The hyperbolic geometry of financial networks

Area of Science:

• Financial network analysis
• Complex systems science
• Econometrics

Background:

• European banking stress tests and transparency exercises provide valuable data for network analysis.
• Understanding the geometry of financial networks is crucial for assessing systemic risk.
• Previous studies have explored network structures, but geometric representations offer new insights.

Purpose of the Study:

• To investigate the applicability of hyperbolic geometry in representing European banking networks.
• To link network structure to established models like popularity-vs-similarity.
• To analyze temporal changes in banking network structure and systemic importance.

Main Methods:

• Construction of European banking networks using data from 2014, 2016, and 2018.
• Application of two hyperbolic embedding methods: hydra+ and Mercator.
• Analysis using the popularity-vs-similarity model based on the Poincaré disc model.

Main Results:

• The latent geometry of European banking networks is well-represented by hyperbolic geometry.
• Network dimensions of 'popularity' and 'similarity' correlate with systemic importance and geographic factors.
• Systemic importance remained stable from 2014-2018, while peripheral structures showed moderate variability.

Conclusions:

• Hyperbolic geometry embeddings offer a robust method for analyzing financial networks.
• This approach can effectively monitor structural changes and differentiate between systemic and peripheral shifts.
• The findings provide a novel framework for understanding and managing financial system stability.