Supernetworks and Systemic Risk

Abstract

We give a formal and computable definition of systemic risk that is firmly grounded in network dynamics and using our definition we show that the dynamics driving network formation generate a finite set of basins of attraction. The presence of basins of attraction has major implications for our understanding of systemic risk. First, we show that each basin is homogeneous with respect to its network failure characteristics. Second, we show that the profile of basins comes equipped with a unique set of tipping points. Thus, using our definition of systemic risk, we formally define the notion of a tipping point. Each tipping point is the gateway to some sequence of future networks leading inexorably to some basin, and depending on the failure characteristics of this basin, this sequence might best be described as a failure cascade. Thus, tipping points are the supernetwork’s early warning system for network failure. Finally, we define and characterize the notions of systemic and killer nodes. The big picture take away from our approach to systemic risk is that what is critical in assessing systemic risk is the allocation of failure levels across the basins of attraction.