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The banking system is highly interconnected and these connections can be conveniently represented as an interbank network. This survey presents a systematic overview of the recent advances in the theoretical literature on interbank networks. We assess our current understanding of the structure of interbank networks, of how network characteristics affect contagion in the banking system and of how banks form connections when faced with the possibility of contagion and systemic risk. In particular, we highlight how the theoretical literature on interbank networks offers a coherent way of studying interconnections, contagion processes and systemic risk, while emphasizing at the same time the challenges that must be addressed before general results on the link between the structure of the interbank network and financial stability can be established. The survey concludes with a discussion of the policy relevance of interbank network models with a special focus on macroprudential policies and monetary policy.
We present a network model of the interbank market in which optimizing risk averse banks lend to each other and invest in non-liquid assets. Market clearing takes place through a tâtonnement process which yields the equilibrium price, while traded quantities are determined by means of a matching algorithm. We compare three alternative matching algorithms: maximum entropy, closest matching and random matching. Contagion occurs through liquidity hoarding, interbank interlinkages and fire sale externalities. The resulting network configurations exhibits a core-periphery structure, dis-assortative behavior and low clustering coefficient. We measure systemic importance by means of network centrality and input-output metrics and the contribution of systemic risk by means of Shapley values. Within this framework we analyze the effects of prudential policies on the stability/efficiency trade-off. Liquidity requirements unequivocally decrease systemic risk but at the cost of lower efficiency (measured by aggregate investment in non-liquid assets); equity requirements tend to reduce risk (hence increase stability) without reducing significantly overall investment.