  In this paper we estimate the propagation of liquidity shocks through
interbank markets when the information about the underlying credit network is
incomplete. We show that techniques such as Maximum Entropy currently used to
reconstruct credit networks severely underestimate the risk of contagion by
assuming a trivial (fully connected) topology, a type of network structure
which can be very different from the one empirically observed. We propose an
efficient message-passing algorithm to explore the space of possible network
structures, and show that a correct estimation of the network degree of
connectedness leads to more reliable estimations for systemic risk. Such
algorithm is also able to produce maximally fragile structures, providing a
practical upper bound for the risk of contagion when the actual network
structure is unknown. We test our algorithm on ensembles of synthetic data
encoding some features of real financial networks (sparsity and heterogeneity),
finding that more accurate estimations of risk can be achieved. Finally we find
that this algorithm can be used to control the amount of information regulators
need to require from banks in order to sufficiently constrain the
reconstruction of financial networks.
