金融模型和收益率分布形式的正确选择是估计波动率至关重要的一步
Realized GARCH 模型将 GARCH 模型与已实现波动率结合，用已实现测度来更
灵敏地反应波动水平，有效地减轻了传统波动模型中存在的弊端。而 NIG 分布
由于包含了广义双曲列维过程的诸多优点，适用于很多种情况，尤其是市场极
端时期。因此，本文采用误差项服从 NIG 分布的 Realized GARCH 模型，拟合
上证综指的收益率分布和波动率，并与先前使用较为广泛的误差项服从正态分
布、t 分布、偏 t 分布的 Realized GARCH 模型和误差项服从正态分布、t 分布、
偏 t 分布、NIG 分布的 GARCH 模型进行对比分析。随后，本文又进一步将样
本数据进行了更为细致的划分，根据不同经济形势将整体观测时段分为了金融
危机前期、金融危机时期、金融危机后期和中国股市振荡期四个阶段。实证结
果证明，在极端情况下，Realized GARCH-NIG 模型能够更为精确地描述中国
股市的波动性，Realized GARCH 模型的预测能力也优于 GARCH 模型，体现了
其在风险模拟以及风险预测方面的优越性。而相比于对总体样本直接建模，将
分段后的数据进行分别建模可以更为精准地反映股市的波动状况。同时，在对
厚尾分布模型的 VaR 和 ES 风险预测结果进行对比后发现， ES 风险测量方法
可以弥补 VaR 模型可能会低估厚尾分布模型尾部风险的不足
关键词：Realized GARCH，NIG 分布，厚尾分布，波动率，VaR，ES，金融
危机III
ABSTRACT
As the trend of economic globalization increases obviously, the volatility of
stock markets are also inextricably linked. For developing China, economic
globalization brings more opportunities and resources, which promotes China’s
unprecedented economic leap in a short time. On the other hand, the economic
environment of China, even the world, is bocoming more complex and changeable.
Morever, the risk is increasing. Therefore, only grasping the law of volatility of stock
markets, especially the volatility in extreme times, can we predict and avoid risk
effectively.
The correct selection of both the financial models and the distribution of returns
is of vital importance when estimating the volatility of stock market. Realized
GARCH model combines GARCH model with realized volatility. Using realized
measures to reflect volatility can overcome the drawbacks in the traditional
fluctuation model. And because NIG distribution contains many advantages of
generalized hyperbolic levy process, it is applicable to a variety of situations,
especially the extreme times of stock market. Hence, In this paper, Realized GARCH
model which error term follows NIG distribution, is used to fit the volatility and
return distribution of Shanghai composite index. And then, the result is compared
with another results when using Realized GARCH model which error term follows
normal distribution, t distribution, skewed-t distribution respectively as well as
GARCH model which error term follows normal distribution, t distribution,
skewed-t distribution, NIG distribution respectively. Afterwards, according to
different economic environments, this paper divides the samples in a more detailed
way. The whole observation period is divided into four time phases: the pre-financial
crisis period, the financial crisis period, the post-financial crisis period and the
oscillation period of China’s stock market. The empirical result shows that, in
extreme cases, Realized GARCH-NIG model can describe the volatility of China’s
stock market much more accurately. The forcasting ability of Realized GARCH
model is also superior to GARCH model, which reflects its superiority in risk
simulation and prediction. Furthermore, compared to using the overall samples
directly, modeling the data of different time phases gives more precise outcome of
stock market’s volatility. At the same time, after making a comparison between VaRIV
and ES risk prediction results, it is found that ES risk measurement can make up the
shortfall of VaR model when estimating the tail risk of the models based on fat-tailed
distribution.
KEY WORDS: Realized GARCH，NIG distribution，Fat-tailed distribution，
Volatility，VaR，ES，Financial crisis目录
中文摘要I
ABSTRACT ... III
第 1 章 绪论......1
1.1 研究背景及研究意义..1
1.1.1 研究背景1
1.1.2 研究意义2
1.2 文献综述..........2
1.2.1 GARCH 模型......2
1.2.2 已实现测度........5
1.2.3 Realized GARCH 模型...6
1.2.4 模型分布7
1.2.5 VaR 测量 .9
1.2.6 ES 测量 .11
1.3 文章创新点....13
1.4 研究思路及文章框架14
1.5 本章小结........16
第 2 章 理论模型及分布选择17
2.1 理论模型........17
2.1.1 GARCH 模型....17
2.1.2 已实现测度......17
2.1.3 Realized GARCH 模型.18
2.2 分布选择........19
2.2.1 学生 t 分布.......19
2.2.2 偏 t 分布...........19
2.2.3 NIG 分布...........20
2.3 本章小结........21
第 3 章 基于 Realized GARCH 模型的上证综指波动性研究.......23
3.1 数据选取及预处理.....23
3.2 收益率序列的自相关检验.....24
3.3 收益率序列的 Q-Q 图253.4 收益率序列的核密度曲线.....25
3.5 收益率序列的直方图.
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