Functional Hypergraphs of Stock Markets

Area of Science:

• Quantitative Finance
• Network Science
• Information Theory

Background:

• Stock market prices exhibit complex, nonlinear interdependencies.
• Network analysis has been used to study stock market behavior, but often assumes pairwise correlations.
• Real-world market interactions can be higher-order, involving more than two entities simultaneously.

Purpose of the Study:

• To develop a novel methodology for representing higher-order interactions in stock market data.
• To introduce functional hypergraphs as a framework for analyzing these complex relationships.
• To compare the analytical power of hypergraphs versus traditional networks in understanding market dynamics.

Main Methods:

• Utilized information-theoretic tools to construct functional hypergraphs from stock market data.
• Applied higher-order network analysis techniques.
• Calculated and compared functional hypergraph quantities (Forman-Ricci curvature, von Neumann entropy, eigenvector centrality) with traditional network metrics.
• Analyzed the evolution of network and hypergraph structures over time, particularly around market events.

Main Results:

• Functional hypergraphs provide a richer representation of stock market interdependencies compared to pairwise networks.
• Analysis of hypergraph quantities revealed distinct patterns and signals related to market events.
• The hypergraph framework demonstrated robustness in analyzing market behavior, even during stock market crashes.

Conclusions:

• Higher-order representations, such as functional hypergraphs, are crucial for a comprehensive understanding of stock market dynamics.
• This approach offers new insights into market behavior and resilience.
• The methodology provides a powerful tool for analyzing complex systems beyond financial markets.