Intrinsic Geometry of the Stock Market from Graph Ricci Flow

Battle Count: 83

The paper provides a novel structural analysis tool for understanding market geometry and identifying hidden hierarchies/communities without pre-specifying cluster numbers. While not directly a trading strategy, the insights into market structure (e.g., semiconductor clustering, Big Tech grouping, outlier identification) could inform sector rotation strategies, risk factor decomposition, and portfolio construction. The method's ability to detect neckpinch singularities could potentially signal regime changes. However, it lacks predictive power, backtesting, and direct trading signal generation.

The method requires: (1) computing Pearson correlation matrices and converting to distance weights, (2) implementing Ollivier-Ricci curvature via optimal transport/Wasserstein distance computation on each edge, (3) iterative Ricci flow with simultaneous edge weight updates, (4) identifying neckpinch singularities from curvature histograms, (5) performing surgery along zero-curvature links, (6) repeating the process hierarchically. The optimal transport computation is the most expensive step. The algorithm is available via a referenced GitHub package, reducing implementation burden. The conceptual complexity (differential geometry on discrete graphs) is high, but the computational implementation is moderate with existing libraries.

The paper references a GitHub repository (saibalmars/GraphRicciCurvature) for the Ricci flow algorithm. Data is publicly available via Yahoo Finance and Wikipedia. The mathematical framework (ORC definition, Ricci flow update rule, surgery criterion) is fully specified with equations. However, the specific surgery implementation details, exact iteration counts for each level, and the complete algorithmic pseudocode for the multi-level decomposition are not fully detailed. The paper is a letter/short communication, so some implementation specifics are deferred to a longer companion paper.