Norges Bank

Working Paper

Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities

Author:
Zachary Feinstein, Weijie Pang, Birgit Rudloff, Eric Schaanning, Stephan Sturm and Mackenzie Wildman
Series:
Working Paper
Number:
13/2017

Abstract:

We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often estimate this matrix because complete information on bilateral liabilities is rarely available. As a result, the clearing vector may suffer from estimation errors in the liabilities matrix. We quantify the clearing vector's sensitivity to such estimation errors and show that its directional derivatives are, like the clearing vector itself, solutions of fixed point equations. We describe estimation errors utilizing a basis for the space of matrices representing permissible perturbations and derive analytical solutions to the maximal deviations of the Eisenberg-Noe clearing vector. This allows us to compute upper bounds for the worst case perturbations of the clearing vector. Moreover, we quantify the probability of observing clearing vector deviations of a certain magnitude, for uniformly or normally distributed errors in the relative liability matrix. Applying our methodology to a dataset of European banks, we find that perturbations to the relative liabilities can result in economically sizeable differences that could lead to an underestimation of the risk of contagion. Importantly, our results allow regulators to bound the error of their simulations.

Norges Bank’s working papers present research projects and reports that are generally not in their final form. Other analyses by Norges Bank’s economists are also included in the series. The views and conclusions in these documents are those of the authors.

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ISSN 1502-8190 (online)

Published 4 August 2017 15:00
Published 4 August 2017 15:00