16 research outputs found
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
Measures of Systemic Risk
Systemic risk refers to the risk that the financial system is susceptible to
failures due to the characteristics of the system itself. The tremendous cost
of systemic risk requires the design and implementation of tools for the
efficient macroprudential regulation of financial institutions. The current
paper proposes a novel approach to measuring systemic risk.
Key to our construction is a rigorous derivation of systemic risk measures
from the structure of the underlying system and the objectives of a financial
regulator. The suggested systemic risk measures express systemic risk in terms
of capital endowments of the financial firms. Their definition requires two
ingredients: a cash flow or value model that assigns to the capital allocations
of the entities in the system a relevant stochastic outcome; and an
acceptability criterion, i.e. a set of random outcomes that are acceptable to a
regulatory authority. Systemic risk is measured by the set of allocations of
additional capital that lead to acceptable outcomes. We explain the conceptual
framework and the definition of systemic risk measures, provide an algorithm
for their computation, and illustrate their application in numerical case
studies.
Many systemic risk measures in the literature can be viewed as the minimal
amount of capital that is needed to make the system acceptable after
aggregating individual risks, hence quantify the costs of a bail-out. In
contrast, our approach emphasizes operational systemic risk measures that
include both ex post bailout costs as well as ex ante capital requirements and
may be used to prevent systemic crises.Comment: 35 pages, 11 figure