基于极值理论的动态极端风险度量及其应用研究

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浙江财经学院硕士学位论文

摘要

2008 金融危机对各国金融市场秩序造成了严重破坏，大量金融机构倒闭，金

融资产价格大幅震荡，甚至连政府都陷入了破产的境地。虽然金融风险无处不在、

无时不有，但能够产生这样大规模破坏性影响的是这类隔几年甚至几十年才遭遇

一次的极端市场变动。因此，发展新的能够在极端情况下有效度量风险的工具对

于金融机构和监管当局来说有重大意义。对风险，特别是这类极端风险的防范不

应随着经济的逐渐复苏而放松。

本文旨在对用极值理论作为度量风险价值 VaR 的准确性和适用性作一改进。

极值理论作为对极端变动情况进行描述的一种统计方法，只对分布的尾部，而非

整个分布进行建模，且无需假设具体的分布类型，避免了模型风险。这是极值理

论的一大优点，但是用极值理论模型得到的 VaR 值可能相对保守，使得一些金融

机构没有动力运用这一模型来度量风险。而动态的极端风险度量模型则对此作了

改进。

本文将基于极值理论的动态 VaR 度量模型应用于中国的沪深股市，并将所得

结果与用传统的 VaR 度量方法所得结果进行比较，以分析本文所提出的模型所具

体适用的情况。本文主要分为理论环节和实证环节两个部分进行分析。

在本文的理论研究环节，首先简要介绍了 VaR 的相关理论，包括 VaR 的定义、

VaR 的传统计算方法、VaR 模型的准确性检验方法——回测检验以及用 VaR 度量风

险的优缺点。接着详细介绍了极值理论及其相关概念，在此基础上引入了基于极

值理论的 VaR 度量模型——区组最大值模型 BMM 和超阈值模型 POT，并将 GARCH

族模型与 POT 模型相结合，建立了基于 POT 模型的三个动态的 VaR 度量模型——

GARCH-POT 模型、GJR-POT 模型和 EGARCH-POT 模型。

在实证研究环节，本文选择了上证综指和深证成指较长期间的日收益率数据

作为样本。对其进行了基本的统计分析后，发现和大部分金融时间序列一样，我

们选择的样本数据具有尖峰厚尾的特征，且波动呈现集群现象，异方差性明显。

我们不假设样本的具体分布，用 BMM 模型和 POT 模型来拟合样本数据，根据参数

估计结果计算了 1 日的 VaR 值。根据本文提出的三个动态 VaR 度量模型，在估计

了 GARCH 模型、GJR 模型和 EGARCH 模型的参数后，用 POT 模型计算了标准化残差

的高分位数，最终结合条件均值和条件方差的预测值计算出 1 日的动态 VaR 值，

并与用传统方法计算的 1 日 VaR 作了最简单直观的比较。但要比较模型的好坏需

要作动态比较。最后，对本文所用的 VaR 计算模型进行回测检验，得出了比较分

析结果。

浙江财经学院硕士学位论文

结果发现，对于不同的金融机构或投资者，面对不同的市场需要适合特定情

况的风险度量模型。BMM 模型和 POT 模型，特别是 POT 模型，适合保守的金融机

构或投资者用于度量较高置信水平下的 VaR 值，而本文提出的三个动态风险度量

模型则对 POT 模型作了改进，使得其也适用于较激进的金融机构或投资者。相信

本文对于金融机构或监管当局管理金融风险具有一定的参考价值。

本文的研究工作系国家自然科学基金：期权组合非线性 VaR 度量模型及数值

方法研究（项目编号：70771099）资助项目。

关键词：风险价值(VaR)；极值理论（EVT）；广义极值分布(GEVD)；广义帕累托

分布(GPD)；GARCH 族

浙江财经学院硕士学位论文

III

ABSTRACT

The financial crisis started in 2008 has caused serious damage to the order of the

world’s financial markets, leading to collapse of large financial institutions, swings of

financial asset price and even the bankruptcy of governments. It takes such experience

only one extreme market movements few years or even decades to produce devastating

effects that such a large scale, though the financial risk is everywhere and at all times

there. Therefore, the development of new and effective risk measurement tool for

financial institutions and regulatory authorities in extreme cases is of great significance.

Risk, in particular the prevention of such extreme risk as the economy gradually

recovered should not be relaxed.

This thesis is intended to improve the accuracy and applicability of VaR based on

extreme value theory (EVT). As a statistical method of describing extreme changes,

extreme value theory only models the tail, rather than the entire distribution. And

without assuming a specific distribution type, EVT avoids the model risk. This is one

of the major advantages of extreme value theory, but the VaR values based on the

extreme value theory model are relatively conservative, this may make some financial

institutions have no incentive to use this model to measure risk. In this thesis, three

improved dynamic risk measurement models have been proposed.

In this thesis, the dynamic VaR measurement models based on EVT is applied to

measure China's Shanghai and Shenzhen stock market to analyze the proposed models

for the specific situation through the compare of the VaR measured with the traditional

method. This thesis is divided into theoretical part and empirical part.

Aspects of theoretical research, the related VaR theory, including the definition of

VaR, VaR of the traditional method, VaR model accuracy test methods - backtesting

and the advantages and disadvantages of VaR has been first introduced. Then based on

the extreme value theory models – BMM model and POT model, three dynamic

models - GARCH-POT models, GJR-POT model and the EGARCH-POT model have

been proposed.

In the empirical research part, we choose Shanghai Composite Index and

Shenzhen Component Index on a longer return period data as a sample. Its basic

statistical analysis shows that, like most financial time series, we selected sample data

浙江财经学院硕士学位论文

is fat-tailed and the fluctuations is clustered, which shows the heteroscedasticity. We do

not assume a specific distribution of the sample. After fitting the BMM model and the

POT model to the sample data, 1-day VaR value is obtained. Then we estimate the

parameters of proposed three dynamic VaR measurement models, predict 1-day ahead

conditional mean and conditional variance and calculate the median score of

standardized residuals with the POT model. The 1-day VaR values based on dynamic

VaR measurement models are finally obtained. Then we made a simple and intuitive

comparison. But to tell a good model needs to compare dynamically. Finally, the thesis

uses the backtesting to test the models, and make a comparison.

The results show that, faced with different market situations, different financial

institutions or investors need specific VaR measurement tools. The BMM model and

the POT model, especially the POT model, are suitable for conservative investors or

financial institutions to measure the VaR value at higher confidence levels. While the

proposed models have improved the performance of POT model, making it also apply

to aggressive financial institutions or investors.

Keywords: Value-at-Risk; Extreme Value Theory; Generalized Pareto

Distribution; Generalized Extreme Value Distribution; GARCH Family Models

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摘要：

浙江财经学院硕士学位论文I摘要2008金融危机对各国金融市场秩序造成了严重破坏，大量金融机构倒闭，金融资产价格大幅震荡，甚至连政府都陷入了破产的境地。虽然金融风险无处不在、无时不有，但能够产生这样大规模破坏性影响的是这类隔几年甚至几十年才遭遇一次的极端市场变动。因此，发展新的能够在极端情况下有效度量风险的工具对于金融机构和监管当局来说有重大意义。对风险，特别是这类极端风险的防范不应随着经济的逐渐复苏而放松。本文旨在对用极值理论作为度量风险价值VaR的准确性和适用性作一改进。极值理论作为对极端变动情况进行描述的一种统计方法，只对分布的尾部，而非整个分布进行建模，且无需假设具体的分布类型，避免了模...

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