An online-decision algorithm for the multi-period bank clearing problem

Zongwei Chen

doi:10.3934/jimo.2021091

Article Contents

2022, Volume 18, Issue 4: 2783-2803. Doi: 10.3934/jimo.2021091

This issue Previous Article The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain Next Article Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

An online-decision algorithm for the multi-period bank clearing problem

Zongwei Chen^,

School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China

^* Corresponding author: Zongwei Chen, czw@163.sufe.edu.cn
^* Corresponding author: Zongwei Chen, czw@163.sufe.edu.cn

Received: January 31, 2021

Revised: February 28, 2021

Published: July 2022

Abstract Full Text(HTML) Figure(7) / Table(6) Related Papers Cited by

Abstract

The bank clearing problem (BCP) refers to the problem of designing an optimal clearing algorithm for the interbank payment system. Due to the way in which for the payment system has evolved, the classical BCP model is insufficient for addressing this problem accurately. In particular, delayed settlements are allowed in the now popular high-frequency deferred net settlement (DNS) system. In practice, the characteristics of incoming payment instructions are heavily connected to the time of day, and can be predicted with reasonable precision based on historical data. In this paper, we study the multi-period bank clearing problem (MBCP) by introducing the time dimension and considering future instructions in the decision-making process. We design a new clearing algorithm for MBCP using a model predictive control (MPC) policy, which uses historical data to predict payment instructions in the future. We benchmark the designed algorithm's performance with the classical greedy algorithm on the basis of BCP. Given that the liquidity is regular or relatively low, the numerical results indicate that the designed algorithm significantly improves the quality of clearing decision-making and is robust with respect to forecasting errors and fluctuation of future transactions.

Correction: Instances of “sanitized data from CNAPS” have been corrected to “simulated data of CNAPS”. We apologize for any inconvenience this may cause.

Keywords:

Mathematics Subject Classification: Primary: 93-10.

Citation:

Full Text(HTML)

Figure 1. Results of the greedy policy

Download: Full-size image PowerPoint slide

Figure 2. Results of a clearing policy considering future payments

Download: Full-size image PowerPoint slide

Figure 3. Aggregated settlement interval

Download: Full-size image PowerPoint slide

Figure 4. The empirical cumulative distribution function of $ \eta(x) $ with different reference periods $ (P) $

Download: Full-size image PowerPoint slide

Figure 5. Performance under the three policies during a working day

Download: Full-size image PowerPoint slide

Figure 6. Comparing Different Policies

Download: Full-size image PowerPoint slide

Figure 7. The empirical cumulative distribution function of $ \eta $$ (x) $ with different interval lengths

Download: Full-size image PowerPoint slide

Table 1. Data sample

Sending Bank ID	Receiving Bank ID	Payment Amount	Submit Time
12	4	56000.00	Day1 9:40:06
4	11	532200.00	Day2 8:30:21
13	11	367506.68	Day3 8:30:46

| Show Table

DownLoad: CSV

Table 2. $ payment_i $ of banks (in billion CNY)

BankID	1	2	3	4	5	6	7	8	9	10
$ payment_i $	61.93	17.22	10.99	46.82	44.34	0.71	18.86	6.78	14.05	26.11
Bank ID	11	12	13	14	15	16	17	18	19	20
$ payment_i $	16.64	23.39	7.90	3.19	7.36	10.87	6.10	3.47	1.76	1.91

| Show Table

DownLoad: CSV

Table 3. Descriptive statistics of the MPC policy's $ \eta $$ (x) $ under different values of $ P $

Reference Period$ (P) $	Mean	S.D.	Upper 5%	Lower 5%
20 days	1.22	0.26	2.30	0.90
10 days	1.19	0.25	2.28	0.86
5 days	1.19	0.28	2.00	0.78
2 days	1.15	0.31	1.98	0.73
1 day	1.08	0.29	2.02	0.68

| Show Table

DownLoad: CSV

Table 4. Mean, standard deviation, and lower $ 5 $th percentile of $ \eta $$ (x) $ for different values of $ L $ and different $ R $

