兰州大学机构库 >数学与统计学院
基于R-vine的高维简化Pair Copula-GARCH类模型及应用
Alternative TitleSimplified Pair Copula-GARCH Models base on regular vines in high dimensions
毛泽强
Thesis Advisor焦桂梅
2013-05-26
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
KeywordCopula函数 GARCH类模型 Pair Copula分解 简化的正则藤 最大生成树 Vuong检验
Abstract近几年,利用图形藤的逻辑结构,将多资产组合的联合分布分解成一系列的Pair Copula模块,再利用Copula理论来研究资产组合间的相依结构与风险测度。这种Pair Copula-GARCH类模型流行的原因在于: 在模拟高维资产组合的相依结构时,其构造模块的灵活性与处理高维问题思想的简单性。然而,在实际应用与操作中,它暴露出以下缺点: 首先,Pair Copula的数目是维数的二次方,随着维数的增加迅速变大, 为选择Pair Copula类型带来很大不便; 其次,模型中待估参数的数目也会随着维数的增加迅速增大,极大的增加了计算的工作量; 最后,在实际应用中,当求出各资产的联合分布函数后,在计算风险度量指标VaR与CVaR时,增加了Monte Carlo 模拟的工作量,致使实际应用性较差。为了增强实际应用性,减少工作量与计算的复杂性,在有限的时间内得到比较满意的结果,大部分文献只介绍了基于特殊正则藤C-vine的简化方法,本文在此基础上研究了基于更一般正则藤的高维简化Pair Copula-GARCH类模型,此模型的主要构造方法是:首先利用变量间的相依测度,结合图论中的最大生成树算法构建一个恰当的易于简化的R-vine结构; 其次,尝试通过AIC/BIC或Vuong检验对R-vine进行简化,确定出有效简化水平k; 最后,对k之前的树选择不同的Pair Copula类函数描述每对资产相依结构,对k和k之后的树选择二变量Gaussian Copula函数进行简化,从而方便的构建出高维联合资产的分布函数。本文结尾部分通过16维的资产数据进行实证分析,结果表明简化的高维Pair Copula-GARCH类模型在实际应用中的简易性与有效性。
Other AbstractIn recent years, it is very popular to use a series of Pair Copula building blocks to construct joint distribution of the portfolio by the logical structure of regular vine and copula theory. This is due to their high flexibility, which makes them able to model a wide range of complex dependency structure in the high-dimensional portfolio. Nevertheless, these structures have some shortcomings in the practical application and operation. First of all, the number of Pair Copulas are quadratic of the dimension and increases rapidly as the dimension becomes larger. As a result, it will be to bring great inconvenience for the select of pair copulas type. Secondly, The number of estimated parameters grows exponentially with the dimension, the computational effort is very enormous and burdensome. In the end, it is also horrendous and burdensome to calculate the VaR or CVaR of the portfolio by means of the Monte Carlo simulation after we workout the joint distribution function of all the assets. In order to find the proper fitting one under limited time and computational resources, the paper introduces the Simplified Pair Copula-GARCH Models base on a more general regular vines in high dimensions, while most of the literatures proposed the simplified canonical vine copula using a multivariate copula. The main construction methods of this model are as follows. First of all, we will build a proper easy to simplify the structure of R-vine by the measures of dependence between variables and the maximum spanning tree algorithm in graph theory. Second, we try to determine the effective simplified level k of the structure of R-vine by means of AIC/BIC test or Vuong test. Then we choose different Pair Copulas to fit the structure of R-vine before the k trees and Gauss copulas to fit the rest trees of the structure of R-vine. At the end of the paper, we use them to investigate a 16-dimensional financial data set to testify and prove the feasibility and effectiveness in practical application.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225207
Collection数学与统计学院
Recommended Citation
GB/T 7714
毛泽强. 基于R-vine的高维简化Pair Copula-GARCH类模型及应用[D]. 兰州. 兰州大学,2013.
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