Phase separation and scaling in correlation structures of financial markets

Abstract

Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to critical phenomena in physics, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigenvector centralities of different stocks in the cross-correlation matrix, to extract information about the disorder in the market. We construct a 'phase space', where different market events (bubbles, crashes, etc) undergo phase separation and display order–disorder movements. An entropy functional exhibits scaling behavior. We propose a generic indicator that facilitates the continuous monitoring of the internal structure of the market—important for managing risk and stress-testing the financial system. Our methodology would help in understanding and foreseeing tipping points or fluctuation patterns in complex systems.