Seminar by Agostino Capponi (Columbia IEOR)
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 so as to meet prescribed capital requirements. Each bank 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 mean-field limit of the interacting measure-valued processes as the number of banks in the system grows large. We then use the limiting results to develop asymptotic approximations for two macro-measures, the liquidity stress index and the concentration index, both capturing the dynamics of systemic risk. Our results indicate that higher connectivity mitigates and eventually absorbs a small shock, but may become a mechanism that propagates and enhances large shocks, leading to severe system-wide liquidity stress.