基于计算实验的证券价格跳跃的人类动力学研究

The goals of the project are to deduce financial derivation pricing model with the statistical characteristics of the stock price jump's amplitude and frequency which mirror the dynamic mechanism, and to discover the dynamic mechanism of human behavior about the jump's amplitude and frequency, especially the jump's frequency. Jump diffusion model is an important model in continuous finance, but most researches are focused to the distribution form of jump amplitude, and the feature of jump frequency is usually considered as a product of Poisson process. In earlier stage, we found that the jump frequency has the feature with power law. The jumping behavior of the stock market price volatility represents the relation between the heterogeneous investor behaviors and market equilibrium, and it is necessary to research the financial derivation pricing model with the realistic statistical characteristics and to analyze the dynamic mechanism of investor behavior leading to the jump of price volatility. Introducing the realistic statistical characteristics of jump (amplitude and frequency) to financial asset price model, financial derivatives pricing model with the characteristics of China's securities market will be deduced. By comparison to the differences from the different market characteristics, as well as China's market characteristics of different historical periods (the longitudinal comparison), the structural analysis is given. Constructing agent-based model with cognitive structure in artificial financial market, the influence from agent's cognitive to finance asset price will be study. Through improving modeling agent behavior and internal decision-making mechanism, broader ideas and methods are provided to agent-based computational finance. The mechanism underlying price volatility is deduced by agent-based modeling and the analysis to differences from jump characteristics under different conditions. Based on the classic financial economics and human behavior dynamics, human behavior law of stock price movement and its application in the pricing of financial derivative products are researched in this project, which has important theoretical value to financial risk management and asset pricing.

研究股票市场价格波动的跳跃行为特征；分析跳跃幅度与频度，尤其是跳跃频度的人类行为动力学机制；将反映股票市场价格的跳跃幅度与频度动力学机制的统计特征引入到金融衍生品定价模型中，获得符合我国证券市场特征的金融衍生品定价模型。通过不同市场特征差异的横向比较，以及我国市场不同历史时期特征（尤其是股指期货推出前后）的纵向比较，进行结构化分析。构建agent认知结构模型，研究agent的认知对人工金融市场上资产定价的影响，改进目前计算金融模型中agent行为以及内在决策机制的建模，对金融市场上agent行为的建模提供更广阔的思路和方法。通过基于agent的建模，比较不同条件下股票价格跳跃行为特征的差异，推演背后的价格机制。 本研究基于金融经济学与人类行为动力学，研究股票价格运动的人类行为动力学规律，及其在金融衍生品定价中的应用，对金融风险管理、金融资产定价具有重要理论价值。

本研究从市场特征出发给出包含人类行为动力学特征的股票价格动力学模型。将Merton的跳跃扩散模型拓展为幂律跳跃扩散模型．首先，将计数过程由 过程修正为带有幂律性质的更新过程；然后，在考虑收益损失状态下跳跃幅度不同的同时，也赋予跳跃幅度以幂律分布的特征．通过实证研究发现幂律跳跃扩散模型所作出的两个修正可以更加准确的描述股票价格的运动过程，同时得到具有胖尾特征的收益率分布和波动聚集性。引入更新过程后也为金融风险管理提供了跳跃发生的时间期望以及某一时间跳跃发生的概率这两个来源于市场本身的可操作的指标．.对多市场证券价格跳跃人类动力学行为实证对比研究。我们同时考查了上证指数（国内指数代表）、S&P500指数（国外指数代表）以及恒生指数的低频数据（日收盘）和高频数据（15min）发生跳跃的时间间隔分布。实证研究发现它们都具有幂律特性（相对于指数分布尖峰厚尾），这与Barabási关于人类动力学的结论非常吻合。代表幂律特性的参数 具有一定的规律，对向上跳跃参数 的范围是：0<α<1 ，而向下跳跃参数 的范围是： α>1 ；认为幂律指数 很可能是连续存在的，即可能存在着更广泛的普适类，而不仅仅是Barabási提出的α=1 和α=1.5 两个普适类。.基于人工金融市场的证券价格跳跃行为的人类动力学机制研究。采用计算实验金融的研究方法，建立一个新型人工股票市场模型，进行模拟实验研究，实验结果发现人工股票市场表现出了与现实市场相似的特征。通过设计agent不同的学习频率的对比实验，发现学习机制的有无及学习频率对市场收益率的分布有影响。通过采用模拟市场5010期产生的数据包进行回归检验发现，幂律跳跃扩散模型能够很好地拟合市场中股价的跳跃情况，支持了股价跳跃的时间间隔符合幂律形式的理论，并且市场中agent投资策略的非单一性和动态变化性是股价变化不连续的一个原因。