	$ R $	$ 20\% $	$ 10\% $	$ 8\% $	$ 6\% $	$ 4\% $	$ 2\% $
	Mean	1.35	1.33	1.34	1.23	1.17	1.16
$ L=600 $	S.D.	0.94	0.82	0.81	0.33	0.24	0.15
	Lower 5%	0.23	0.61	0.78	0.84	0.84	0.94
	Mean	1.23	1.38	1.30	1.21	1.24	1.18
$ L=300 $	S.D.	0.55	0.89	0.68	0.27	0.23	0.15
	Lower 5%	0.40	0.68	0.80	0.84	0.91	0.97
	Mean	1.24	1.31	1.31	1.23	1.21	1.21
$ L=120 $	S.D.	0.50	0.66	0.61	0.26	0.21	0.16
	Lower 5%	0.62	0.76	0.91	0.90	0.95	0.97
	Mean	1.22	1.25	1.27	1.22	1.22	1.21
$ L=60 $	S.D.	0.54	0.51	0.49	0.22	0.21	0.16
	Lower 5%	0.66	0.74	0.83	0.94	0.95	1.01
	Mean	1.23	1.29	1.25	1.22	1.21	1.23
$ L=30 $	S.D.	0.49	0.66	0.45	0.23	0.21	0.16
	Lower 5%	0.68	0.73	0.83	0.95	0.96	1.00

| Show Table

DownLoad: CSV

Table 5. Computation time (upper $ 99\% $) at different values of $ g $

	$ g=1 $	$ g=2 $	$ g=5 $	$ g=10 $	$ g=20 $	$ g=40 $
$ L $=600	0.73	0.52	0.13	0.06	0.03	0.01
$ L $=300	3.20	1.11	0.41	0.16	0.13	0.05
$ L $=120	28.68	5.95	1.38	0.89	0.42	0.39
$ L $=60	$>60.00 $	28.44	3.78	1.42	1.39	1.39
$ L $=30	$>30.00 $	$>30.00 $	14.42	3.80	1.83	1.56

| Show Table

DownLoad: CSV

Table 6. Mean, standard deviation, and lower $ 5 $th percentile of $ \eta $$ (x) $ for different values of $ L $ and $ g $ with $ R $ = $ 6\% $

		$ g=1 $	$ g=2 $	$ g=5 $	$ g=10 $	$ g=20 $	$ g=40 $
	mean	1.27	1.25	1.22	1.11	1.08	1.03
$ L $=600	S.D.	0.37	0.29	0.33	0.23	0.24	0.24
	lower 5%	0.79	0.89	0.81	0.76	0.67	0.68
	mean	1.24	1.24	1.21	1.17	1.09	1.06
$ L $=300	S.D.	0.26	0.29	0.27	0.26	0.20	0.21
	lower 5%	0.85	0.88	0.84	0.82	0.75	0.72
	mean	1.22	1.24	1.23	1.22	1.18	1.12
$ L $=120	S.D.	0.26	0.26	0.27	0.24	0.22	0.20
	lower 5%	0.91	0.93	0.89	0.92	0.88	0.81
	mean	-	1.21	1.22	1.20	1.19	1.16
$ L $=60	S.D.	-	0.25	0.23	0.21	0.21	0.19
	lower 5%	-	0.93	0.93	0.93	0.95	0.90
	mean	-	-	1.22	1.21	1.21	1.19
$ L $=30	S.D.	-	-	0.23	0.22	0.22	0.19
	lower 5%	-	-	0.96	0.89	0.91	0.94

