Abstract
In Zawadowski (Rev Financ Stud 26:1291–1323, 2013) introduces a banking network model in which the asset and counter-party risks are treated separately and the banks hedge their asset 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 defaults, 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 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 Zawadowski (Rev Financ Stud 26:1291–1323, 2013) to show that as the number of counter-party neighbors increases 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.
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Thus, the owners will decide to hedge their counter-party risk thereby helping to contain an economic crisis.
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DasGupta, B., Kaligounder, L. (2014). Densely Entangled Financial Systems. In: Kalyagin, V., Pardalos, P., Rassias, T. (eds) Network Models in Economics and Finance. Springer Optimization and Its Applications, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-09683-4_5
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