Liquidity in Financial Networks

This study investigates the amount of liquidity that is necessary to settle a given network of financial obligations. In our analysis, we assume sequential settlement, which is standard in real-world interbank settlement systems, instead of simultaneous settlement, which is typically assumed in relevant research. We develop a graph-theoretic model and apply a flow network technique to investigate how the interconnected feature could affect the required liquidity. Our main contribution is to show that the effect of the interconnected feature is characterized with our original concepts regarding ``twist" properties---arc-twisted and vertex-twisted---that are defined on the basis of the concept of ``cycles." Each of the ``twist" properties refers to certain inconsistency in the dynamics of settlements. The characterization provides a consistent and fundamental perspective of how a hub or other network structures affect the required liquidity. We further investigate the quantitative implications of the ``twist" properties for real-world networks of obligations by examining networks with clustered structures and small-world structures. We show that ``twist" properties have non-linear effects on the required liquidity against an increase in the amount of obligations