Alonso-Marroquin Fernando, Arias-Calluari Karina, Harré Michael, Najafi Morteza N, Herrmann Hans J
School of Civil Engineering, The University of Sydney, NSW 2006, Australia.
Department of Physics, University of Mohaghegh Ardabili, Ardabil, Iran.
Phys Rev E. 2019 Jun;99(6-1):062313. doi: 10.1103/PhysRevE.99.062313.
We analyze the Standard & Poor's 500 stock market index from the past 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong superdiffusion together with short-time correlations and the second one corresponds to weak superdiffusion with weak time correlations. Both regimes are well described by q-Gaussian distributions. The porous media equation-a special case of the Tsallis-Bukman equation-is used to derive the governing equation for these regimes and the Black-Scholes diffusion coefficient is explicitly obtained from the governing equation.
我们分析了过去22年标准普尔500股票市场指数。价格回报的概率密度函数呈现出两种具有自相似结构的显著不同状态：第一种表现出强烈的超扩散以及短时间相关性，第二种对应于具有弱时间相关性的弱超扩散。两种状态都可以用q-高斯分布很好地描述。多孔介质方程（Tsallis-Bukman方程的一个特殊情况）被用于推导这些状态的控制方程，并且从控制方程中明确得到了布莱克-斯科尔斯扩散系数。
