Collective behavior in financial markets

¹ Instituto de Física de São Carlos, Universidade de São Paulo - Av. Trabalhador São Carlense 400, Caixa Postal 369, CEP 13560-970, São Carlos, São Paulo, Brazil
² Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo - Caixa Postal 668, CEP 13560-970 São Carlos, São Paulo, Brazil

^a franciscoifsc@gmail.com

Received: 22 August 2011
Accepted: 3 October 2011

Abstract

The financial market is an example of a complex system characterized by a highly intricate organization and the emergence of collective behavior. In this paper, this emergent dynamics in the financial market is quantified by using concepts of network synchronization. We consider networks constructed by the correlation matrix of asset returns and study the time evolution of the phase coherence among stock prices. It is verified that during a financial crisis a synchronous state emerges in the system, defining the market's direction. Furthermore, the paper proposes a statistical regression model able to identify the topological features that mostly influence such an emergence. The coefficients of the proposed model indicate that the average shortest path length is the measurement most related to network synchronization. Therefore, during an economic crisis, the stock prices present a similar evolution, which tends to shorten the distances between stocks indicating a collective dynamics.