基于Hawkes过程与计算实验的股票市场极值风险传播的研究

When the range of the stock market fluctuation exceeds a certain threshold, the market may form extreme risk, which performs as the drastic volatility in stock prices. Moreover, the extreme risk in stock market will stimulate the occurrence of new extreme risks. The extreme risk in stock market possesses the self-exciting spreading characteristic, which may cause its continuous spreading and thus greatly influences the stock market. When focusing on the spreading characteristics of the extreme risk in stock market, a study on the microstructure of the market is of the same significance. Based on the Chinese stock market, this project defines the extreme risk in stock market as the range of fluctuation exceeding a certain threshold. Next, the spreading dynamic process of the extreme risk in stock market is seen as the spreading dynamic process of a series of aftershocks triggered by the principal earthquake. A marked Hawkes process with twofold shot noise characteristics is introduced to construct the spreading model of the extreme risk in stock market and depict the spreading dynamic process of the extreme risk in stock market. Then, a study is carried out to analyze the spreading characteristics of the extreme risk (drastic rising/ drastic falling) under a specific market state (bull/ bear/ volatile) and its corresponding numerical techniques from several aspects (the duration of the aftershocks, the frequency of the aftershocks, the severity of the aftershocks, the scenario prediction of the aftershocks). Finally, Ising agent-based computational finance model is utilized to study the spreading influences of the extreme risk in stock market caused by the microstructure of the market. This project possesses both important theoretical value and practical meaning when improving the management of the extreme risk in stock market.

当股市涨跌幅超过一定阈值时，市场会产生极值风险，表现为股价暴涨暴跌，且股市极值风险的发生将会刺激新的极值风险发生，这种自激发传播特性会导致股市极值风险持续传播，进而带来巨大影响。在关注股市极值风险传播特征的同时，其背后市场微观机理研究也同样重要。本项目以中国股市为研究对象，视涨跌幅超过一定阈值的暴涨/暴跌为股市极值风险，将股市极值风险传播过程类比于由主震激发的一系列余震的传播过程，利用具有双重散粒噪声特征的标值Hawkes过程，构建股市极值风险传播模型，刻画股市极值风险传播的动态过程，从多重视角（余震传播持续时间、余震活跃程度、余震强度、余震情景概率预测）开展特定市态(牛市/熊市/平衡市)下极值风险（暴涨/暴跌）传播特征以及数值实现技术的研究，引入Ising计算实验金融模型，探究市场微观机理对股票市场极值风险传播的影响。本项目对提高股票市场极值风险管理水平具有重要的理论价值和现实意义。

当股市涨跌幅超过一定阈值时，市场会产生极值风险，表现为股价暴涨暴跌，且股市极值风险的发生将会刺激新的极值风险发生，这种自激发传播特性会导致股市极值风险持续传播，进而带来巨大影响。在关注股市极值风险传播特征的同时，其背后市场微观机理研究也同样重要。本项目围绕着中国股票市场极值风险传播、中美股市间极端风险传染以及国际原油市场与中国股票市场间极端风险传染等方面开展了研究。主要研究内容为：（1）将Hawkes过程与极值理论结合，考虑中国股票市场的涨跌停板限制，构建了极值风险传播模型，基于主余震识别结果，从多重视角开展极值风险传播特征的研究。（2）在Franke和Westerhoff（2012）提出的DCA-HPM简单代理人模型的基础上引入涨跌停板限制和基础价值的随机波动，构建了修正后的DCA-HPM模型，利用此模型研究羊群效应、初始策略偏好以及价格偏差等三个微观机理对中国股票市场极值风险传播特征的影响。（3）基于异质性假设，引入市场恐慌来构建噪声交易者和风险交易者的交互策略，提出了一个简单的代理人模型来研究投资者恐慌心理这一微观机理对中国股票市场极值风险传播特征的影响。（4）利用交易量刻画股市不同活跃程度，将股票市场大幅波动事件发生的概率拆分成基于当前市场交易活跃程度的大幅波动事件发生的基础概率和历史大幅波动事件自激发影响的概率，构建交易量修正Hawkes模型研究股市不同交易活跃程度下中国股市极值风险发生的概率以及风险预警机制。（5）将涨跌幅度超过一定阈值的暴涨和暴跌收益率称为大幅波动，以时变的大幅波动发生频率作为研究的切入点，将大幅波动在时间和空间尺度上的蔓延类比于地震学中的地震传播过程，采用二维的标值Hawkes模型分别构建中美国股票市场之间大幅波动联动模型以及国际原油市场和中国股票市场之间的动态联动模型，实证研究中美股市间极端风险传染以及国际原油市场与中国股票市场之间极端风险传染。本项目对提高股票市场极值风险管理水平具有重要的理论价值和现实意义。