We model a payment system with internal queues and look at how much liquidity/delay a liquidity -saving mechanism could reduce when the behavior of participants is taken into account via a agent-based model.

1. Liquidity saving mechanisms and
bank behaviour
Marco Galbiati – BoE
Kimmo Soramäki – VerticeTree
ABM-BaF
Torino - 10 February 2009

2. Interbank payment systems
Real Time Gross Settlement (RTGS) mode
• Incentives to queue
• ‘Games’ being played on a liquidity/delay tradeoff

3. Interbank payment systems
Real Time Gross Settlement (RTGS) mode
• Incentives to queue
• ‘Games’ being played on a liquidity/delay tradeoff
• Pool internal queues!

4. Interbank payment systems
Real Time Gross Settlement (RTGS) mode
• Incentives to queue
• ‘Games’ being played on a liquidity/delay tradeoff
• Pool internal queues!
Liquidity Saving Mechanisms (LSMs)

5. Aims
1. Model a system with internal queues (LMM)
2. Look at how much liquidity/delay a LSM
reduces in theory
3. Look at how banks would use a LSM
 An ‘agent-based’ model

6. Model of a payment system
• N banks
• A ‘day’ of several ‘seconds’
• Random payment orders
 random pairs ‘payer&payee’
 for each payment a ‘urgency’ parameter u ~ U[0,1]
• Each bank sends payment orders in either of two ‘pipes’
(streams): RTGS or Queue

7. A
E B
D
C

8. A
E B
D
C

9. A
E B
D
C

10. Low urgency? RTGS
A
1
E B
D
C

11. Low urgency? RTGS
A
1
E B
D
C

12. High urgency? Queue
A
1
E B
D
C

13. High urgency? Queue
A
E B
D
C

14. A
E B
D
C

15. A
E B
D
C

16. A
E B
D
C

17. A
E B
D
C

18. A
E B
D
C

19. A
E B
high u
D
C

20. A
E B
low u
D
C

21. A
E B
D
C

22. A
E B
D
C

23. A
E B
D
C

24. A
E B
D
C

25. A
E B
D
C

26. A
E B
D
C

27. A
E B
D
C

28. A
E B
D
C

29. A
E B
D
C
End of day
Cost = delay cost + liquidity costs
= _ uk • (tk - tk’) + _ • a

30. Illustration of costs
Very low liquidity
cost
Liquidity cost
% routed to RTGS

31. Illustration of costs
Very low liquidity
Delay cost
cost
% routed to RTGS

32. Illustration of costs
Very low liquidity
Total cost
cost
% routed to RTGS

33. Illustration of costs
Very low liquidity Very high liquidity
Total cost
Total cost
cost
% routed to RTGS % routed to RTGS

34. The game
• Banks choose
–opening liquidity balance: _
–urgency threshold to queue: _
• For each strategy profile (_1, _1), (_2, _2), (_3, _3)… (_N, _N)
a payoff (cost) function
• We look at Nash equilibrium for 2 cases:
• ‘LMM’ - low urgency payments in internal queues
• ‘LSM’ - low urgency payments in central queue

35. AB
A
E B
D
C

36. AB
A
E B
D
C

37. AB
A
E B
AB
D
C

38. A
E B
D
C

39. A
E B
D
C

40. Agent-based modelling
Liquidity flows very complex 
simulate the settlement process
to compute costs,
and hence equilibria

41. Agent-based modelling
Liquidity flows very complex 
simulate the settlement process
to compute costs,
and hence equilibria
We look at symmetric equilibria:
{(_1, _1), (_2, _2), (_3, _3)… (_N, _N)} : (_i, _i) = (_j, _j) for each i, j

42. 1
Model with internal queues
(LMM)

