A flow network analysis of direct balance-sheet contagion in financial networks

This paper puts forward a novel approach to the analysis of direct contagion in

financial networks. Financial systems are here represented as flow networks -i.e., directed

and weighted graphs endowed with source nodes and sink nodes – and the propagation of

losses and defaults, originated by an exogenous shock, is here represented as a flow that

crosses such a network. In establishing existence and uniqueness of such a flow function,

we address a know problem of indeterminacy that arise, in financial networks, from the

intercyclicity of payments. Sufficient and necessary conditions for uniqueness are pinned

down. We embed this result in an algorithm that, while computing the propagation caused by

a shock, controls for the emergence of possible indeterminacies. We then apply some

properties of network flows to investigate the relation between the structures of a financial

network-i.e. the size and the pattern of obligations - and its exposure to default contagion.