We introduce a general model for the balance-sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the presence of uncertainty on banks external assets. At the same time, it also provides a natural extension of classic structural credit risk models to the case of an interconnected system. We characterize the existence and uniqueness of a valuation that maximises individual and total equity values for all banks. We apply our model to the assessment of systemic risk, and in particular for the case of stress-testing. Further, we provide a fixed-point algorithm to carry out the network valuation and the conditions for its convergence.
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