Intraday liquidity management in gross settlement system as a coordination game

Real time gross settlement systems (RTGS-systems) operated by central banks are the predominant form of large value payment systems. They allow execution of fund transfers between central bank accounts of commercial banks and other financial institutions as a continuous process by settling payments individually, with their full value and with immediate finality. Because individual payments are settled in gross, the amount of liquidity needed for smooth processing of payments in RTGS-system is large. Central banks mitigate this problem by offering intraday credit for RTGS-system participants (banks henceforth) against eligible collateral or against interest. Both of these options create expenses for banks either in form of opportunity cost of collateral or explicit interest payments. Since the liquidity obtained from incoming payments from counterparties is free for banks, they may have an incentive to delay payments in expectation of forthcoming payments from other banks, which would decrease the cost of liquidity. This thesis theoretically analyzes the strategic behavior of banks that are processing stochastic payment orders from their customers in an RTGS-system. The purpose of the thesis is to (1) extend earlier theoretical studies into multi-player games and, especially, (2) analyze the possibility of emergence of a coordination game in which multiple equilibrium outcomes would be possible. Starting points for the thesis have been the models presented by Bech – Garratt (2002) and Angelini (1998). In the formulated model intraday liquidity is assumed to be available against collateral, the amount of which can be dynamically managed by the banks. The game has two periods, and information possessed by banks is incomplete and imperfect. Banks are modelled as heterogeneous and risk neutral agents who minimize the total costs of payment processing. These consist of the cost of liquidity and the cost of delaying payments. The latter is used to describe reputation risk and possible loss of future revenues due to customer dissatisfaction. Strategy of a bank is describing decision of overall share of payment orders received from customers in the first period, which are processed immediately. It was found that the formulated multi-player model did not have an analytical solution. Thus Bayesian equi-libria for the game were solved numerically as a function of paremeters for cost structure and payment distribution in an example case with a quadratic form for cost functions. The resulting optimal responses of banks were shown to be inversely related with the average decision of counterparties especially when the cost …