The hyperbolic geometry of financial networks

Martin Keller-Ressel; Stephanie Nargang

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arXiv · 2005.00399

The hyperbolic geometry of financial networks

Martin Keller-Ressel·Stephanie Nargang

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Abstract

Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. This allows us to connect the network structure to the popularity-vs-similarity model of Papdopoulos et al., which is based on the Poincar\'e disc model of hyperbolic geometry. We show that the latent dimensions of `popularity' and `similarity' in this model are strongly associated to systemic importance and to geographic subdivisions of the banking system. In a longitudinal analysis over the time span from 2014 to 2018 we find that the systemic importance of individual banks has remained rather stable, while the peripheral community structure exhibits more (but still moderate) variability.

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Martin Keller-Ressel, Stephanie Nargang. 2020-05-01. The hyperbolic geometry of financial networks. https://arxiv.org/abs/2005.00399

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