Systemic risk in a mean-field model of interbank lending with self-exciting shocks

TL;DR

This paper models interbank reserves with self-exciting shocks using a mean-field approach, revealing that such shocks significantly increase systemic risk in financial networks.

Contribution

It introduces a mean-field model incorporating self- and cross-exciting shocks and derives explicit limit processes to analyze systemic risk.

Findings

Self-exciting shocks elevate systemic risk levels.

The derived limit process provides explicit measures for systemic risk.

Numerical verification supports the theoretical results.

Abstract

In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis and find an explicit measure-valued process associated with a large interbanking system. We define systemic risk indicators and derive, using the limiting process, several law of large numbers results and verify these numerically. We conclude that self-exciting shocks increase the systemic risk in the network and their presence in interbank networks should not be ignored.