Financial Network Risk via Optimal Transport Theory and Ricci Curvature

Abstract

Quantitative risk management is a central challenge in the field of finance. Many risk evaluation methods have been proposed, but measuring the fragility of financial networks is a fundamentally important problem. Previous studies have shown that discrete curvature characterizes financial networks, particularly the negative correlation between network fragility and Ricci curvature. However, previous studies have calculated discrete curvature on metric unweighted graphs, which, as pointed out in this paper, do not allow for proper curvature calculation. In this study, we modify the financial network of previous studies as nonmetric weighted graphs at the optimal transportation stage and propose a suitable discrete curvature as an indicator. We also theoretically derive the effect of link metrics and weights on the discrete curvature. We show that our proposed curvature is appropriate in numerical examples and confirm that our proposed curvature is lower in normal states and increases more sharply when a stress event occurs in actual price data.