A Dynamic Network Model of Interbank Lending Systemic Risk and Liquidity Provisioning

Abstract

We develop a dynamic model of interbank borrowing and lending activities in which banks are organized into clusters, and adjust their monetary reserve levels to meet prescribed capital requirements. Each bank has its own initial monetary reserve level and faces idiosyncratic risks characterized by an independent Brownian motion; whereas system wide, the banks form a hierarchical structure of clusters. We model the interbank transactional dynamics through a set of interacting measure-valued processes. Each individual process describes the intra-cluster borrowing/lending activities, and the interactions among the processes capture the inter-cluster financial transactions. We establish the weak limit of the interacting measure-valued processes as the number of banks in the system grows large. We then use the weak limit to develop asymptotic approximations of two proposed macro-measures, the liquidity stress index and the concentration index, both capturing the dynamics of systemic risk. We use numerical examples to illustrate the applications of the asymptotics and conduct related sensitivity analysis with respect to various indicators of financial activity.