摘要
论文题目：基于ARJI-GARCH-JUMP模型的股票指数跳跃风险预警方案研究
论文类型:方案策划
专业方向：金融数据分析
摘要
在资产价格波动的研究中，股票收益率的大幅变动通常被认定为跳跃行为。
跳跃行为发生的概率很小，可是一旦发生跳跃，会对证券和衍生品的价格产生较
大影响，会给使用金融杠杆的投资者带来巨大的风险。特别是对金融市场仍处于
逐步改革阶段的发展中国家而言，市场收益率容易受到各种突发事件的影响，从
而引发跳跃行为，导致投资风险。在经历了2008年美国金融危机和2012年欧洲
金融危机等紧急情况后，国际金融市场的波动性和跳跃性变得更加明显，国内金
融市场的股价大幅崩盘现象也是经常发生，而针对股票的跳跃行为，目前国内的
研究相对较少，本文研究在此背景下展开。
本文主要基于金融资产价格波动相关理论，运用时变的自回归条件跳跃强度
模型，通过理论分析和实证研究相结合的方法，研究了股票指数跳跃风险的识别
和预警问题，并给出了相应的跳跃风险识别方案。文章以2006年1月4日至2021
年8月31日的上证50指数、沪深300指数和中证500指数为研究对象，利用
Matlab等数据分析软件较为全面地剖析了基于GARCH-JUMP模型和ARJI模型的
股价跳跃风险的预警效果。
在对模型的预警方案的合理性进行检验之后，对模型在实际应用中的预警效
果做了验证，初步得到的研究结论如下。首先，三大股票指数收益率均存在跳跃
行为，且跳跃强度值并非是恒定不变的，而是会随着时间的变化而变化。其次，
股票指数收益率存在显著的波动聚集效应，且可以通过跳跃强度相关指标对市场
跳跃风险进行有效预警。在市场高波动阶段，指数跳跃风险呈现逐步减弱的态势；
而在市场低波动阶段，指数跳跃风险则呈现逐步增强的态势。最后，
ARJI-GARCH-JUMP模型能够很好地对可能发生的股价跳跃风险进行预警，对投资
者合理控制股票指数期货的投资风险具有实际意义。
关键词：股票指数；跳跃行为；ARJI模型；风险预警
I

Abstract
Abstract
In the study of asset price volatility, large movements in stock returns are often
identified as jumping behaviors. The probability of jumping behavior is very small,
but once jumping occurs, it will have a greater impact on the prices of securities and
derivatives, and will bring huge risks to investors who use financial leverage.
Especially for developing countries whose financial markets are still in the stage of
gradual reform, market yields are easily affected by various emergencies, which lead
to jumping behaviors and investment risks. After experiencing emergencies such as
the US financial crisis in 2008 and the European financial crisis in 2012, the volatility
and jumping of the international financial market became more obvious, and the sharp
collapse of stock prices in the domestic financial market also occurred frequently. At
present, there are relatively few domestic studies on behavior, and this study is carried
out in this context.
This paper is mainly based on the relevant theory of financial asset price
fluctuations, using the time-varying autoregressive conditional jump intensity model,
through a combination of theoretical analysis and empirical research, to study the
identification and early warning of stock index jump risk, and give the corresponding
Jump risk identification scheme. The article takes the Shanghai Stock Exchange 50
Index, CSI 300 Index and CSI 500 Index from January 4, 2006 to August 31, 2021 as
the research objects, and uses Matlab and other data analysis software to
comprehensively analyze the GARCH-JUMP model and the Early warning effect of
stock price jump risk of ARJI model.
After checking the rationality of the early warning scheme of the model, the
early warning effect of the model in practical application is verified, and the
preliminary research conclusions are as follows. First, the returns of the three major
stock indexes all have jumping behavior, and the value of jumping intensity is not
constant, but changes with time. Secondly, there is a significant volatility clustering
effect in the stock index returns, and the market jump risk can be effectively warned
through the jump intensity-related indicators. In the period of high market volatility,
the risk of index jumping shows a trend of gradually weakening; while in the stage of
low market volatility, the risk of index jumping shows a trend of increasing gradually.
Finally, the ARJI-GARCH-JUMP model can give a good early warning of the
II

Abstract
possible stock price jump risk, which is of practical significance for investors to
reasonably control the investment risk of stock index futures.
Key Words: Stock index; Jumping behavior; ARJI model; Risk warning
III
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