基于Pair-Copula的外汇投资组合风险分析
发布时间：2018-09-11 10:40
【摘要】：随着金融全球化,各国金融市场之间的关联性越来越密切,那么准确地度量金融市场间的相关性越来越重要。由于传统的相关性分析方法只能度量变量间的线性相关关系,且目前的金融市场间的相关性已经呈现出非线性、非对称和厚尾相依性等特点,所以原来的方法已远远不能够满足要求。Copula方法的出现给度量多变量间非线性相关关系提供了一个有效的工具。 本文主要研究多元Copula函数在金融风险管理上的一些应用,首先介绍了传统的多元Copula函数的类型及性质,并结合GARCH模型构建了Copula-GARCH模型来刻画金融时间序列间的相依结构。然后在传统多元Copula-GARCH模型的基础上,引入了最新的多元藤结构Pair-Copula来构建高维相关关系,由于它在刻画高维资产组合中两两资产间尾部相关性时可以根据实际数据的特征来选择不同类型的Copula函数,从而能够更好的刻画金融资产间尾部的相关性。 另外在Pair-Copula函数模型的选择上面,选择了三种类型的Copula函数：t-Copula、Clayton Copula和SJC Copula,二元t-Copula可以很好地反映变量间的上下尾相关性,Clayton Copula则可以快速捕捉下尾无条件相关的变化,SJC Copula可以快速捕捉下尾条件相关的变化。采用这三种函数类型,既关注了尾部的整体相关又特别描述了下尾的相关。 在实证部分,以我国外汇市场间的美元、日元、欧元、英镑对人民币四种汇率收益率序列为研究对象,分别采用多元正态Copula、 t-Copula函数与Pair-Copula函数来描述变量间的相依结构,并通过拟合优度检验得知,Pair-Copula在描述变量间的相依结构时更加准确。再将Pair-Copula-GARCH模型与Monte Carlo仿真技术相结合,计算了此模型下的多资产组合的VaR及ES,并与传统多元Copula-GARCH模型下计算出的资产组合VaR进行了比较,并给出了在风险最小原则下投资组合的最优解。结果表明,在所选择的样本期间内,基于Pair-Copula模型的预测的VaR结果要好于多元正态或多元t-Copula模型的预测效果,由此可以验证Pair-Copula-GARCH模型在构建多元相关结构的优越性。
[Abstract]:With the development of financial globalization, it is more and more important to measure the correlation between financial markets accurately. Because the traditional correlation analysis method can only measure the linear correlation between variables, and the correlation between financial markets has become nonlinear, asymmetric and thick tail. The Copula method provides an effective tool to measure the nonlinear correlation among multivariates.
This paper mainly studies the application of multivariate Copula function in financial risk management. Firstly, the types and properties of traditional multivariate Copula function are introduced, and then a Copula-GARCH model is constructed to describe the dependence structure of financial time series. Then, based on the traditional multivariate Copula-GARCH model, the newest one is introduced. Pair-Copula, a multivariate rattan structure, is used to construct the high-dimensional correlation. Because it can select different types of Copula functions according to the characteristics of the actual data when describing the tail correlation between two assets in a high-dimensional portfolio, it can better describe the tail correlation between financial assets.
In addition, on the selection of Pair-Copula function model, three types of Copula functions are selected: t-Copula, Clayton Copula and SJC Copula, binary t-Copula can well reflect the upper and lower tail correlation between variables, Clayton Copula can quickly capture the lower tail unconditionally related changes, SJC Copula can quickly capture the lower tail conditional phase. With these three types of functions, both the overall tail correlation and the tail correlation are described in particular.
In the empirical part, we take the US dollar, Japanese yen, Euro and Pound-to-Renminbi exchange rate return series as the research object, and use the multivariate normal Copula, t-Copula function and Pair-Copula function to describe the dependence structure between variables. Through the goodness of fit test, we find that Pair-Copula describes the dependence between variables. Combining Pair-Copula-GARCH model with Monte Carlo simulation technique, VaR and ES of multi-asset portfolio are calculated, and compared with VaR of portfolio calculated by traditional multi-element Copula-GARCH model, and the optimal solution of portfolio under the principle of minimum risk is given. During the selected sample period, the predicted VaR results based on Pair-Copula model are better than those based on multivariate normal or multivariate t-Copula model, which verifies the superiority of Pair-Copula-GARCH model in constructing multivariate correlation structure.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.59;F224;F830.7
本文编号：2236462
[Abstract]:With the development of financial globalization, it is more and more important to measure the correlation between financial markets accurately. Because the traditional correlation analysis method can only measure the linear correlation between variables, and the correlation between financial markets has become nonlinear, asymmetric and thick tail. The Copula method provides an effective tool to measure the nonlinear correlation among multivariates.
This paper mainly studies the application of multivariate Copula function in financial risk management. Firstly, the types and properties of traditional multivariate Copula function are introduced, and then a Copula-GARCH model is constructed to describe the dependence structure of financial time series. Then, based on the traditional multivariate Copula-GARCH model, the newest one is introduced. Pair-Copula, a multivariate rattan structure, is used to construct the high-dimensional correlation. Because it can select different types of Copula functions according to the characteristics of the actual data when describing the tail correlation between two assets in a high-dimensional portfolio, it can better describe the tail correlation between financial assets.
In addition, on the selection of Pair-Copula function model, three types of Copula functions are selected: t-Copula, Clayton Copula and SJC Copula, binary t-Copula can well reflect the upper and lower tail correlation between variables, Clayton Copula can quickly capture the lower tail unconditionally related changes, SJC Copula can quickly capture the lower tail conditional phase. With these three types of functions, both the overall tail correlation and the tail correlation are described in particular.
In the empirical part, we take the US dollar, Japanese yen, Euro and Pound-to-Renminbi exchange rate return series as the research object, and use the multivariate normal Copula, t-Copula function and Pair-Copula function to describe the dependence structure between variables. Through the goodness of fit test, we find that Pair-Copula describes the dependence between variables. Combining Pair-Copula-GARCH model with Monte Carlo simulation technique, VaR and ES of multi-asset portfolio are calculated, and compared with VaR of portfolio calculated by traditional multi-element Copula-GARCH model, and the optimal solution of portfolio under the principle of minimum risk is given. During the selected sample period, the predicted VaR results based on Pair-Copula model are better than those based on multivariate normal or multivariate t-Copula model, which verifies the superiority of Pair-Copula-GARCH model in constructing multivariate correlation structure.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.59;F224;F830.7
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