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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 sense.2 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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