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

Mathematics of Operations Research. Forthcoming

35 Pages Posted: 30 Aug 2017 Last revised: 21 Jun 2019

See all articles by Agostino Capponi

Agostino Capponi

Columbia University

Xu Sun

University of Florida

David Yao

Columbia University

Date Written: June 20, 2019

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.

Keywords: Dynamic Interbanking Networks, Systemic Risk, Large Networks Asymptotics

JEL Classification: C50, G18, G20, D85

Suggested Citation

Capponi, Agostino and Sun, Xu and Yao, David, A Dynamic Network Model of Interbank Lending — Systemic Risk and Liquidity Provisioning (June 20, 2019). Mathematics of Operations Research. Forthcoming, Available at SSRN: https://ssrn.com/abstract=3028417 or http://dx.doi.org/10.2139/ssrn.3028417

Agostino Capponi (Contact Author)

Columbia University ( email )

S. W. Mudd Building
New York, NY 10027
United States

Xu Sun

University of Florida ( email )

PO Box 117165, 201 Stuzin Hall
Gainesville, FL 32610-0496
United States

David Yao

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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