【作者】 李琳；

【导师】 史道济；

【作者基本信息】 天津大学 ， 应用数学， 2003， 硕士

【摘要】 风险价值(Value-at-Risk, VaR)是从20世纪90年代初期开始发展起来的一种金融市场风险测量的方法,其核心思想是计算由于市场价格波动导致金融资产所面临的市场风险的大小.精确度量风险价值VaR和由此衍生来的条件风险价值 CVaR是对风险管理者的挑战.广泛应用的正态分布不足以描述金融收益的厚尾特征,尤其是风险管理者最为关心的较大分位数.而应用极值理论计算风险时注重对分布尾部的近似表达,而不是对整个分布进行建模,从而能更有效地捕捉可能导致的尾部风险,所以,把极值理论应用于风险量化分析不失为一种比较理想的方法.极值理论(EVT)主要是研究随机变量或过程的极端情况的统计规律性.经典的极值模型要求数据是独立同分布的,实际中,我们发现很多数据存在局部相关性,从而引起极值的成串出现.对于平稳序列,可以引入极值指标来描述数据之间的相关结构,利用分串(declustering)方法去除数据间的相关性,得到独立同分布序列,再按传统的方法,建立超阈值模型(POT模型),得到改进后的VaR和CVaR.本篇论文首先介绍了金融风险的相关知识,回顾了金融风险测量技术的演变历程,总结了VaR在国内外的研究现状,介绍了VaR的概念、计算原理及方法. 由于VaR的计算方法多样,适用于不同的市场条件、数据水平、精度要求等,本文综合比较了VaR的多种计算方法,指出各自的优缺点及适用的场合.接着分析了VaR风险管理技术之所以被国际金融界广泛认可的优点,同时也指出了作为一个金融数理模型所存在的缺陷,以及对我国的借鉴意义.并对由VaR衍生出来、更接近于投资者真实心里感受的一致性风险价值度量方法条件风险价值CVaR进行了介绍和分析.然后借助于日元/美元的汇率数据,对平稳序列对应的VaR和CVaR展开研究.为了能更准确地反映金融机构面临的市场风险,进行深层次的、全面的管理金融风险,本文最后从以下几方面展开了风险价值度量方法的研究:多元非正态分布族,投资组合中相关性度量方法及Copula函数.本篇论文旨在运用极值理论等相关知识提高VaR的适用性和估计的精确度,相信本文对金融机构应用VaR、CVaR控制市场风险具有重要的参考价值和指导意义.更多还原

【Abstract】 As a financial market risk measurement, VaR (Value-at-Risk) appeared at the early part of 1990’s. The risk management technique about VaR is a statistical model and method used to estimate and measure finance market risk. The correct estimates of VaR and CVaR are the real challenges to risk managers. The normal distribution is very often inadequate for the description of real financial data with heavy-tail distributions, especially very large quantile that interest to a risk manager. Extreme Value Theory models the tail of the return distribution rather than the whole distribution. It can capture the tail risk that often causes large losses in financing institutions, so it is a good approach for risk measurement in finance field.Extreme Value Theory is used to analysis the extreme values of random vectors and processes by the statistic methods. The classic extreme value theory requests that series is independent and has identical distribution. This paper introduces the extremal index under the assumption that the series is stationary, builds a POT model by using the method of declustering, and then calculates the estimates of VaR and CVaR.In this article, I introduce the knowledge about financial risk, look back the development of the technology of risk measurement, sum up the present situation about domestic and foreign VaR research, and introduce the concept and computing theorem in detail, synthetically compare all these computing methods, and analyze the advantages and the disadvantages as the model of mathematical statistical model. Then I analyze CVaR which be derived from VaR and approach more closely to the real feeling of investors. Following,I research the VaR and CVaR of JPY/USD foreign exchange rate, the result proved that the accurate for the estimations have been improved by introducing the extremal index. In order to expose more exactly of the market risk faced by financing institutions, and manage risk more deeply and completely, This article expands research in the following aspects: multivariate abnormal distribution family, the measurement of correlation function in the portfolio selection and Copula function.This article aims at improving the applicability and precision of VaR by using the knowledge of Extreme value theory and etc.. I believe that this article is instructive for our financial institutions to control market risk.更多还原