兰州大学机构库 >数学与统计学院
基于Copula与Monte Carlo方法的投资组合风险计量
Alternative TitleRisk measurement of portfolio based on Copula and Monte Carlo approach
李育峰
Thesis Advisor严定琪
2009-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
KeywordVaR MaxVaR Copula GARCH Monte Carlo模拟
AbstractCopula是把多维随机变量的边缘分布连接起来形成联合分布的函数。变量间的相关结构可以完全由Copula描述,各变量的统计特征由 其边缘分布确定。Copula已经成为流行的多变量建模工具,广泛地应用于风险管理、投资组合选择、资产定价等金融领域。 VaR的出现使得金融资产组合在一定时期所面临的最大可能损失的定量化成为可能。目前,VaR已经成为金融风险管理系统的奠基石。然而,VaR只考虑持有期末的风险,没有考虑持有期内资产价格变动及可能的现金流出问题,也没有考虑在持有期末之前进行交易的问题。MaxVaR与标准VaR方法相比,不只考虑期末的风险,还考虑持有期内的风险,它是盯市环境下的有力的风险度量工具。 本文应用Copula-VAR-GARCH模型描述金融数据,通过Monte Carlo模拟计算投资组合的VaR与MaxVaR。在实证分析中,选取五种代表性的Copula并结合带正态分布和学生t分布的GARCH模型描述沪深300指数与恒生指数收益率,通过Monte Carlo模拟计算投资组合的VaR与MaxVaR,并对各种模型的拟合能力做了对比。最后,对不同置信度下MaxVaR与VaR的大小关系进行了分析。
Other AbstractCopula couples the marginal distributions together to form a joint distribution.The dependence relationship is entirely determined by the Copula,while statistical descriptions are entirely determined by the marginal distribution.Copulas have become a popular multivariate modeling tool in many fields such as risk management, portfolio selection and asset pricing. The emergence of VaR enables us to quantify the maximum loss of financial portfolios in certain period.And it has become the foundation of financial risk measurement system up to now.Comparing with the standard VaR approach,MaxVaR considers not only terminal risk but also interim risk.It is a powerful risk measurement tool in a mark-to-market environment.We use Copula-VAR-GARCH model to imitate financial time series and compute the MaxVaR and VaR by Monte Carlo simulation. In empirical research,we apply five different Copulas and GARCH model to imitate the return rate of HuShen 300 index and Hang Seng Index,then compute the MaxVaR and VaR by Monte Carlo simulation.We find that the model with normal marginal distribution can give better VaR and MaxVaR estimations than the model with student-t marginal distribution which significantly overestimate the risk of the investment portfolio.At the end of this paper,we analyze the ratio of MaxVaR to VaR.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225250
Collection数学与统计学院
Recommended Citation
GB/T 7714
李育峰. 基于Copula与Monte Carlo方法的投资组合风险计量[D]. 兰州. 兰州大学,2009.
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