# Reverse stress testing interbank networks

## TL;DR

This paper introduces a reverse stress testing method for interbank networks to identify minimal shocks causing systemic failures, aiding in systemic risk assessment and policy formulation.

## Contribution

It develops a novel reverse stress testing approach for interbank networks, linking shock size to network eigenvalues and ranking banks by systemic importance.

## Key findings

- Smaller shocks are needed to trigger systemic failure as eigenvalue increases.
- The distribution of shocks across banks becomes more localized with higher eigenvalues.
- The method effectively ranks banks by systemic importance based on minimal shock size.

## Abstract

We reverse engineer dynamics of financial contagion to find the scenario of smallest exogenous shock that, should it occur, would lead to a given final systemic loss. This reverse stress test can be used to identify the potential triggers of systemic events, and it removes the arbitrariness in the selection of shock scenarios in stress testing. We consider in particular the case of distress propagation in an interbank market, and we study a network of 44 European banks, which we reconstruct using data collected from Bloomberg. By looking at the distribution across banks of the size of smallest exogenous shocks we rank banks in terms of their systemic importance, and we show the effectiveness of a policy with capital requirements based on this ranking. We also study the properties of smallest exogenous shocks as a function of the largest eigenvalue $\lambda_{\rm max}$ of the matrix of interbank leverages, which determines the endogenous amplification of shocks. We find that the size of smallest exogenous shocks reduces and that the distribution across banks becomes more localized as $\lambda_{\rm max}$ increases.