Collateralized debt networks with lender default

The Lehman Brothers' 2008 bankruptcy spread losses to its counterparties even when Lehman was a lender of cash, because collateral for that lending was tied up in the bankruptcy process. I study the implications of such lender default using a general equilibrium network model featuring endogenous leverage, endogenous asset prices, and endogenous network formation. The multiplex graph model has two channels of contagion: a counterparty channel of contagion and a price channel of contagion through endogenous collateral price. Borrowers diversify their lenders because of the counterparty risk, but they have to deal with lenders who lend at a higher margin. This diversification generates positive externalities by reducing systemic risk, but any decentralized equilibrium is constrained inefficient due to under-diversification. The key externalities here, arising from the tradeoff between counterparty risk and leverage (margin), are absent in models with exogenous leverage or exogenous networks. I use this framework to analyze the introduction of a central counterparty (CCP). I show that the loss coverage by the CCP reduces diversification incentives and exacerbates the externality problem which can rather increase systemic risk