Liquidity saving mechanisms and
         bank behaviour

          Marco Galbiati – BoE
       Kimmo Soramäki – VerticeTre...
Interbank payment systems

Real Time Gross Settlement (RTGS) mode
  • Incentives to queue
  • ‘Games’ being played on a li...
Interbank payment systems

Real Time Gross Settlement (RTGS) mode
  • Incentives to queue
  • ‘Games’ being played on a li...
Interbank payment systems

Real Time Gross Settlement (RTGS) mode
  • Incentives to queue
  • ‘Games’ being played on a li...
Aims
1. Model a system with internal queues (LMM)

2. Look at how much liquidity/delay a LSM
   reduces in theory

3. Look...
Model of a payment system
• N banks

• A ‘day’ of several ‘seconds’

• Random payment orders
    random pairs ‘payer&paye...
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
Low urgency? RTGS
        A
             1

E                  B




    D
            C
Low urgency? RTGS
        A
             1

E                  B




    D
            C
High urgency? Queue
                      A

                          1
           E                      B




         ...
High urgency? Queue
                      A



           E                  B




               D
                      ...
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



         E               B
high u




             D
                     C
A



        E               B
low u




            D
                    C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



E               B




    D
            C
A



    E                               B




        D
                            C

                End of day
Cost = ...
Illustration of costs
       Very low liquidity
cost




         Liquidity cost



         % routed to RTGS
Illustration of costs
       Very low liquidity




         Delay cost
cost




         % routed to RTGS
Illustration of costs
       Very low liquidity




       Total cost
cost




         % routed to RTGS
Illustration of costs
       Very low liquidity      Very high liquidity




                                   Total cost...
The game
• Banks choose
    –opening liquidity balance: _
    –urgency threshold to queue: _


• For each strategy profile...
AB
              A



E                     B




    D
                  C
AB
              A



E                     B




    D
                  C
AB
              A



E                     B
                          AB




    D
                  C
A



E               B




    D
            C
A



E               B




    D
            C
Agent-based modelling

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

Liquidity flows very complex 
       simulate the settlement process
                  to compute ...
1
Model with internal queues
        (LMM)
Delay costs with LMM


Delay costs




                            1
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          1
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          2
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          3
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          4
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          5
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          6
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          7
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          8
Delay costs with LMM
              Increase “your” threshold


Delay costs




                                          9
Delay costs with LMM
      system level
Equilibria - LMM
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM
  Increase liquidity price a
Equilibria - LMM

                                     Equil.

                                *    Planner
Cost
 Liquidit...
2
Potential savings from a LSM
       (‘LSM mechanics’)
Savings in liquidity




             RTGS + LMM

                          RTGS + LSM
Savings in liquidity
All in RTGS     All queued




                               RTGS + LMM

                         ...
Savings in delay costs
3
How would banks
 use the LSM ?
Delay costs with LSM
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
      Increasing “your” threshold

UAD
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
Increasing “your” threshold
Delay costs with LSM
Increasing “your” threshold
_ - equilibria with LSM
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price




                               At high liquidity cost
          ...
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price




                               At very high
                    ...
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
_ - equilibria with LSM

    Increase liquidity price
LMM vs LSM (good) equilibria

 costs




liquidity




 thresh.
LMM vs LSM (good) equilibria

 costs




liquidity




 thresh.
LMM vs LSM (good) equilibria


costs
LMM vs LSM (good) equilibria


  costs




cost ratio
LMM vs LSM (bad) equilibria

  costs




liquidity




  thresh.
Conclusions

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

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

         In the hands of a ‘planner’,
LSM can save substantial amounts of liquidity,
    and largely improve ...
Slide 112
Slide 113 (!)
   ~_~
Many thanks
Liquidity saving mechanisms and bank behaviour
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Liquidity saving mechanisms and bank behaviour

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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.

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Liquidity saving mechanisms and bank behaviour

