Hierarchical structure of stock price fluctuations in financial markets

The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous scaling exponents deviated from Kolmogorov monofractal scaling of the velocity fluctuation in fluid turbulence, is applied to study and quantify the hierarchical structure of stock price fluctuations in financial markets. We therefore observed certain interesting results: (i) The hierarchical structure related to multifractal scaling generally presents in all the stock price fluctuations we investigated. (ii) The quantitatively statistical parameters that describes SL hierarchy are different between developed financial markets and emerging ones, distinctively. (iii) For the high-frequency stock price fluctuation, the hierarchical structure varies with different time period. All these results provide a novelty analogy in turbulence and financial market dynamics and a insight to deeply understand the multifractality in financial markets. PACS numbers: 89.65.Gh, 05.45.Df, 89.75.Fb, 05.45.Tp