【作者】 周广路；

【导师】 刘迎洲；

【作者基本信息】 西北农林科技大学 ， 应用数学， 2010， 硕士

【摘要】 近年来,世界上一些知名金融机构如巴林银行、日本大和银行等,虽具有较高管理水平,但都因对金融资产的管理或监控力度不足而遭受巨大损失乃至破产。这说明随着世界金融一体化进程的加快和各种衍生金融工具的创新和发展,在强化金融服务多元化、专业化、科学化的同时,风险的波动性和隐蔽性也增加了。因此,针对金融市场风险,如何较为准确地加以度量,建立完善的风险预警体制机制,成为金融机构和监管当局研究的热点问题。由J P Morgan集团开发的VaR模型,由于该方法简单有效,而且能全面度量整个机构的综合风险,于是很快得到了广泛的应用。Copula理论在金融领域上的应用是近几年的事情,它刻画了随机变量因子之间的相依关系。有研究表明,应用Copula技术描述风险之间的相依性更加符合金融市场的实际。Copula是利用样本数据和各种风险资产收益率的边缘分布来确定其联合分布的数学方法,是在构造多元联合分布以及随机变量之间相关结构分析中常用的工具,而VaR是基于统计分析基础上的风险度量技术,它的核心在于描述金融时间序列的统计分布或概率密度函数。因此copula技术在研究风险价值VaR时大有用武之地。本文介绍了VaR的定义及VaR的主要计算方法,然后简要介绍Copula相关理论,并应用Copula函数理论推导出投资组合收益率的概率密度函数,最后应用蒙特卡罗模拟方法和积分变换理论给出资产组合的风险价值VaR。以往国内对资产组合的风险价值VaR的实证研究,多数文献对收益率均采用正态性或对数正态性假设,而事实上,金融资产相关指标的统计特性是尖峰厚尾的,并非正态,文中拟构建模型、方法突破正态性限制。本文采用Copula函数构建了反映随机变量实际分布与相关性的联合分布函数及其联合概率密度函数,具有一般理论意义,克服了描述资产组合收益率分布的困难;同时以蒙特卡罗模拟方法和积分变换方法给出了VaR求解步骤,使得根据更接近现实的收益率联合分布函数来度量金融资产组合风险成为可能。模型能够反映收益率的时变相关性和波动性。更多还原

【Abstract】 In resent years, many well-known financial Institutions such as the Daiwa Bank, the Bahrain Bank, though sophisticated in administration, all suffered great loss as to the extent of collapse, due to inadequate administration or monitor. All this adds to the fact that with the acceleration of global finance integration and the innovation and development of the derivative financial instruments, while we are strengthening the diversification, specialization and scientificalization of financial services, the volatility and concealment of risks are also increased. So, how to accurately measure financial risks, establish perfect risk warning systems and mechanisms, has become a hot issue of financial institutions and regulatory authorities.The VaR (Value at risk) model, developed by the J P Morgan Group, due to its simplicity, efficiency and capacity to measure the integrated risks of financial institutions, has got widespread application.The application of copula theory in the financial sector happened just a few years ago. It describes the dependence of random variables. Research shows that it meets the real financial market when using the copula theory to describe risk dependences. Copula is a theory which uses sample data and marginal distributions of the returns’ratio to determine the joint distribution of the portfolio’s return, it is one of the tools that are mostly used in both the construction of joint distributions and the analysis of the dependence between random variables. Based on the statistical analysis, the VaR model, as a risk measure technique, has a core issue which lies in the description of the statistical distribution or the probabilistic density of financial time series. So, it comes in handy when using the copula theory to study VaR.This paper showed the definition and the main calculation methods of VaR and then briefly introduced the related theories of copula, and using the copula theory, this paper deduced the probabilistic density of portfolio’s return ratio. At last, this paper gives the solution of VaR based on both the Monte Carlo simulation method and the integral transformation method. In the past, most empirical literature adopted a normal or lognormal assumption on return’s ratio; however, it turned out to be not the case. The statistical characteristics of some financial assets’indicator are peak and fat tail, not normal. This paper intended to establish a model or method to overcome the normal restrictions. This paper established the random variables’joint distribution and probabilistic density which can reflect their dependence. The result is theoretically significant and overcomes the difficulty when describing the joint distributions of returns’ratio. Meanwhile, this paper gives the solution of VaR based on both the Monte Carlo simulation method and the integral transformation method and makes it possible to calculate the risks of portfolios according to some real distributions. This method could reflect time-varying relevance and volatility of returns’ratio.更多还原