Real-Time Gross Settlement and Hybrid Payment Systems: A Comparison

1. Real-Time Gross Settlement and Hybrid Payment Systems: A Comparison Matthew Willison Bank of England The views expressed in this paper are those of the author, and do not necessarily reflect those of the Bank of England.

2. Background • DNS versus RTGS credit risk versus liquidity demands. • Hybrids no credit and settlement risk but more liquidity efficient (?).

3. Literature Review • BIS Report (1997) • McAndrews and Trundle (2001) • Roberds (1999) • Simulations; e.g., Johnston et al. (2003)

4. Aim of the paper • Assess the welfare properties of RTGS and hybrid payment systems. • But while allowing bank behaviour to fully depend on the payment system design in place.

5. Criteria • Liquidity demands (≡ Collateral posted) • Speed of settlement ( system’s exposure to operational risk) • First-best: - Total collateral posted is minimised. - All payments are settled early in the day.

6. The Model • n(settlement) banks; n>2 • All payments have a value = 1 • Each bank has a single payment to send to each other bank • A payment between bank i and bank j; i→j

7. The Model • Two periods: morning and afternoon • Collateral costs: - ¹ per unit in the morning - ² per unit in the afternoon

8. The Model • ¹  ²  a bank only posts collateral in the morning that it uses in the morning. • Morning payments can be used to make afternoon payments. • Afternoon payments can be used to repay the CB at the end of the day.

9. The Model • Delay cost; incurred when a payment is not settled in the morning. • Delay cost, (i→j) • (i→j) takes one of n-1 possible values.

10. The Model • (i→j)=(i→k) iff j=k • Highest (i→j)>¹ • Lowest (i→j) ¹- ²

11. The Model • Delay costs are bank’s private information; I.e., only i knows (i→j) • A bank forms internal queue Qi • Position of payment in Qi is inversely related to its delay cost.

12. The Model • Cancellation cost,  • Incurred when a payment is not settled in the afternoon, given that it is not settled in the morning. •  > ²

13. RTGS Banks borrow liquidity from the CB Banks borrow liquidity from the CB Banks repay the CB Banks make payments Banks make payments Morning Afternoon

14. RTGS • Morning action: • Morning action set: • Afternoon action: • Afternoon action set:

15. Afternoon •  > ²; optimal for a bank to settle all remaining payments in the afternoon, for any • Value of i’s afternoon payments is

16. Morning • A bank is affected by other banks’ morning actions through effect on afternoon collateral needs. • Internal queue ordering is private information  a bank is uncertain about the value of its incoming payments in the morning.

17. Morning • Bank chooses morning action to minimise expected total cost. • Expected total cost = Morning collateral cost + Delay cost + Expected afternoon cost

19. Equilibrium • Equilibrium (in pure strategies)

20. Equilibrium • Each bank settles at least one payment in the morning because (1)>¹ • {Q1,…,Qn} is not an eqm. because expected afternoon collateral costs = 0 and (n-1)<¹

21. Hybrids • Two ways of settling a payment: RTGS and offset. • Offset: a payment has to be submitted to the central queue.

22. Hybrids • H1: Offset in the afternoon • H2: Offset in the morning • H3: Offset in both periods

23. Hybrids • Central queue transparency: - Opaque; a bank cannot see other banks’ payments in the central queue. - Visible; a bank can see payments to it in the central queue. • May effect how well banks co-ordinate use of the central queue.

24. Hybrids • Split each period into two sub-periods. • Sub-periods, 1a, 1b, 2a, 2b. • Results for RTGS with four sub-periods are the same as those with two periods.

25. Hybrids • Placing a payment in the central queue in one sub-period is not≡ a commitment to keep the payment in the central queue in subsequent sub-periods. • Submission behaviour depends on what a bank expects other banks to do.

26. Hybrids •  there is the potential for co-ordination problems. • Not guaranteed that visibility will overcome problems.

27. H1 • If j→i is received in the morning, i→j is settled by RTGS in the afternoon. • All RTGS payments settled in 2b.

28. H1 • If j→i is not received in the morning, a bank submits i→j to the central queue in 2a if each other bank submits at least one payment. • Because each payment should be offset with a positive probability.

29. H1 • So all payments that can be offset will be offset in 2a. • If a payment is offset, needs no liquidity.

30. H1 • If a payment is settled by RTGS in 2b, the offsetting payment arrived in the morning. So need no liquidity. • Expected afternoon collateral = 0

32. H1 • Bank’s cost minimisation problems are disentangled from each other. • Each bank settles the same value of payments in the morning (have the same cost structure).

33. H1 • Value of morning payment in H1  value of morning payments under RTGS. • Liquidity in H1  liquidity in RTGS • H1 is not necessarily better than RTGS.

34. H2 • In 2a, a bank submits all payments if each other bank submits at least one payment. • Because each payment could be settled with positive probability. • All payments offset in 1a.

35. H3 • In 2a, a bank submits all payments if each other bank submits at least one payment. • Because each payment could be settled with positive probability. • All payments offset in 1a.

36. H2 and H3 • First-best since all payments are offset ( no liquidity required) in sub-period 1a.

37. Delay costs are private information • Under H2 and H3 there exist ‘bad’ equilibria where the central queue is not used at all in 1a. • But no intermediate cases because each payment could be settled with positive probability if each other bank submits 1 payment.

38. Delay costs are private information • If delay costs are public information we can show there exist intermediate cases, where some but not all payments are submitted to the central queue in 2a.

39. Conclusion • The first-best is attained under Hybrid payment systems if offset is available in the morning. • Offering offset in the afternoon can only be as good than RTGS.

40. Conclusion • Central queue transparency is unimportant. • Maybe because of the information structure and that the cost of using the central queue = 0