  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.

Risk Management;Physics and Society