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This paper analyzes counterparty risk in entangled financial systems in which banks hedge risks using a network of bilateral over-the-counter contracts. If banks have large exposures to a few counterparties, they do not buy insurance against a low probability counterparty default even though it is socially desirable. This is because they do not take into account that their own failure also drags down other banks - a network externality. Given that banks choose short-term financing, the failure of a single large bank prompts a systemic run. Taxing over-the-counter contracts to finance a bailout fund or mandatory counterparty insurance is welfare improving.
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