Systemic Risk and the Dynamics of Financial Networks

Abstract

This paper has two main objectives: first, to provide a formal definition of endogenous systemic risk that is firmly grounded in equilibrium dynamics of financial networks; and second, to construct a discounted stochastic game (DSG) model of the emergence of equilibrium network dynamics that fully takes into account the feedback between network structure, strategic behavior, and risk. Based on our definition of systemic risk we also propose a formal definition of tipping points. Using these tools we then provide a strategic approach to making global assessments of systemic risk in financial networks. Our approach is based on three key facts: (1) the equilibrium dynamics which emerge from the game of network formation generate finitely many disjoint basins of attraction as well as finitely many ergodic measures (implying that, starting from any financial network, in finite time with probability one, the dynamic sequence of financial networks arrives at one of these basins and once there stays there), (2) each basin of attraction is homogenous with respect to its default characteristics (meaning that if a basin contains states having a particular set of defaulted players, then all states contained in this basin have the same set of defaulted players), and (3) the unique profile of basins generated by the equilibrium dynamics carries with it a unique set of tipping points (special states) - and these tipping points provide an early warning of network failure.

Keywords: systemic risk, counter-party risk, financial networks, supernetworks, tipping points, default cascades, basins of attraction, Pareto optimal stationary Markov equilibrium, first passage probabilities, hitting times, hitting time probabilities

JEL Classification: C7