证券市场极端风险价值(VaR)计算方法研究和实证分析.pdf

重庆大学硕士学位论文中文摘要

摘要

近年来,金融市场的波动日益剧烈,一些金融危机事件接连发生,这些都对风
险管理提出了挑战,需要更加适合的模型方法来处理这些情况。实际研究表明传统
的正态分布模型假设严重低估了风险,为了更加精确的度量风险,很多学者提出用
在工程和寿险精算上得到广泛使用的极值理论来度量市场风险。极值分布不需要对
整个回报分布做任何假设,而是让数据说话,仅仅拟合分布的尾部,很适合度量风
险。由于采用基于极值理论的广义 Pareto 分布来研究市场风险在最近得到了广泛讨
论,所以本文拟采用它来研究中国股市。
本文在极值理论研究的基础上,探讨怎样用改进的历史模拟法来更加精确的估
计中国股市所面临的金融风险。其中核心的部分就是:目前对 EVT 理论的运用一般
都是选取 POT 模型,在 POT 模型中一个重要的问题就是阈值的选取,该值的大小
影响 VaR 值的准确性。阈值的选取方法目前常用的有三种,一种是超额限望图,二
是 Hill 图,另一种是与正态比较法。这三种阈值选取方法在实际应用中都有很多不
足之处。为了寻找其他阈值选取方法,本文创新性的应用格列汶科定理对历史模拟
法进行改进,以提高历史模拟法的计算准确性;并利用该方法来确定 POT 模型中的
阈值,以此新方法计算金融市场的风险价值(VaR)。并且考虑到金融收益不相关或
者弱相关的特性,即考虑到收益极值表现出来的波动聚类现象——幅度较大的波动
会相对聚集在某一时间段里,而小幅度波动会相对聚集在另一段时间上,故引入了
ARMA-AGARCH 模型过滤收益率数据的波动性和相关性。最后通过对上证指数
进行数值模拟研究,使用改进的 POT 模型计算金融市场的风险价值(VaR),取得
了比较理想的研究成果。

关键词:证券市场,极端风险价值,历史模拟法,POT 模型


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重庆大学硕士学位论文英文摘要

ABSTRACT

Recently, with the daily volatility of financial market and some financial catastrophic
events happened one by one, which put a challenge for risk management, we have been
long for some more appropriate models to deal with such events. Because the
conventional method to measure is based on normal distribution assumption which has
been proved to underestimate risk, in order to measure the risk more accurate, more and
more researchers put forward using extreme-value-theory to measure market risk which
has been used in engineering field widely. Because extreme-value-distribution need not to
put any hypothesis on the whole distribution of return but only by data themselves, fitting
the tail of distribution, which is fitted to measure risk. Currently, the Generalized Pare to
distribution based on extreme-value theory was widely used to study market risk. In the
paper, we prepare to use Generalized Pareto distribution based on extreme-value-theory to
study Chinese stock market.
It mainly on the basis of their predecessor’s Research of the extreme value theory, it
discussed how to use extreme value theory to es