基于Copula理论的多金融资产定价与风险测度
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摘要
Copula理论的提出为解决多元联合分布的构建以及变量间的非线性相关性问题提供了一个灵活实用的统计方法。本文主要探讨了将Copula理论应用在金融领域,分析基于Copula理论的多金融资产定价与风险测度的建模方法与应用。本文的主要工作如下:
简单介绍了Copula理论的基本原理与应用方法,目前国内外对Copula理论研究的进展情况,本文的研究思路、方法与应用方向。目前将Copula理论应用于金融领域存在许多问题:多应用在金融风险分析领域;大多采用同一种分析方法(Copula-GARCH方法)对不同金融问题进行分析;很少用Copula理论来分析多个标的资产的衍生品定价问题。本文从如下几个角度对Copula理论在金融领域的应用进行了系统分析研究。
一,虽然Copula-GARCH模型在分析多元时间序列中具有很多优越性,但是目前Copula-GARCH模型只是用于测度多个资产的收益率的相关模式与相依性,对波动之间的关系描述几乎没有涉及。因为SV模型亦是金融波动性建模的一种重要方法,而且在刻画变量波动性方面较GARCH模型更加细致。基于此,本文应用Copula理论,建立Copula-SV模型,该模型可以同时描述多个资产的收益率之间的相依关系与波动之间的相关关系。
二,高频数据的单变量的已实现波动建模理论比较成熟。但是对多变量高频数据波动之间的相依关系的细致刻画以及建模问题,国内外文献探讨较少。本文基于Copula理论,用对分析高频数据的已实现波动方法,建立Copula-RV模型,讨论了多变量高频数据已实现波动的动态相依关系。
三,目前对衍生品定价的研究多考虑单个标的资产衍生品的定价问题,对多个标的物衍生品定价模型与求解比较复杂,本文考虑衍生品的多个标的资产相依关系,建立了基于Copula理论的多个股票为标的物的期权定价模型,并给出了基于多个资产标的物的期权定价方法。
四,Copula函数对多个变量的联合分布的构建具有重要作用,但是边缘分布也是构建联合分布的重要内容。本文通过仿真试验分析了Copula函数可以将变量的边缘分布与相依结构统一在联合分布中研究,解释了联合分布不依赖于其边缘分布的原因,说明了Copula函数在构建联合分布的重要作用。
Copula functions provide a flexible and useful statistic tool to construct the multivariate joint distribution and to analyze the multivariate dependency structure. The paper studies the application of the Copula theory in the financial field including modeling and analysis of financial assets pricing and risk measurement. The main work of the dissertation is as follows:
It is briefly reviewed that the basic theories and methods, recently empirical research and then provides the technical methods and makes the prospect on the key research in the future. There are problems in recent application of Copula theory, such as many researches are in the field of financial risk management, during the course of being used, only the Copula-GARCH model is considered, and rare Copula models are used in the derivate assets pricing. As for these reasons, the paper does some work analyzing the application of the Copula theory in the financial field from five points of view.
1. The Copula-GARCH model has widely been used in the multivariate time series to measure the dependence of the assets returns rather than assets volatilities. The SV model can describe the volatility more exactly than the GARCH model. The Copula-SV model is used to analyze the dependence of the assets returns and volatilities at the same time.
2. The research of high-frequency data has been prevail but now is fasten on one variant mostly and rare multivariate high-frequency data problems are studied. Realized volatility is a volatility estimator based on high-frequency data. Modeling the Copula-RV we analyze the dynamic dependence structure of Shanghai and Shenzhen stock markets.
3. There are many difficulties in derivative pricing such as the departure from normality, emerging from the smile effect and market incompleteness. Many models about derivative pricing are based derivative. The main advantage of Copula functions enables to pricing derivatives based on several options. This paper models multivariate options pricing model based on the Copula theory and presents the modeling methods.
