Understanding changes in the topology and geometry of financial market correlations during a market crash
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 paradig...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/153765 |
| _version_ | 1826117031578042368 |
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| author | Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann |
| author_sort | Yen, Peter Tsung-Wen |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T04:21:07Z |
| format | Journal Article |
| id | ntu-10356/153765 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:21:07Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1537652023-02-28T20:05:25Z Understanding changes in the topology and geometry of financial market correlations during a market crash Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann School of Physical and Mathematical Sciences Science::Physics Science::Mathematics Econophysics Financial Markets 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. Published version 2022-06-01T05:46:15Z 2022-06-01T05:46:15Z 2021 Journal Article 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-. https://dx.doi.org/10.3390/e23091211 1099-4300 https://hdl.handle.net/10356/153765 10.3390/e23091211 9 23 1211 en Entropy © 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 (https://creativecommons.org/licenses/by/4.0/). application/pdf |
| spellingShingle | Science::Physics Science::Mathematics Econophysics Financial Markets Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann Understanding changes in the topology and geometry of financial market correlations during a market crash |
| title | Understanding changes in the topology and geometry of financial market correlations during a market crash |
| title_full | Understanding changes in the topology and geometry of financial market correlations during a market crash |
| title_fullStr | Understanding changes in the topology and geometry of financial market correlations during a market crash |
| title_full_unstemmed | Understanding changes in the topology and geometry of financial market correlations during a market crash |
| title_short | Understanding changes in the topology and geometry of financial market correlations during a market crash |
| title_sort | understanding changes in the topology and geometry of financial market correlations during a market crash |
| topic | Science::Physics Science::Mathematics Econophysics Financial Markets |
| url | https://hdl.handle.net/10356/153765 |
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