78 research outputs found
Densely Entangled Financial Systems
In [1] Zawadoski introduces a banking network model in which the asset and
counter-party risks are treated separately and the banks hedge their assets
risks by appropriate OTC contracts. In his model, each bank has only two
counter-party neighbors, a bank fails due to the counter-party risk only if at
least one of its two neighbors default, and such a counter-party risk is a low
probability event. Informally, the author shows that the banks will hedge their
asset risks by appropriate OTC contracts, and, though it may be socially
optimal to insure against counter-party risk, in equilibrium banks will {\em
not} choose to insure this low probability event.
In this paper, we consider the above model for more general network
topologies, namely when each node has exactly 2r counter-party neighbors for
some integer r>0. We extend the analysis of [1] to show that as the number of
counter-party neighbors increase the probability of counter-party risk also
increases, and in particular the socially optimal solution becomes privately
sustainable when each bank hedges its risk to at least n/2 banks, where n is
the number of banks in the network, i.e., when 2r is at least n/2, banks not
only hedge their asset risk but also hedge its counter-party risk.Comment: to appear in Network Models in Economics and Finance, V. Kalyagin, P.
M. Pardalos and T. M. Rassias (editors), Springer Optimization and Its
Applications series, Springer, 201
On the Computational Complexity of Measuring Global Stability of Banking Networks
Threats on the stability of a financial system may severely affect the
functioning of the entire economy, and thus considerable emphasis is placed on
the analyzing the cause and effect of such threats. The financial crisis in the
current and past decade has shown that one important cause of instability in
global markets is the so-called financial contagion, namely the spreading of
instabilities or failures of individual components of the network to other,
perhaps healthier, components. This leads to a natural question of whether the
regulatory authorities could have predicted and perhaps mitigated the current
economic crisis by effective computations of some stability measure of the
banking networks. Motivated by such observations, we consider the problem of
defining and evaluating stabilities of both homogeneous and heterogeneous
banking networks against propagation of synchronous idiosyncratic shocks given
to a subset of banks. We formalize the homogeneous banking network model of
Nier et al. and its corresponding heterogeneous version, formalize the
synchronous shock propagation procedures, define two appropriate stability
measures and investigate the computational complexities of evaluating these
measures for various network topologies and parameters of interest. Our results
and proofs also shed some light on the properties of topologies and parameters
of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic
Systemic importance of financial institutions: regulations, research, open issues, proposals
In the field of risk management, scholars began to bring together the quantitative methodologies with the banking management issues about 30 years ago, with a special focus on market, credit and operational risks. After the systemic effects of banks defaults during the recent financial crisis,
and despite a huge amount of literature in the last years concerning the systemic risk, no standard methodologies have been set up to now. Even the new Basel 3 regulation has adopted a heuristic indicator-based approach, quite far from an effective quantitative tool. In this paper, we refer to the different pieces of the puzzle: definition of systemic risk, a set of coherent and useful measures, the computability of these measures, the data set structure. In this challenging field, we aim to build a comprehensive picture of the state of the art, to illustrate the open issues, and to outline some paths for a more successful future research. This work appropriately integrates other useful surveys and it is directed to both academic researchers and practitioners
Geometrical validity of curvilinear finite elements
In this paper, we describe a way to compute accurate bounds on Jacobian determinants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the distortion of curvilinear elements. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates
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