Abstract
AbstractIn this paper the authors focus on credit connections as a potential source of systemic risk. In particular, they seek to answer the following question: how do we find densely connected subsets of nodes within a credit network? The question is relevant for policy, since these subsets are likely to channel any shock affecting the network. As it turns out, a reliable answer can be obtained with the aid of complex network theory. In particular, the authors show how it is possible to take advantage of the ‘‘community detection’‘ network literature. The proposed answer entails two subsequent steps. Firstly, the authors verify the hypothesis that the network under study truly has communities. Secondly, they devise a reliable algorithm to find those communities. In order to be sure that a given algorithm works, they test it over a sample of random benchmark networks with known communities. To overcome the limitation of existing benchmarks, the authors introduce a new model and test alternative algorithms, obtaining very good results with an adapted spectral decomposition method. To illustrate this method they provide a community description of the Japanese bank-firm credit network, getting evidence of a strengthening of communities over time and finding support for the well-known Japanese main ‘‘bank’‘ system. Thus, the authors find comfort both from simulations and from real data on the possibility to apply community detection methods to credit markets. They believe that this method can fruitfully complement the study of contagious defaults. Since network risk depends crucially on community structure, their results suggest that policy maker should identify systemically important communities, i.e. those able extend the initial shock to the entire system.
Highlights
Since the outbreak of the global crisis, policy makers have been haunted by the nightmare of a global financial meltdown breaking out of incontrollable feedbacks spreading across financial markets
We introduce the following two modifications with respect to Donetti and Munoz (2005): 1. the number q of communities is determined by means of eq (3.4) and not by means of modularity optimization; 2. spectral decomposition is performed over K and not over the Laplacian L
The procedure runs as follows: 1. we start with a preliminary partition of the network into q communities; 2. for each community we compute, either on a binary version of the original network or on the SVnet, the number k of links running between that community and each external node; 3. we evaluate the probability of observing k links under the null model using the binomial distribution (4.3) with suitably adapted parameters; 4. we correct for multiple hypothesis testing by requiring that, in order to validate the inclusion of r nodes into the q communities, the overall probability of their links doesn’t exceed a threshold p, i. e. we employ again Bonferroni
Summary
Since the outbreak of the global crisis, policy makers have been haunted by the nightmare of a global financial meltdown breaking out of incontrollable feedbacks spreading across financial markets. The interconnectedness of credit institutions is a source of counterparty risk on interbank credit markets, which has been addressed recently by a number of theoretical models tackling the problem of contagious defaults (Gai and Kapadia, 2010; Amini et al, 2010, 2012; Battiston et al, 2012). These models, which go beyond previous simulation based works (Nier et al, 2007; Elsinger et al, 2006), rely on complex network theory, which has become a prominent tool in this field.
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