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doi: 10.3934/jimo.2021091
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An online-decision algorithm for the multi-period bank clearing problem

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

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

Received  February 2021 Revised  March 2021 Early access April 2021

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.

Citation: Zongwei Chen. An online-decision algorithm for the multi-period bank clearing problem. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021091
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.  Google Scholar

[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.   Google Scholar

[3]

M. L. BechC. Preisig and K. Soramaki, Global trends in large-value payments, Economic Policy Review, 14 (2008), 59-81.  doi: 10.2139/ssrn.1141387.  Google Scholar

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D. Bertsimas and J. N. Tsitsiklis, Introduction to linear optimization, 2$^nd$ edition, Cambridge, MA, USA: Athena Scientific, (1997), 139–199. Google Scholar

[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.   Google Scholar

[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.  Google Scholar

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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. Google Scholar

[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.  Google Scholar

[9]

M. M. GüntzerD. Jungnickel and M. Leclerc, Efficient algorithms for the clearing of interbank payments, European Journal of Operational Research, 106 (1998), 212-219.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[12]

J. McAndrews and S. Rajan, The timing and funding of fedwire funds transfers, Economic Policy Review, 6 (2000), 17-32.   Google Scholar

[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.   Google Scholar

[14]

J. NanduriY. Jia and A. Oka et al., Microsoft uses machine learning and optimization to reduce E-commerce fraud, Interfaces, 55 (2020), 64-79.   Google Scholar

[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.  Google Scholar

[16]

S. J. Qin and T. A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice, 11 (2003), 733-764.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

K. SoramäkiM. L. BechJ. ArnoldR. J. Glass and W. E. Beyeler, The topology of interbank payment flows, Physica A Statistical Mechanics & Its Applications, 379 (2007), 317-333.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[22]

Y. Wang and S. Boyd, Fast model predictive control using online optimization, IEEE Transactions on Control Systems Technology, 18 (2010), 267-278.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

show all references

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.  Google Scholar

[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.   Google Scholar

[3]

M. L. BechC. Preisig and K. Soramaki, Global trends in large-value payments, Economic Policy Review, 14 (2008), 59-81.  doi: 10.2139/ssrn.1141387.  Google Scholar

[4]

D. Bertsimas and J. N. Tsitsiklis, Introduction to linear optimization, 2$^nd$ edition, Cambridge, MA, USA: Athena Scientific, (1997), 139–199. Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[9]

M. M. GüntzerD. Jungnickel and M. Leclerc, Efficient algorithms for the clearing of interbank payments, European Journal of Operational Research, 106 (1998), 212-219.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[12]

J. McAndrews and S. Rajan, The timing and funding of fedwire funds transfers, Economic Policy Review, 6 (2000), 17-32.   Google Scholar

[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.   Google Scholar

[14]

J. NanduriY. Jia and A. Oka et al., Microsoft uses machine learning and optimization to reduce E-commerce fraud, Interfaces, 55 (2020), 64-79.   Google Scholar

[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.  Google Scholar

[16]

S. J. Qin and T. A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice, 11 (2003), 733-764.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

K. SoramäkiM. L. BechJ. ArnoldR. J. Glass and W. E. Beyeler, The topology of interbank payment flows, Physica A Statistical Mechanics & Its Applications, 379 (2007), 317-333.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[22]

Y. Wang and S. Boyd, Fast model predictive control using online optimization, IEEE Transactions on Control Systems Technology, 18 (2010), 267-278.   Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

Figure 1.  Results of the greedy policy
Figure 2.  Results of a clearing policy considering future payments
Figure 3.  Aggregated settlement interval
Figure 4.  The empirical cumulative distribution function of $ \eta(x) $ with different reference periods $ (P) $
Figure 5.  Performance under the three policies during a working day
Figure 6.  Comparing Different Policies
Figure 7.  The empirical cumulative distribution function of $ \eta $$ (x) $ with different interval lengths
Table 1.  Data sample
Sending Bank ID Receiving Bank ID Payment Amount Submit Time
12 4 56000.00 Day1 9:40:06
4 11 532200.00 Day2 8:30:21
13 11 367506.68 Day3 8:30:46
Sending Bank ID Receiving Bank ID Payment Amount Submit Time
12 4 56000.00 Day1 9:40:06
4 11 532200.00 Day2 8:30:21
13 11 367506.68 Day3 8:30:46
Table 2.  $ payment_i $ of banks (in billion CNY)
BankID 1 2 3 4 5 6 7 8 9 10
$ payment_i $ 61.93 17.22 10.99 46.82 44.34 0.71 18.86 6.78 14.05 26.11
Bank ID 11 12 13 14 15 16 17 18 19 20
$ payment_i $ 16.64 23.39 7.90 3.19 7.36 10.87 6.10 3.47 1.76 1.91
BankID 1 2 3 4 5 6 7 8 9 10
$ payment_i $ 61.93 17.22 10.99 46.82 44.34 0.71 18.86 6.78 14.05 26.11
Bank ID 11 12 13 14 15 16 17 18 19 20
$ payment_i $ 16.64 23.39 7.90 3.19 7.36 10.87 6.10 3.47 1.76 1.91
Table 3.  Descriptive statistics of the MPC policy's $ \eta $$ (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
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
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
$ 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
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
$ 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
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
$ 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
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