Sensitivity of the Eisenberg-Noe Clearing Vector to Individual Interbank Liabilities

35 Pages Posted: 8 Sep 2017

See all articles by Zachary Feinstein

Zachary Feinstein

Stevens Institute of Technology - School of Business

Weijie Pang

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences

Birgit Rudloff

Vienna University of Economics and Business

Eric Schaanning

European Systemic Risk Board - EUROPEAN SYSTEMIC RISK BOARD; Norges Bank

Stephan Sturm

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences

Mackenzie Wildman

University of California, Santa Barbara (UCSB)

Date Written: August 4, 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.

Keywords: Systemic Risk, Model Risk, Eisenberg–Noe Clearing Vector, Sensitivity Analysis, Interbank Networks, Contagion

Suggested Citation

Feinstein, Zachary and Pang, Weijie and Rudloff, Birgit and Schaanning, Eric and Sturm, Stephan and Wildman, Mackenzie, Sensitivity of the Eisenberg-Noe Clearing Vector to Individual Interbank Liabilities (August 4, 2017). Norges Bank Working Paper 13/2017, Available at SSRN: https://ssrn.com/abstract=3033476 or http://dx.doi.org/10.2139/ssrn.3033476

Zachary Feinstein

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

Weijie Pang

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences ( email )

United States

Birgit Rudloff

Vienna University of Economics and Business ( email )

Welthandelsplatz 1
Vienna, Wien 1020
Austria

Eric Schaanning (Contact Author)

European Systemic Risk Board - EUROPEAN SYSTEMIC RISK BOARD ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany

Norges Bank ( email )

P.O. Box 1179
Oslo, N-0107
Norway

Stephan Sturm

Worcester Polytechnic Institute (WPI) - Department of Mathematical Sciences ( email )

United States
5088315921 (Phone)
5088315824 (Fax)

HOME PAGE: http://users.wpi.edu/~ssturm

Mackenzie Wildman

University of California, Santa Barbara (UCSB) ( email )

Santa Barbara, CA 93106
United States

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