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Functional Hypergraphs of Stock Markets.

Jerry Jones David1, Narayan G Sabhahit2, Sebastiano Stramaglia3

  • 1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Indore 453552, India.

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This study introduces functional hypergraphs to model complex stock market interactions beyond pairwise correlations. This higher-order approach reveals market dynamics and robustness during stock market crashes.

Keywords:
complex systemshypergraphsstock markets

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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.