43. Delay costs with LMM
Delay costs
1

44. Delay costs with LMM
Increase “your” threshold
Delay costs
1

45. Delay costs with LMM
Increase “your” threshold
Delay costs
2

46. Delay costs with LMM
Increase “your” threshold
Delay costs
3

47. Delay costs with LMM
Increase “your” threshold
Delay costs
4

48. Delay costs with LMM
Increase “your” threshold
Delay costs
5

49. Delay costs with LMM
Increase “your” threshold
Delay costs
6

50. Delay costs with LMM
Increase “your” threshold
Delay costs
7

51. Delay costs with LMM
Increase “your” threshold
Delay costs
8

52. Delay costs with LMM
Increase “your” threshold
Delay costs
9

53. Delay costs with LMM
system level

54. Equilibria - LMM

55. Equilibria - LMM
Increase liquidity price a

56. Equilibria - LMM
Increase liquidity price a

57. Equilibria - LMM
Increase liquidity price a

58. Equilibria - LMM
Increase liquidity price a

59. Equilibria - LMM
Increase liquidity price a

60. Equilibria - LMM
Increase liquidity price a

61. Equilibria - LMM
Increase liquidity price a

62. Equilibria - LMM
Equil.
* Planner
Cost
Liquidity
Too little liquidity,
too much queueing

63. 2
Potential savings from a LSM
(‘LSM mechanics’)

64. Savings in liquidity
RTGS + LMM
RTGS + LSM

65. Savings in liquidity
All in RTGS   All queued
RTGS + LMM
RTGS + LSM

66. Savings in delay costs

67. 3
How would banks
use the LSM ?

68. Delay costs with LSM

69. Delay costs with LSM
Increasing “your” threshold

70. Delay costs with LSM
Increasing “your” threshold
UAD

71. Delay costs with LSM
Increasing “your” threshold

72. Delay costs with LSM
Increasing “your” threshold

73. Delay costs with LSM
Increasing “your” threshold

74. Delay costs with LSM
Increasing “your” threshold

75. Delay costs with LSM
Increasing “your” threshold

76. Delay costs with LSM
Increasing “your” threshold

77. Delay costs with LSM
Increasing “your” threshold

78. _ - equilibria with LSM

79. _ - equilibria with LSM
Increase liquidity price

80. _ - equilibria with LSM
Increase liquidity price

81. _ - equilibria with LSM
Increase liquidity price

82. _ - equilibria with LSM
Increase liquidity price

83. _ - equilibria with LSM
Increase liquidity price

84. _ - equilibria with LSM
Increase liquidity price

85. _ - equilibria with LSM
Increase liquidity price

86. _ - equilibria with LSM
Increase liquidity price

87. _ - equilibria with LSM
Increase liquidity price

88. _ - equilibria with LSM
Increase liquidity price

89. _ - equilibria with LSM
Increase liquidity price

90. _ - equilibria with LSM
Increase liquidity price

91. _ - equilibria with LSM
Increase liquidity price

92. _ - equilibria with LSM
Increase liquidity price

93. _ - equilibria with LSM
Increase liquidity price

94. _ - equilibria with LSM
Increase liquidity price
At high liquidity cost
this is the only
equilibrium

95. _ - equilibria with LSM
Increase liquidity price

96. _ - equilibria with LSM
Increase liquidity price

97. _ - equilibria with LSM
Increase liquidity price

98. _ - equilibria with LSM
Increase liquidity price
At very high
liquidity cost
planner and
banks choose the
same

99. _ - equilibria with LSM
Increase liquidity price

100. _ - equilibria with LSM
Increase liquidity price

101. _ - equilibria with LSM
Increase liquidity price

102. _ - equilibria with LSM
Increase liquidity price

104. LMM vs LSM (good) equilibria
costs
liquidity
thresh.

105. LMM vs LSM (good) equilibria
costs
liquidity
thresh.

106. LMM vs LSM (good) equilibria
costs

107. LMM vs LSM (good) equilibria
costs
cost ratio

108. LMM vs LSM (bad) equilibria
costs
liquidity
thresh.

109. Conclusions
In the hands of a ‘planner’,
LSM can save substantial amounts of liquidity,
and largely improve settlement speed

110. Conclusions
In the hands of a ‘planner’,
LSM can save substantial amounts of liquidity,
and largely improve settlement speed
(but may require radical choices)
In the hands of individual banks,
LSM may require some ‘coordination device’
to yield its potential benefits

111. Conclusions
In the hands of a ‘planner’,
LSM can save substantial amounts of liquidity,
and largely improve settlement speed
In the hands of individual banks,
LSM may require some ‘coordination device’
to yield its potential benefits

112. Slide 112

113. Slide 113 (!)
~_~
Many thanks