Equity Market Description under High and Low Volatility Regimes Using Maximum Entropy Pairwise Distribution

Area of Science:

• Quantitative Finance
• Complex Systems Analysis
• Financial Econometrics

Background:

• Financial markets exhibit intricate interdependencies between assets, leading to correlated returns and price movements.
• Understanding these interactions is crucial, especially during periods of high market volatility such as financial crises.
• Previous studies often focus on linear correlations, potentially missing deeper structural relationships.

Purpose of the Study:

• To analyze asset interactions within financial markets using a Maximum Entropy Principle approach.
• To investigate the role of second-order interactions in explaining system entropy during the 2008 Subprime Crisis and 2020 COVID-19 outbreak.
• To assess how these interactions influence asset correlations and market stability under different volatility regimes.

Main Methods:

• Application of the Maximum Entropy Principle to model asset interactions.
• Implementation of a pairwise Ising distribution model for discretized asset returns.
• Inference of first and second-order moments of asset return distributions.
• Analysis of interaction networks during high and low volatility periods of major financial events.

Main Results:

• Second-order interactions account for over 80% of system entropy during the Subprime Crisis and over 50% during the COVID-19 outbreak.
• Minor adjustments in second-order interactions can cause substantial shifts in asset correlations.
• The proportion of positive and negative interactions remains consistent, preserving a stable 'ferromagnetic' state.
• These findings hold true across different volatility levels and even when considering triadic structures.

Conclusions:

• Second-order interactions are a dominant factor in financial market dynamics, particularly during crisis periods.
• The stability of interaction proportions suggests inherent resilience mechanisms within the market structure.
• The Ising model provides a robust framework for understanding complex financial system behavior and predicting correlation dynamics.