  1. 1. Liquidity saving mechanisms and bank behaviour Marco Galbiati – BoE Kimmo Soramäki – VerticeTree ABM-BaF Torino - 10 February 2009
  2. 2. Interbank payment systems Real Time Gross Settlement (RTGS) mode • Incentives to queue • ‘Games’ being played on a liquidity/delay tradeoff
  3. 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. 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. 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. 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. 7. A E B D C
  8. 8. A E B D C
  9. 9. A E B D C
  10. 10. Low urgency? RTGS A 1 E B D C
  11. 11. Low urgency? RTGS A 1 E B D C
  12. 12. High urgency? Queue A 1 E B D C
  13. 13. High urgency? Queue A E B D C
  14. 14. A E B D C
  15. 15. A E B D C
  16. 16. A E B D C
  17. 17. A E B D C
  18. 18. A E B D C
  19. 19. A E B high u D C
  20. 20. A E B low u D C
  21. 21. A E B D C
  22. 22. A E B D C
  23. 23. A E B D C
  24. 24. A E B D C
  25. 25. A E B D C
  26. 26. A E B D C
  27. 27. A E B D C
  28. 28. A E B D C
  29. 29. A E B D C End of day Cost = delay cost + liquidity costs = _ uk • (tk - tk’) + _ • a
  30. 30. Illustration of costs Very low liquidity cost Liquidity cost % routed to RTGS
  31. 31. Illustration of costs Very low liquidity Delay cost cost % routed to RTGS
  32. 32. Illustration of costs Very low liquidity Total cost cost % routed to RTGS
  33. 33. Illustration of costs Very low liquidity Very high liquidity Total cost Total cost cost % routed to RTGS % routed to RTGS
  34. 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. 35. AB A E B D C
  36. 36. AB A E B D C
  37. 37. AB A E B AB D C
  38. 38. A E B D C
  39. 39. A E B D C
  40. 40. Agent-based modelling Liquidity flows very complex  simulate the settlement process to compute costs, and hence equilibria
  41. 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. 42. 1 Model with internal queues (LMM)
  43. 43. Delay costs with LMM Delay costs 1
  44. 44. Delay costs with LMM Increase “your” threshold Delay costs 1
  45. 45. Delay costs with LMM Increase “your” threshold Delay costs 2
  46. 46. Delay costs with LMM Increase “your” threshold Delay costs 3
  47. 47. Delay costs with LMM Increase “your” threshold Delay costs 4
  48. 48. Delay costs with LMM Increase “your” threshold Delay costs 5
  49. 49. Delay costs with LMM Increase “your” threshold Delay costs 6
  50. 50. Delay costs with LMM Increase “your” threshold Delay costs 7
  51. 51. Delay costs with LMM Increase “your” threshold Delay costs 8
  52. 52. Delay costs with LMM Increase “your” threshold Delay costs 9
  53. 53. Delay costs with LMM system level
  54. 54. Equilibria - LMM
  55. 55. Equilibria - LMM Increase liquidity price a
  56. 56. Equilibria - LMM Increase liquidity price a
  57. 57. Equilibria - LMM Increase liquidity price a
  58. 58. Equilibria - LMM Increase liquidity price a
  59. 59. Equilibria - LMM Increase liquidity price a
  60. 60. Equilibria - LMM Increase liquidity price a
  61. 61. Equilibria - LMM Increase liquidity price a
  62. 62. Equilibria - LMM Equil. * Planner Cost Liquidity Too little liquidity, too much queueing
  63. 63. 2 Potential savings from a LSM (‘LSM mechanics’)
  64. 64. Savings in liquidity RTGS + LMM RTGS + LSM
  65. 65. Savings in liquidity All in RTGS   All queued RTGS + LMM RTGS + LSM
  66. 66. Savings in delay costs
  67. 67. 3 How would banks use the LSM ?
  68. 68. Delay costs with LSM
  69. 69. Delay costs with LSM Increasing “your” threshold
  70. 70. Delay costs with LSM Increasing “your” threshold UAD
  71. 71. Delay costs with LSM Increasing “your” threshold
  72. 72. Delay costs with LSM Increasing “your” threshold
  73. 73. Delay costs with LSM Increasing “your” threshold
  74. 74. Delay costs with LSM Increasing “your” threshold
  75. 75. Delay costs with LSM Increasing “your” threshold
  76. 76. Delay costs with LSM Increasing “your” threshold
  77. 77. Delay costs with LSM Increasing “your” threshold
  78. 78. _ - equilibria with LSM
  79. 79. _ - equilibria with LSM Increase liquidity price
  80. 80. _ - equilibria with LSM Increase liquidity price
  81. 81. _ - equilibria with LSM Increase liquidity price
  82. 82. _ - equilibria with LSM Increase liquidity price
  83. 83. _ - equilibria with LSM Increase liquidity price
  84. 84. _ - equilibria with LSM Increase liquidity price
  85. 85. _ - equilibria with LSM Increase liquidity price
  86. 86. _ - equilibria with LSM Increase liquidity price
  87. 87. _ - equilibria with LSM Increase liquidity price
  88. 88. _ - equilibria with LSM Increase liquidity price
  89. 89. _ - equilibria with LSM Increase liquidity price
  90. 90. _ - equilibria with LSM Increase liquidity price
  91. 91. _ - equilibria with LSM Increase liquidity price
  92. 92. _ - equilibria with LSM Increase liquidity price
  93. 93. _ - equilibria with LSM Increase liquidity price
  94. 94. _ - equilibria with LSM Increase liquidity price At high liquidity cost this is the only equilibrium
  95. 95. _ - equilibria with LSM Increase liquidity price
  96. 96. _ - equilibria with LSM Increase liquidity price
  97. 97. _ - equilibria with LSM Increase liquidity price
  98. 98. _ - equilibria with LSM Increase liquidity price At very high liquidity cost planner and banks choose the same
  99. 99. _ - equilibria with LSM Increase liquidity price
  100. 100. _ - equilibria with LSM Increase liquidity price
  101. 101. _ - equilibria with LSM Increase liquidity price
  102. 102. _ - equilibria with LSM Increase liquidity price
  103. 103. LMM vs LSM (good) equilibria costs liquidity thresh.
  104. 104. LMM vs LSM (good) equilibria costs liquidity thresh.
  105. 105. LMM vs LSM (good) equilibria costs
  106. 106. LMM vs LSM (good) equilibria costs cost ratio
  107. 107. LMM vs LSM (bad) equilibria costs liquidity thresh.
  108. 108. Conclusions In the hands of a ‘planner’, LSM can save substantial amounts of liquidity, and largely improve settlement speed
  109. 109. 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
  110. 110. 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
  111. 111. Slide 112
  112. 112. Slide 113 (!) ~_~ Many thanks

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