On the Indeterminacy of the Clearing Payments Vectors in Numerical Simulations on Financial Networks

This paper points out a methodological lacuna in the recent stream of numerical analyses of contagion in financial networks, and puts forward a solution to emend it. Under some conditions, the intercyclical obligations that connect the agents in a financial network cause the indeterminacy of the vector of payments that clears such obligations. This problem, first pointed out by Eisenberg and Noe (2001), has received little or no attention by authors who investigate payment flows and domino effects in networks using numerical simulations. We here present an original result that pins down necessary and sufficient conditions for the uniqueness of the clearing payments vector for any financial network, and show how to use this result to control for the occurrence of the above mentioned indeterminacy while performing numerical exercises on financial networks.