Intrinsic Geometry of the Stock Market from Graph Ricci Flow

ArXiv ID: 2510.15942 “View on arXiv”

Authors: Bhargavi Srinivasan

Abstract

We use the discrete Ollivier-Ricci graph curvature with Ricci flow to examine the intrinsic geometry of financial markets through the empirical correlation graph of the NASDAQ 100 index. Our main result is the development of a technique to perform surgery on the neckpinch singularities that form during the Ricci flow of the empirical graph, using the behavior and the lower bound of curvature of the fully connected graph as a starting point. We construct an algorithm that uses the curvature generated by intrinsic geometric flow of the graph to detect hidden hierarchies, community behavior, and clustering in financial markets despite the underlying challenges posed by a highly connected geometry.

Keywords: Ollivier-Ricci curvature, Ricci flow, Graph topology, Correlation graph, Surgery singularities, Equities (NASDAQ 100)

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced differential geometry concepts like Ricci flow and Ollivier-Ricci curvature, requiring deep mathematical formalism, while it also applies these methods to real-world NASDAQ 100 data, demonstrating empirical implementation and a specific algorithm for community detection.

  flowchart TD
    A["Research Goal: Analyze intrinsic market geometry via correlation graphs, handling Ricci flow singularities"] --> B["Input: NASDAQ 100 Correlation Graph"]
    B --> C["Compute Ollivier-Ricci Curvature"]
    C --> D["Apply Ricci Flow"]
    D --> E{"Singularities Detected?"}
    E -- Yes --> F["Surgery: Neckpinch Removal"]
    F --> C
    E -- No --> G["Outcome: Stable Geometric State"]
    G --> H["Findings: Hidden Hierarchies & Community Structure"]