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

[1]	P. Angelini, An analysis of competitive externalities in gross settlement systems, Journal of Banking & Finance, 22 (1998), 1-18. doi: 10.1016/S0378-4266(97)00043-5.
[2]	M. L. Bech and R. J. Garratt, Illiquidity in the interbank payment system following wide-scale disruptions, J. Money, Credit Bank, 44 (2012), 903-929.
[3]	M. L. Bech, C. Preisig and K. Soramaki, Global trends in large-value payments, Economic Policy Review, 14 (2008), 59-81. doi: 10.2139/ssrn.1141387.
[4]	D. Bertsimas and J. N. Tsitsiklis, Introduction to linear optimization, 2$^nd$ edition, Cambridge, MA, USA: Athena Scientific, (1997), 139–199.
[5]	N. Davey and D. Gray, How has the liquidity saving mechanism reduced banks' intraday liquidity costs in CHAPS?, Bank of England Quarterly Bulletin, 54 (2014), 180-189.
[6]	E. Denbee and B. Norman, The impact of payment splitting on liquidity requirements in RTGS, Working paper of Bank of England, (2010), 35 pp. Available from: https://www.bankofengland.co.uk/working-paper/2010/the-impact-of-payment-splitting-on-liquidity-requirements-in-rtgs. doi: 10.2139/ssrn.1701172.
[7]	M. Diehl and U. Schollmeyer, Liquidity-Saving Mechanisms: Quantifying the Benefits in TARGET2, Working paper of Deutsche Bundesbank, 2011. Available from: https://www.bis.org/cpmi/publ/d67.pdf.
[8]	R. Garrat and P. Zimmerman, Centralized netting in financial networks, Journal of Banking & Finance, 112 (2020), Article 105270. doi: 10.1016/j.jbankfin.2017.12.008.
[9]	M. M. Güntzer, D. Jungnickel and M. Leclerc, Efficient algorithms for the clearing of interbank payments, European Journal of Operational Research, 106 (1998), 212-219.
[10]	Z. Guo, R. J. Kauffman, M. Lin and D. Ma, Mechanism design for near real-time retail payment and settlement systems, IEEE 2015 48th Hawaii International Conference on System Sciences (HICSS) - HI, USA, (2015), 4824–4833. doi: 10.1109/HICSS.2015.573.
[11]	M. Hellqvist and T. Laine, (eds.), Diagnostics for the financial markets: Computational studies of payment systems, \emphHelsinki, FIN: Edita Prima Oy, (2012), 267–315 and 341–379.
[12]	J. McAndrews and S. Rajan, The timing and funding of fedwire funds transfers, Economic Policy Review, 6 (2000), 17-32.
[13]	O. Merrouche and J. Schanz, Banks' intraday liquidity management during operational outages: Theory and evidence from the UK payment system, Journal of Banking & Finance, 34 (2010), 314-323.
[14]	J. Nanduri, Y. Jia and A. Oka et al., Microsoft uses machine learning and optimization to reduce E-commerce fraud, Interfaces, 55 (2020), 64-79.
[15]	T. Nellen, Intraday liquidity facilities, late settlement fee and coordination, Journal of Banking & Finance, 106 (2019), 124-131. doi: 10.1016/j.jbankfin.2019.06.009.
[16]	S. J. Qin and T. A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice, 11 (2003), 733-764.
[17]	S. Rosati and S. Secola, Explaining cross-border large-value payment flows: Evidence from TARGET and EURO1 data, Journal of Banking & Finance, 30 (2006), 1753-1782. doi: 10.1016/j.jbankfin.2005.09.011.
[18]	Y. M. Shafransky and A. A. Doudkin, An optimization algorithm for the clearing of interbank payments, European Journal of Operational Research, 171 (2006), 743-749. doi: 10.1016/j.ejor.2004.09.003.
[19]	K. Soramäki, M. L. Bech, J. Arnold, R. J. Glass and W. E. Beyeler, The topology of interbank payment flows, Physica A Statistical Mechanics & Its Applications, 379 (2007), 317-333.
[20]	A. Suponenkovs, A. Sisojevs, G. Mosãns et al., Application of image recognition and machine learning technologies for payment data processing review and challenges, 5th IEEE Workshop on Advances in Information, Electronic and Electrical Engineering (AIEEE), (2017), 1–6. doi: 10.1109/AIEEE.2017.8270536.
[21]	H. Tomura, Payment instruments and collateral in the interbank payment system, J. Econom. Theory, 178 (2018), 82-104. doi: 10.1016/j.jet.2018.08.008.
[22]	Y. Wang and S. Boyd, Fast model predictive control using online optimization, IEEE Transactions on Control Systems Technology, 18 (2010), 267-278.
[23]	M. Willison, Real-time gross settlement and hybrid payment systems: A comparison, Bank of England Quarterly Bulletin, 45 (2005), 53. doi: 10.2139/ssrn.724042.
[24]	Bank for International Settlements, Statistics on payment, Clearing and Settlement Systems in the CPMI - Figures for 2015, Report of Bank for International Settlements, 2015. Available from: https://www.bis.org/cpmi/publ/d152.pdf.
[25]	Bank for International Settlements, Real-Time Gross Settlement Systems, Report of Bank for International Settlements, 1997. Available from: https://www.bis.org/cpmi/publ/d22.pdf.
[26]	Bank for International Settlements, Report on Netting Schemes (Angell Report), Report of Bank for International Settlements, 1989. Available from: https://www.bis.org/cpmi/publ/d02.pdf.
[27]	Bank for International Settlements, New Developments in Large-Value Payment Systems, 2005, Report of Bank for International Settlements, 2005. Available from: https://www.bis.org/cpmi/publ/d67.pdf.