Puertas Antonio M, Sánchez-Granero Miguel A, Clara-Rahola Joaquim, Trinidad-Segovia Juan E, de Las Nieves F Javier
Departamento de Física Aplicada, Universidad de Almería, 04.120 Almería, Spain.
Departamento de Matemáticas, Universidad de Almería, 04.120 Almería, Spain.
Phys Rev E. 2020 Mar;101(3-1):032307. doi: 10.1103/PhysRevE.101.032307.
Different attempts to describe financial markets, and stock prices in particular, with the tools of statistical mechanics can be found in the literature, although a general framework has not been achieved yet. In this paper we use the physics of many-particle systems and the typical concepts of soft matter to study two sets of US and European stocks, comprising the biggest and most stable companies in terms of stock price and trading. Upon correcting for the center-of-mass motion, the structure and dynamics of the systems are studied (in the European set, the structure is studied for the UK subset only). The pair distribution of the stocks, corrected to account for the nonuniform distribution of prices, is close to 1, indicating that there is no direct interaction between stocks, similar to an ideal gas of particles. The dynamics is studied with the mean-squared price displacement (MSPD); the price correlation function, equivalent to the intermediate scattering function; the price fluctuation distribution; and two parameters for collective motions. The MSPD grows linearly and the velocity autocorrelation function is zero, as for isolated Brownian particles. However, the intermediate scattering function follows a stretched exponential decay, the fluctuation distributions deviate from the Gaussian shape, and strong collective motions are identified. These results indicate that the dynamics is much more complex than an ideal gas of Brownian particles, and similar, to some extent, to that of undercooled systems. Finally, two physical systems are discussed to aid in the understanding of these results: a low density colloidal gel, and a dense system of ideal, infinitely thin stars. The former reproduces the dynamical properties of stocks, linear mean-squared displacement (MSD), non-Gaussian fluctuation distribution, and collective motions, but also has strong structural correlations, whereas the latter undergoes a glass transition with the structure of an ideal gas, but the MSD has the typical two-step growth of undercooled systems.
在文献中可以找到用统计力学工具描述金融市场，尤其是股票价格的不同尝试，尽管尚未形成一个通用框架。在本文中，我们运用多粒子系统物理学和软物质的典型概念来研究两组美国和欧洲股票，这些股票由股价和交易方面最大且最稳定的公司组成。在修正质心运动后，研究了系统的结构和动力学（在欧洲股票组中，仅对英国子集研究了结构）。经修正以考虑价格非均匀分布的股票对分布接近1，这表明股票之间不存在直接相互作用，类似于理想粒子气体。用均方价格位移（MSPD）研究动力学；价格相关函数，等同于中间散射函数；价格波动分布；以及两个集体运动参数。如同孤立的布朗粒子一样，MSPD呈线性增长且速度自相关函数为零。然而，中间散射函数遵循拉伸指数衰减，波动分布偏离高斯形状，并且识别出了强烈的集体运动。这些结果表明，动力学比布朗粒子的理想气体要复杂得多，并且在某种程度上类似于过冷系统的动力学。最后，讨论了两个物理系统以帮助理解这些结果：低密度胶体凝胶和理想的、无限薄恒星的密集系统。前者再现了股票的动力学特性、线性均方位移（MSD）、非高斯波动分布和集体运动，但也具有很强的结构相关性，而后者经历具有理想气体结构的玻璃化转变，但MSD具有过冷系统典型的两步增长。