4. The Copula functions are the joint distribution of multivariate. They enable us to tackle the problem of specification of marginal univariate separately from the specification of multivariate comovement and the dependence. The copulas do not depend on the marginal distributions explained by the simulation test and they play an important role in the construction of multivariate distributions.
简单介绍了Copula理论的基本原理与应用方法,目前国内外对Copula理论研究的进展情况,本文的研究思路、方法与应用方向。目前将Copula理论应用于金融领域存在许多问题:多应用在金融风险分析领域;大多采用同一种分析方法(Copula-GARCH方法)对不同金融问题进行分析;很少用Copula理论来分析多个标的资产的衍生品定价问题。本文从如下几个角度对Copula理论在金融领域的应用进行了系统分析研究。
一,虽然Copula-GARCH模型在分析多元时间序列中具有很多优越性,但是目前Copula-GARCH模型只是用于测度多个资产的收益率的相关模式与相依性,对波动之间的关系描述几乎没有涉及。因为SV模型亦是金融波动性建模的一种重要方法,而且在刻画变量波动性方面较GARCH模型更加细致。基于此,本文应用Copula理论,建立Copula-SV模型,该模型可以同时描述多个资产的收益率之间的相依关系与波动之间的相关关系。
二,高频数据的单变量的已实现波动建模理论比较成熟。但是对多变量高频数据波动之间的相依关系的细致刻画以及建模问题,国内外文献探讨较少。本文基于Copula理论,用对分析高频数据的已实现波动方法,建立Copula-RV模型,讨论了多变量高频数据已实现波动的动态相依关系。
三,目前对衍生品定价的研究多考虑单个标的资产衍生品的定价问题,对多个标的物衍生品定价模型与求解比较复杂,本文考虑衍生品的多个标的资产相依关系,建立了基于Copula理论的多个股票为标的物的期权定价模型,并给出了基于多个资产标的物的期权定价方法。
四,Copula函数对多个变量的联合分布的构建具有重要作用,但是边缘分布也是构建联合分布的重要内容。本文通过仿真试验分析了Copula函数可以将变量的边缘分布与相依结构统一在联合分布中研究,解释了联合分布不依赖于其边缘分布的原因,说明了Copula函数在构建联合分布的重要作用。
Copula functions provide a flexible and useful statistic tool to construct the multivariate joint distribution and to analyze the multivariate dependency structure. The paper studies the application of the Copula theory in the financial field including modeling and analysis of financial assets pricing and risk measurement. The main work of the dissertation is as follows:
It is briefly reviewed that the basic theories and methods, recently empirical research and then provides the technical methods and makes the prospect on the key research in the future. There are problems in recent application of Copula theory, such as many researches are in the field of financial risk management, during the course of being used, only the Copula-GARCH model is considered, and rare Copula models are used in the derivate assets pricing. As for these reasons, the paper does some work analyzing the application of the Copula theory in the financial field from five points of view.
1. The Copula-GARCH model has widely been used in the multivariate time series to measure the dependence of the assets returns rather than assets volatilities. The SV model can describe the volatility more exactly than the GARCH model. The Copula-SV model is used to analyze the dependence of the assets returns and volatilities at the same time.
2. The research of high-frequency data has been prevail but now is fasten on one variant mostly and rare multivariate high-frequency data problems are studied. Realized volatility is a volatility estimator based on high-frequency data. Modeling the Copula-RV we analyze the dynamic dependence structure of Shanghai and Shenzhen stock markets.
3. There are many difficulties in derivative pricing such as the departure from normality, emerging from the smile effect and market incompleteness. Many models about derivative pricing are based derivative. The main advantage of Copula functions enables to pricing derivatives based on several options. This paper models multivariate options pricing model based on the Copula theory and presents the modeling methods.
4. The Copula functions are the joint distribution of multivariate. They enable us to tackle the problem of specification of marginal univariate separately from the specification of multivariate comovement and the dependence. The copulas do not depend on the marginal distributions explained by the simulation test and they play an important role in the construction of multivariate distributions.
引文
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