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

We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. 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 in our simple setting. 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. Our results are a first step towards allowing regulators to quantify errors in their simulations.Comment: 37 page

Macroprudential Regulation and Systemic Capital Requirements

In the aftermath of the financial crisis, there is interest in reforming bank regulation such that capital requirements are more closely linked to a bank's contribution to the overall risk of the financial system. In our paper we compare alternative mechanisms for allocating the overall risk of a banking system to its member banks. Overall risk is estimated using a model that explicitly incorporates contagion externalities present in the financial system. We have access to a unique data set of the Canadian banking system, which includes individual banks' risk exposures as well as detailed information on interbank linkages including OTC derivatives. We find that systemic capital allocations can differ by as much as 50% from 2008Q2 capital levels and are not related in a simple way to bank size or individual bank default probability. Systemic capital allocation mechanisms reduce default probabilities of individual banks as well as the probability of a systemic crisis by about 25%. Our results suggest that financial stability can be enhanced substantially by implementing a systemic perspective on bank regulation.Financial stability