The Analytics of a Real-time Gross-settlement System

Marco Rossi
IRES, Catholic University of Louvain
dh95@cityscape.co.uk

Abstract

The payment system is a direct channel through which liquidity and credit problems are transferred from one participant in the financial system to another and also one of the first places where financial stress can manifest itself, through the inability of payment system participants to meet their obligations. Moreover its structure might affect the functioning of the interbank market and influence the determination of money market interest rates impacting, in this way, on the monetary policy transmission mechanism.

Most central banks are facing the problem of intraday liquidity provision to RTGS systems. Banks' liquidity needs arise from their payment system activities. If, over a given period of time, they send payment orders whose value exceeds the value of the payment orders they receive, they incur a liquidity shortfall which can be met either out of their preconstituted holdings at the central bank or by obtaining credit from the settlement agent (the central bank in most cases) or from other participants in the payment system.

In this paper I assume that an order, which cannot be settled immediately because insufficient funds are available, is automatically queued and released when necessary fund coverage is provided. The analysis (modelling) of a payment system with a queueing devise is central to the understanding of the reason why intraday liquidity needs to be provided in RTGS systems. In any such system, there are trade-offs to be considered by the single participating bank. If it holds a very large amount of liquid funds, then queues rarely form; however a fraction of its liquidity is likely to remain unused (idle) for most of the time. By contrast, if it holds very few liquid funds, then almost all payments must join a queue before being processed; this might produce dissatisfaction and, eventually, loss of clients. In these circumstances we might want to consider the following issues:

• how long does an order wait in the system and on a queue in particular ?
• how many payment orders will be queueing in the system ?
• under what conditions can the system become congested ? (Congestion in a payment system may easily turn into a liquidity gridlock situation with dire consequences for the functioning of the whole system itself.)

The answer to these questions depends on the interplay of two unpredictable quantities: the arrival time and the processing time. This paper identifies measures of performance and effectiveness such as the waiting time for the payment order to be executed, the number of payment orders in the system at any point in time. These are random variables and, therefore, their probabilistic description (i.e. their probability distribution function) is derived (In a companion paper I extend this basic framework to allow for an arbitrary processing-time distribution and different queueing disciplines.) The paper is organised as follows. Section 1 defines some notation and presents some preliminary, general results. A (realistic) simple stochastic process is introduced in Section 2 to describe payment flows and the random variables describing the payment system and their effects on queueing phenomena are considered. Section 3 presents a simple simulation. Section 4 concludes and discusses some policy implications.

An analytical framework would enable the participating bank to ensure that a proper level of `service' be provided in terms of queueing time, while avoiding excessive costs. Moreover, it could indicate that the expected load in the future will swamp the present system and indicate the higher level of liquidity needed.

The smooth functioning of the payment system would facilitate the circulation of means of payment among economic agents, affecting the efficiency with which goods, services and financial assets are produced and used. This, in turn, would have beneficial effects not only on financial markets, but also across the entire economic system.