correlation models: (1) multivariate time series; (2) multivariate stochastic process; (3) copula theory.
The dissertation includes five sections. After the brief introduction (chapter one), in chapter two, the dissertation reviews the overseas development of multivariate correlation, and then comments the advantage, disadvantage and applicability of different models. Then from chapter three to chapter four, the dissertation uses the different multivariate GARCH model, including ADCC, CCC, and Riskmetrics method, to study the forecast and risk management of Chinese Indices Portfolio. The empirical results show that: ADCC multivariate GARCH model is best among them. This result offers theoretic support to portfolio and risk management.
Chapter five presents a new approach to the modeling of the conditional correlation matrix in the large cross-sectional dimension based on Cholesky method. Many multivariate GARCH models have been developed in the recent years to model the conditional second moments. However, all of them must make the trade-off between parameters' parsimony and richness in the description of the second order moments dynamics. In fact, the number of parameters of a fairly rich multivariate volatility model soon becomes large enough to render estimation infeasible. The key feature of the SCC based on Cholesky is the decomposition of the conditional correlation matrix into the product of a sequence of matrices with desirable characteristics. Then a highly dimensional and intractable optimization problem is converted into a series of simple and feasible estimations. Moreover, the latest methods dealing with two dimensional correlation matrix can combine with SCC to solve complex problems.
In a word, the dissertation studies forecast of dynamic correlation and application in financial risk. And then the dissertation introduces SCC method based on Cholesky decomposition to handle a highly dimensional correlation matrix and gives theory result.
论文第一章对本文的选题意义、方法的创新和缺陷进行了总结。论文的第二章回顾了多维时间序列相关性模型的发展历程以及估计方法和诊断检验,并对各种模型的优缺点和适用性进行了比较评述。论文的第三章和第四章运用各种多维时间序列进行预测分析和风险分析,实证结果表明,同其他模型相比,用ADCC模型拟合中国股指收益率的方差协方差矩阵效果较好,这个结果可以为资产配置决策、风险管理提供理论性的指导。
论文的第五章提出了一种处理高维金融时间序列的新方法一基于Cholesky分解方法的SCC(序列条件相关)方法,并进行理论研究和实证分析。近年来出现了大量多维GARCH模型来模拟资产组合的波动性及相关性,但是在估计多维GARCH模型中仍存在着不尽如人意的地方,资产数量过多困扰着估计时的最优化问题,即使随着模型的逐渐改善,参数估计仍然十分困难,因此许多文献都停留在二维或三维GARCH模型的估计,很难推广到高维GARCH模型。本文提出了一种处理高维相关矩阵的估计方法—SCC方法,此方法非常灵活,可以把高维相关矩阵的估计问题转化为二维相关矩阵的估计,并且允许二维相关矩阵的估计采用各种灵活的二维GARCH模型或其他新的方法进行分别估计,然后再组合为一个高维相关矩阵。这种新方法未来的发展不仅仅局限于和二维GARCH模型相结合,它也可以与任何描述二维动态相关性的最新理论,譬如动态的Copula理论相结合,从而更好地解决高维动态相关性的问题,是一种理论的突破。
论文的最后一章对全文进行了总结,并提出了今后所做的工作,和未来关于动态相关性发展的方向。
总之,论文研究了动态相关性的预测以及在风险上的应用,同时针对金融资产高维相关性目前存在的估计上的困难,提出了一种基于Cholesky分解方法的SCC方法,并给出了理论证明和完善。
Modeling the temporal dependence in the second order moments and forecasting future volatility have key relevance in many financial econometric issues such as risk evaluation, derivatives pricing, and optimal portfolio choice. We review different specifications of dynamic correlation. They differ in various aspects. We distinguish three approaches for constructing correlation models: (1) multivariate time series; (2) multivariate stochastic process; (3) copula theory.
The dissertation includes five sections. After the brief introduction (chapter one), in chapter two, the dissertation reviews the overseas development of multivariate correlation, and then comments the advantage, disadvantage and applicability of different models. Then from chapter three to chapter four, the dissertation uses the different multivariate GARCH model, including ADCC, CCC, and Riskmetrics method, to study the forecast and risk management of Chinese Indices Portfolio. The empirical results show that: ADCC multivariate GARCH model is best among them. This result offers theoretic support to portfolio and risk management.
Chapter five presents a new approach to the modeling of the conditional correlation matrix in the large cross-sectional dimension based on Cholesky method. Many multivariate GARCH models have been developed in the recent years to model the conditional second moments. However, all of them must make the trade-off between parameters' parsimony and richness in the description of the second order moments dynamics. In fact, the number of parameters of a fairly rich multivariate volatility model soon becomes large enough to render estimation infeasible. The key feature of the SCC based on Cholesky is the decomposition of the conditional correlation matrix into the product of a sequence of matrices with desirable characteristics. Then a highly dimensional and intractable optimization problem is converted into a series of simple and feasible estimations. Moreover, the latest methods dealing with two dimensional correlation matrix can combine with SCC to solve complex problems.
In a word, the dissertation studies forecast of dynamic correlation and application in financial risk. And then the dissertation introduces SCC method based on Cholesky decomposition to handle a highly dimensional correlation matrix and gives theory result.
引文
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[7] Bauwens, L, S. Laurent, and J.V.K. Rombouts. Multivariate GARCH Models: A Survey [J]. Journal of Applied Econometrics 2006, 21: 79-110.
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