Markov type models for large-valued interbank payment systems

• Main Author: Che, Xiaonan
• Published: London School of Economics and Political Science (University of London) 2011
• Subjects: 332.1; HA Statistics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.548117

Due to the reform of payment systems from netting settlement systems to Real Time Gross Settlement systems (RTGS) around the world in recent years, there is a dramatic increase in the interest in modeling the large-valued interbank payment system. Recently some queueing facilities have been introduced in the response to the liquidity management within the RTGS systems. Since stochastic process models have been wildly applied in social networks, and some aspects of which have similar statistical properties with the payment system, therefore, based on the existing empirical research, a Markov type model for RTGS payment system with queueing and collateral borrowing facilities was developed. We analysed the effect on the performance of the payment system of the parameters, such as the probabilities of payment delay, the initial cash position of participating banks and the probabilities of cross bank payments. Two models were proposed; one is the simplest model where payments were assumed to be equally distributed among participating banks, the other one is a so-called "cluster" model, that there exists a concentration of payments flow between a few banks according to the evidence from empirical studies. We have found that the performance of the system depends on these parameters. A modest amount of total initial liquidity required by banks would achieve a desired performance, that minimising the number of unsettled payments by the end of a business day and negligible average lifetime of the debts. Because of the change of large-valued interbank payment systems, the concern has shift from credit risk to liquidity risk, and the payment systems around world started considering or already implemented different liquidity saving mechanisms to reduce the high demand of liquidity and maintain the low risk of default in the mean time. We proposed a specified queueing facility to the "cluster" model with modification with the consideration of the feature of the UK RTGS payment system, CHAPS. Some of thepayments would be submitted into a external queue by certain rules, and will be settled according an algorithm of bilateral or multilateral offsetting. While participating banks's post liquidity will be reserved for "important" payments only. The experiment of using simulated data showed that the liquidity saving mechanism was not equally beneficial to every bank, the banks who dominated most of the payment flow even suffered from higher level of debts at the end of a business day comparing with a pure RTGS system without any queueing facility. The stability of the structure of the central queue was verified. There was evidence that banks in the UK payment system would set up limits for other members to prevent unexpected credit exposure, and with these limits, banks also achieved a moderate liquidity saving in CHAPS. Both central bank and participating banks are interested in the probability that the limits are excess. The problem can be reduced to the calculation of boundary crossing probability from a Brownian motion with stochastic boundaries. Boundary crossing problems are very popular in many fields of Statistics. With powerful tools, such as martingales and infinitesimal generator of Brownian motion, we presented an alternative method and derived a set of theorems of boundary crossing probabilities for a Brownian motion with different kinds of stochastic boundaries, especially compound Poisson process boundaries. Both the numerical results and simulation experiments are studies. A variation of the method would be discussed when apply it to other stochastic boundaries, for instances, Gamma process, Inverse Gaussian process and Telegraph process. Finally, we provided a brief survey of approximations of Levy processes. The boundary crossing probabilities theorems derived earlier could be extended to a fair general situation with Levy process boundaries, by using an appropriate approximation.