A flow network analysis of direct balance-sheet contagion in financial networks

In this study we represent a financial system as a flow network and model the process of direct balance-sheet contagion as a flow of losses crossing such a network. In establishing the necessary and sufficient conditions for the uniqueness of this flow of losses, we address a known problem of indeterminacy that arises from the intercyclicity of payments in financial networks. We then focus most of the analysis on the effects that the connectivity and centralization of a financial network have on its exposure to default contagion. To this end, we study three classes of networks, namely complete, star-shaped and ring networks. We find that both the complete and the star networks show a robust yet fragile response to shocks. These networks are resistant to shocks smaller than a given contagion threshold, whilst all agents in these networks default together if the shock is larger than the threshold. We also show that star networks are more resistant to large shocks than complete networks, i.e. the former are less exposed than the latter to the risk of a complete systemic crisis. Conversely, ring networks appear to be vulnerable yet resilient, in the sense that they are exposed to local episodes of contagion caused by small shocks while being more resilient to large shocks than complete and star networks are.