The hyperbolic geometry of financial networks

14:30 - 16:00
Stephanie Nargang (with Martin Keller-Ressel)
TU Dresden
IMB - Seminar
The popularity-vs-similarity model based on hyperbolic geometry (cf. (1)) has been a breakthrough in the research of network structure. It has been the first model resolving the conflicting paradigms of preferential attachment (attraction to popular nodes) and community effects (attraction to similar nodes) in networks and has been successfully used to explain the structure of informational, social and biological networks. Just as the geometric structure of a social network determines the diffusion of news, rumors or infective diseases between individuals, the geometric structure of a financial network influences the diffusion of financial distress between financial institutions. Indeed, the lack of understanding for risks originating from the systemic interaction of financial institutions has been identified as a major contributing factor to the global financial crisis of 2008. While many recent studies have analysed the mechanisms of financial contagion in theoretical or simulation-based settings, less attention has been payed to structural characteristics of real financial networks and on the interaction between this structure and contagion processes. In particular, it has remained an open question whether the paradigm of hyperbolic structure applies to financial and economic networks and what such a structure implies for financial contagion processes.

In this talk we introduce hydra (hyperbolic distance recovery and approximation), a new method for embedding network- or distance-based data into hyperbolic space, which satisfies a certain optimality guarantee: It minimizes the ’hyperbolic strain’ between original and embedded data points. Applying this embedding method to financial networks inferred from bank balance sheet data, we show that these networks can efficiently be embedded into low-dimensional hyperbolic space with considerably smaller distortion than into Euclidean space, suggesting that the paradigm of latent hyperbolic geometry
also applies to financial networks. Furthermore, we follow the approach in (1) and provide a structural decomposition of the embedding coordinates into popularity and similarity dimension and demonstrate that these dimensions align with systemic importance and membership in regional banking clusters respectively. We present rigorous computations to prove that the popularity dimension of a given bank aligns with its systemic importance and that its similarity dimension is associated with sub-sectors of the banking system.

Finally, we exploit the longitudinal structure of the data to track changes in these dimensions over time, i.e., to track systemic importance of individual banks.

(1) F. Papadopoulos, M. Kitsak, M. Serrano, M. Boguná, D. Krioukov (2012). Popularity versus similarity in growing networks. Nature

Letztmalig verändert: 11.02.2020, 11:05:43


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