Coherence and incoherence collective behavior in financial market

Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find that a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves into the stable state, in which the stocks split into two groups: one is represented by coherent, phase-locked oscillators, the other is composed of incoherent, drifting oscillators. It is demonstrated that the size of the coherent stock groups fluctuates during the economic periods according to real-world financial instabilities or shocks. Further, we introduce the coherent characteristic matrix to characterize the involvement dynamics of stocks in the coherent groups. Clustering results on the matrix provides a novel manifestation of the correlations among stocks in the economic periods. Our analysis for components of the groups is consistent with the Global Industry Classification Standard (GICS) classification and can also figure out features for newly developed industries. These results can provide potentially implications on characterizing the inner dynamical structure of financial markets and making optimal investment into tragedies.