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Unformatted text preview: sovereign default by some European countries. These and other examples
highlight concerns that interconnectedness could pose a signiﬁcant threat to the stability of the ﬁnancial
system.1 Moreover there is a growing body of research that shows how this can happen in a theoretical
Although it is intuitively clear that interconnectedness has some eﬀect on the transmission of shocks,
it is less clear whether and how it signiﬁcantly increases the likelihood and magnitude of losses compared
to a ﬁnancial system that is not interconnected. In this paper we propose a general framework for
analyzing this question. There are in fact many diﬀerent types of networks connecting parts of the
ﬁnancial system, including networks deﬁned through ownership hierarchies, payment systems, derivatives
contracts, brokerage relationships, and correlations in stock prices, among other examples. We focus on
the network deﬁned by liabilities between ﬁnancial institutions. These payment obligations create the
most direct channel for the spread of losses.
It turns out that one can derive general bounds on the eﬀects of this source of interconnectedness
with almost no information about the network topology: our bounds hold independently of the degree
distribution, amount of connectivity, node centrality, average path length, and so forth. The topologyfree property of our results is one of the main contributions of this work. Moreover, we impose probability
distributions on the shocks to the nodes and show that the same bounds hold for a wide range of
distributions, including beta, exponential, normal, and many others. This robustness is important
because detailed information about interbank liabilities is often unavailable and the exact form of the
shock distributions is subject to considerable uncertainty.
To model a network of payment obligations, we build on the elegant framework of Eisenberg and
Noe (2001). The model speciﬁes a set of nodes that represent ﬁnancial institutions together with the
obligations between them. Given an initial shock to the balance sheets of one or more nodes, one can
compute a set of payments that clear the network by solving a ﬁxed-point problem. This framework is
1 See, for example, Bank of England 2011, International Monetary Fund 2012, and Oﬃce of Financial Research 2012.
in particular Allen and Gale (2000), Upper and Worms (2002), Degryse and Nguyen (2004), Goodhart, Sunirand,
and Tsomocos (2004), Elsinger, Lehar, and Summer (2006), Allen and Babus (2009), Gai and Kapadia (2010), Gai,
Haldane, and Kapadia (2011), Haldane and May (2011), Upper (2011), Allen and Carletti (2011), Georg (2011), Rogers
and Veraart (2012), Acemoglu, Ozdaglar, and Tahbaz-Salehi (2013), and Elliott, Golub, and Jackson (2013).
2 See 1 very useful for analyzing how losses propagate through the ﬁnancial system. A concrete example would
be delinquencies in mortgage payments: if some fraction of a banks mortgages are delinquent and it has
insuﬃcient reserves to cover the shortfall, then it will be unable...
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- Spring '11