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Title: Understanding changes in the topology and geometry of financial market correlations during a market crash
Authors: Yen, Peter Tsung-Wen
Xia, Kelin
Cheong, Siew Ann
Keywords: Science::Physics
Issue Date: 2021
Source: Yen, P. T., Xia, K. & Cheong, S. A. (2021). Understanding changes in the topology and geometry of financial market correlations during a market crash. Entropy, 23(9), 1211-.
Journal: Entropy
Abstract: In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.
ISSN: 1099-4300
DOI: 10.3390/e23091211
Schools: School of Physical and Mathematical Sciences 
Rights: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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