We present an agent based model where banks choose the amount of liquidity to post to an interbank payment system

1. An agent-based model of payment systems Marco Galbiati Bank of England Kimmo Soramäki ECB, www.soramaki.net ECB-BoE Conference Payments and Monetary and Financial Stability 12-13 November 2007

2. Motivation, related work Model Results Conclusions Overview of the presentation Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

3. Motivation, related work Model Results Conclusions Overview of the presentation Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

4. Motivation, related work Model Results Conclusions Overview of the presentation Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

5. Motivation, related work Model Results Conclusions Overview of the presentation Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

6. Motivation, related work Model Results Conclusions Overview of the presentation Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

7. Liquidity in payment systems Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

8. Liquidity in payment systems Deferred Net Settlement vs Real Time Gross Settlement Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

9. Liquidity in payment systems Deferred Net Settlement vs Real Time Gross Settlement Liquidity risk (and operational risk) Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

10. Liquidity in payment systems Deferred Net Settlement vs Real Time Gross Settlement Liquidity risk (and operational risk) Liquidity as a common good Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

11. Liquidity is costly: tradeoff cost-of-liquidity / cost-of-delay Liquidity in payment systems Deferred Net Settlement vs Real Time Gross Settlement Liquidity risk (and operational risk) Liquidity as a common good Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

12. Related literature Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

15. Model overview RTGS á la UK CHAPS: banks choose an opening balance at the beginning of each day, used to settle payments during the day. Banks face a random stream of payment orders, to be settled out of their liquidity. Beside funding costs, banks (may) experience delay costs Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

16. Model overview RTGS á la UK CHAPS: banks choose an opening balance at the beginning of each day, used to settle payments during the day. Banks face a random stream of payment orders, to be settled out of their liquidity. Beside funding costs, banks (may) experience delay costs Banks adapt their opening balances over time, learning from experience, until equilibrium is reached We look at properties of equilibrium liquidity Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

17. Model overview We consider two scenarios: “ normal conditions” and “operational failures” RTGS á la UK CHAPS: banks choose an opening balance at the beginning of each day, used to settle payments during the day. Banks face a random stream of payment orders, to be settled out of their liquidity. Beside funding costs, banks (may) experience delay costs Banks adapt their opening balances over time, learning from experience, until equilibrium is reached We look at properties of equilibrium liquidity Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

18. Settlement algorithm i receives order to pay to i time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

19. Settlement algorithm i receives order to pay to i if i has funds the order is settled : j receives funds else, the order is queued time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

20. Settlement algorithm i receives order to pay to i if i has funds the order is settled : j receives funds if j has queued payments, the first one (say to k ) is settled else, the order is queued time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

21. Settlement algorithm i receives order to pay to i if i has funds the order is settled : j receives funds if j has queued payments, the first one (say to k ) is settled if k has queued payments, the first one (to ...) is settled else, the order is queued time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

22. Settlement algorithm i receives order to pay to i if i has funds the order is settled : j receives funds if j has queued payments, the first one (say to k ) is settled if k has queued payments, the first one (to ...) is settled ... cascade ends when the recipient of the payment has no queued payments else, the order is queued time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

23. Settlement algorithm i receives order to pay to i if i has funds the order is settled : j receives funds if j has queued payments, the first one (say to k ) is settled if k has queued payments, the first one (to ...) is settled ... cascade ends when the recipient of the payment has no queued payments else, the order is queued the algorithm is run 30 million times, for different liquidity levels k receives order to pay to z time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

24. Settlement algorithm i receives order to pay to i if i has funds the order is settled : j receives funds if j has queued payments, the first one (say to k ) is settled if k has queued payments, the first one (to ...) is settled ... cascade ends when the recipient of the payment has no queued payments else, the order is queued the algorithm is run 30 million times, for different liquidity levels k receives order to pay to z Payment orders arrive according to a Poisson process. Each bank equally likely as sender/ recipient  complete symmetric network time Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

30. Learning the equilibrium Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1

34. Total costs price of delays = 1 price of delays = 2 price of delays = 5 price of delays = 20 cost, i cost, i cost, i cost, i funds committed by i funds committed by i funds committed by i funds committed by i funds committed by <j> funds committed by others funds committed by others funds committed by others funds committed by others Social Optimum 11 Size I 12 Size II 13 Conclusions 16 Incident II 15 Incident I 14 Base case 10 Total costs 9 Learning 8 The game 7 Algorithm II 6 Algorithm 5 Model 4 Literature 3 Liquidity 2 Overview 1