基于Copula理论的金融时间序列统计特征的研究

发布时间：2018-09-14 20:26

【摘要】：任何金融产品投资都有风险,汇率也同样带有风险,但它是把双刃剑,由于内在的不确定性,使得汇率风险不仅能够给企业带来一定的损失,同样还有可能带来收益。越来越多的散户投资者及企业开始进入外汇市场,在充分了解外汇市场汇率波动情况后,利用一定规律来获得利润,特别是对于一些出口企业而言,他们可以重视外汇风险的估计和度量,以此来降低风险,提高抵抗风险的能力。同时,要与相关部门紧密联系,例如政府财政部门、银行、保险公司等,获得更多的信息,加强风险预警。在对金融资产投资组合进行分析时,相关性研究及其使用一种有效的联合分布模型十分重要,但是,传统的相关性分析,系数确定方面带有很大的局限性。因此,要充分了解和研究相关性分析中的每一个环节,例如投资组合、风险管理、资产定价、波动传导及溢出等多种变量,争取做到恰当更精准地分析金融资产风险问题。风险度量方面,VaR已成为应用最为广泛的方法,也是金融风险研究的重点；通过Copula构建金融资产组合的联合分布函数创造了一条便捷、科学的方法,使该联合分布可以满足金融资产所固有的尖峰厚尾特性——非正态、非线性相关,可以解决传统风险管理模型的正态线性相关性假设。本文研究内容主要是多种金融资产投资组合的相关性分析、度量问题,通过实例来研究Copula理论的建模方法及应用。基于Copula理论,通过将Copula函数.GARCH模型、VaR以及Monte Carlo方法有机结合,解决了多种金融资产的非正态、非线性相关建模问题,并且通过使用嵌套阿基米德Copula建立高维资产组合模型。首先第一部分实证研究对象是中国外汇市场几种主要外汇资产的投资组合,先通过GARCH模型族的比较研究确定了单个风险资产收益率的边际分布波动模型；然后运用PC算法估计了表示资产间相关结构,基于嵌套阿基米德Copula建模思想构建了高维嵌套阿基米德Copula模型,该模型能更好的描述资产组合间的相依结构；在高维嵌套阿基米德Copula模型的基础上利用Monte Carlo方法模拟了资产组合的VaR,并通过返回检验证明了模型的有效性。其次第二部分的实证研究是以中国外汇市场上四种外汇资产组合为对象,在该部分的研究中采用基于Pair Copula高维建模方法的混合C藤Copula模型及D藤Copula模型比较研究,实证外汇资产投资组合VaR的研究。在实证研究中,将两类模型在资产组合VaR计算精度方面进行比较。两部分的实证研究结果都表明,所建立的Copula模型都能更好的刻画金融资产间的相关结构,为风险度量方面提供便利条件。
[Abstract]:Any investment in financial products has risks, and exchange rate also has risks, but it is a double-edged sword. Because of the inherent uncertainty, exchange rate risk can not only bring certain losses to enterprises, but also may bring benefits. More and more retail investors and enterprises begin to enter the foreign exchange market. After fully understanding the exchange rate fluctuations in the foreign exchange market, they make use of certain rules to make profits, especially for some export enterprises. They can value the estimation and measurement of foreign exchange risk to reduce risk and improve their ability to resist it. At the same time, close contact with relevant departments, such as government finance departments, banks, insurance companies and so on, to obtain more information, strengthen risk warning. In the analysis of financial asset portfolio, it is very important to study the correlation and use an effective joint distribution model. However, the traditional correlation analysis and coefficient determination have great limitations. Therefore, we should fully understand and study every link in the correlation analysis, such as portfolio, risk management, asset pricing, volatility conduction and spillover, in order to analyze financial asset risk properly and accurately. In the aspect of risk measurement, VaR has become the most widely used method, and it is also the focus of financial risk research, which creates a convenient and scientific method to construct the joint distribution function of financial portfolio through Copula. The joint distribution can satisfy the characteristics of the financial assets such as non-normal, nonlinear correlation, and can solve the normal linear correlation hypothesis of the traditional risk management model. This paper mainly focuses on the correlation analysis and measurement of the portfolio of various financial assets, and studies the modeling method and application of Copula theory through examples. Based on Copula theory, by combining Copula function. GARCH model with Monte Carlo method, this paper solves the problem of non-normal and nonlinear correlation modeling of various financial assets, and establishes a high-dimensional portfolio model by using nested Archimedes Copula. The first part of the empirical research object is the portfolio of several major foreign exchange assets in China's foreign exchange market. Firstly, through the comparative study of GARCH model family, the marginal distribution volatility model of the return rate of individual risk assets is determined. Then using PC algorithm to estimate the correlation structure between assets, based on nested Archimedes Copula modeling idea to construct a high-dimensional nested Archimedean Copula model, this model can better describe the dependent structure between asset combinations; Based on the high dimensional nested Archimedes Copula model, the Monte Carlo method is used to simulate the VaR, of the portfolio and the validity of the model is proved by the return test. The second part of the empirical research is based on the Chinese foreign exchange market four foreign exchange portfolio as the object, in this part of the study based on Pair Copula high-dimensional modeling method based on mixed C-rattan Copula model and D-rattan Copula model comparative study. Empirical study of foreign exchange portfolio VaR. In the empirical study, the two models are compared in the accuracy of portfolio VaR calculation. The results of the two parts of empirical research show that the established Copula model can better describe the correlation structure between financial assets and provide convenient conditions for risk measurement.
【学位授予单位】：天津科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830;F224

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