【作者】 王皓；

【导师】 蒋岳祥；

【作者基本信息】 浙江大学 ， 金融学， 2008， 硕士

【摘要】 目前,很多有关金融风险的研究都是针对均值、方差、相关性,很少有人关注极端的波动情况。然而,一个又一个的教训已明确地表明忽略极端风险会带来巨大的损失,因此迫切需要一种工具来准确地测度它。极值理论(EVT)正是这样一种方法,它能有效地预测和防范金融极端风险。本文就是要将极值理论应用于测度中国股市VaR的实证研究之中。本文首先介绍了有关VaR的基本内容,包括其定义、应用领域及传统的测度方法,并系统地对国内外文献进行了综述,接着阐述了极值理论自诞生以来的主要研究成果。在极值理论基本原理的基础上,本文总结了应用于VaR研究的三个极值模型,随后将其用于中国深沪两市股指日对数收益率的研究中。通过分析与比较,得到以下结论:(1)传统的VaR测度方法会低估潜在的损失,特别是在极端风险的刻画上,其估计值是无效的;(2)BMM模型能较好地反映故股指日对数收益率极大值和极小值序列的尾部特性;(3)GPD模型没有理论描述的那么完美,但通过与GARCH模型相结合,能显著提高其预测能力;(4)实证研究表明深沪两市股指日对数收益率的极大值序列是服从Frechet分布,极小值序列服从Gumbel分布,并由此得到了较为准确的VaR估计值。(5)股指日对数收益率极值序列所属的极值分布类型会随着市场形势的变化而变化。最后,本文探讨了极值方法未来在理论和实践上的一些研究方向,并对全文进行了总结。更多还原

【Abstract】 Nowadays, most of the empirical studies and models concern average properties like expected returns, volatility, or correlations, and little attention has been given to the extreme movements. However, a lot of lessons have told us that neglecting extreme risk will cause huge loss, and we must find certain tool to reflect and estimate it correctly. Extreme value theory (EVT) is one of the best choices, which can effectively forecast and guard against the financial risk. This article presents an application of extreme value theory to compute the value at risk of Chinese stock market.Firstly, this article talks about some basic idea on the VaR, such as its definition, application and some traditional ways to compute it. Secondly the representative studies from foreign and domestic scholars are systematically summarized. Then this article introduces the principle of EVT, and based on these theories, three VaR models are discussed, including the different ways on estimating the parameters. Thirdly, these EVT-VaR models are applied to the study on Chinese stock index daily returns. Through the application and comparison, some results were found: (1) The traditional ways to compute the VaR will underestimate the potential risk, so they are not effective, especially when used to analyzing the extreme risk; (2) BMM model can accurately reflect the tail of the distribution of stock index minimum and maximum daily returns; (3) GPD model is not as good as expectation, but its combination with GARCH model can raise the accuracy of forecasting; (4) The empirical study discovered that the tail of the distribution of stock index maximum daily returns follows Frechet distribution, and the tail of the distribution of stock index minimum daily returns follows Gumbel distribution. (5) The tail of the distribution of stock index daily returns will change with time. Based on EVT, the accurate estimator of VaR was got, which is very helpful in analyzing the extreme movements. At the last, this part discusses the further development of the research on EVT, and summarizes the whole article.更多还原