Intrinsic Geometry of the Stock Market from Graph Ricci Flow
Bhargavi Srinivasan
TL;DR
The paper addresses revealing the intrinsic geometry of financial markets without pruning the fully connected correlation graph. It adopts a discrete Ollivier-Ricci curvature framework on the NASDAQ-100 edge-weighted graph and evolves edge weights under a discrete Ricci flow with curvature-driven surgery to expose hierarchical structure. A key contribution is an algorithm that detects communities and substructures via neckpinch singularities, using the lower bound of curvature as a robust guide for surgery. The method yields multi-level clustering and identifies outliers, offering a geometry-based alternative to MST or PCA for market analysis and enabling analysis of regime changes and crashes.
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.