Congestion and cascades in payment systems

We develop a parsimonious model of the interbank payment system to study congestion and the role of liquidity markets in alleviating congestion. The model incorporates an endogenous instruction arrival process, scale-free topology of payments between banks, fixed total liquidity that limits banks’ capacity to process arriving instructions, and a global market that distributes liquidity. We find that at low liquidity, the system becomes congested and payment settlement loses correlation with payment instruction arrival, becoming coupled across the network. The onset of congestion is evidently related to the relative values of three characteristic times: the time for banks’ net position to return to zero, the time for banks to exhaust their liquidity endowments, and the liquidity market relaxation time. In the congested regime, settlement takes place in cascades having a characteristic size. A global liquidity market substantially diminishes congestion, requiring only a small fraction of the payment-induced liquidity flow to achieve strong beneficial effects.