Intrinsic Geometry of the Stock Market from Graph Ricci Flow

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.