Phase separation and scaling in correlation structures of financial markets

TL;DR

This paper introduces a novel method using eigenvalue decomposition and eigen-entropy to detect phase transitions and scaling behaviors in financial market correlation structures, aiding in risk management and early warning of market events.

Contribution

It presents a new approach to analyze market phase transitions through eigen-entropy and constructs a phase space for understanding market disorder and order during different events.

Findings

Correlation structures change during market crashes and bubbles.

Eigen-entropy exhibits scaling behavior during market transitions.

The proposed indicator can monitor market internal structure continuously.

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 phase transitions in physical phenomena, 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 eigen-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 transitions. 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.