SLIDE 1 Liquidity saving mechanisms and bank behaviour
Marco Galbiati – BoE Kimmo Soramäki – VerticeTree
ABM-BaF Torino - 10 February 2009
SLIDE 2 Interbank payment systems
Real Time Gross Settlement (RTGS) mode
- Incentives to queue
- ‘Games’ being played on a liquidity/delay tradeoff
SLIDE 3 Interbank payment systems
Real Time Gross Settlement (RTGS) mode
- Incentives to queue
- ‘Games’ being played on a liquidity/delay tradeoff
- Pool internal queues!
SLIDE 4 Interbank payment systems
Real Time Gross Settlement (RTGS) mode
- Incentives to queue
- ‘Games’ being played on a liquidity/delay tradeoff
Liquidity Saving Mechanisms (LSMs)
SLIDE 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
SLIDE 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
SLIDE 7
A B C E D
SLIDE 8
A B C E D
SLIDE 9
A B C E D
SLIDE 10
1 A B C E D Low urgency? RTGS
SLIDE 11
1 A B C E D Low urgency? RTGS
SLIDE 12
1 High urgency? Queue A B C E D
SLIDE 13
High urgency? Queue A B C E D
SLIDE 14
A B C E D
SLIDE 15
A B C E D
SLIDE 16
A B C E D
SLIDE 17
A B C E D
SLIDE 18
A B C E D
SLIDE 19 A B C E D
high u
SLIDE 21
A B C E D
SLIDE 22
A B C E D
SLIDE 23
A B C E D
SLIDE 24
A B C E D
SLIDE 25
A B C E D
SLIDE 26
A B C E D
SLIDE 27
A B C E D
SLIDE 28
A B C E D
SLIDE 29
End of day Cost = delay cost + liquidity costs = _ uk • (tk - tk’) + _ • a A B C E D
SLIDE 30 Very low liquidity
% routed to RTGS cost
Illustration of costs
Liquidity cost
SLIDE 31 Illustration of costs
Delay cost
Very low liquidity
% routed to RTGS cost
SLIDE 32 Total cost
Very low liquidity
% routed to RTGS
Illustration of costs
cost
SLIDE 33 Total cost
Very low liquidity
Total cost
Very high liquidity
% routed to RTGS % routed to RTGS
Illustration of costs
cost
SLIDE 34
–opening liquidity balance: _ –urgency threshold to queue: _
The game
- 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
SLIDE 37 A B C E D
AB AB
SLIDE 38
A B C E D
SLIDE 39
A B C E D
SLIDE 40
Agent-based modelling
Liquidity flows very complex simulate the settlement process to compute costs, and hence equilibria
SLIDE 41 Agent-based modelling
We look at symmetric equilibria: {(_1, _1), (_2, _2), (_3, _3)… (_N, _N)} : (_i, _i) = (_j, _j) for each i, j
Liquidity flows very complex simulate the settlement process to compute costs, and hence equilibria
SLIDE 42
1 Model with internal queues (LMM)
SLIDE 43 1
Delay costs with LMM
Delay costs
SLIDE 44 Increase “your” threshold 1
Delay costs
Delay costs with LMM
SLIDE 45 2 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 46 3 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 47 4 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 48 5 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 49 Increase “your” threshold
Delay costs with LMM
Delay costs
6
SLIDE 50 7 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 51 8 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 52 9 Increase “your” threshold
Delay costs with LMM
Delay costs
SLIDE 53
Delay costs with LMM
system level
SLIDE 54
Equilibria - LMM
SLIDE 55
Equilibria - LMM
Increase liquidity price a
SLIDE 56
Equilibria - LMM
Increase liquidity price a
SLIDE 57
Equilibria - LMM
Increase liquidity price a
SLIDE 58
Equilibria - LMM
Increase liquidity price a
SLIDE 59
Equilibria - LMM
Increase liquidity price a
SLIDE 60
Equilibria - LMM
Increase liquidity price a
SLIDE 61
Equilibria - LMM
Increase liquidity price a
SLIDE 62 Cost Liquidity
Equil.
*
Planner Too little liquidity, too much queueing
Equilibria - LMM
SLIDE 63
2 Potential savings from a LSM
(‘LSM mechanics’)
SLIDE 64 RTGS + LMM RTGS + LSM
Savings in liquidity
SLIDE 65 All in RTGS All queued
RTGS + LMM RTGS + LSM
Savings in liquidity
SLIDE 66
Savings in delay costs
SLIDE 67
3 How would banks use the LSM ?
SLIDE 68
Delay costs with LSM
SLIDE 69 Increasing “your” threshold
Delay costs with LSM
SLIDE 70 UAD
Delay costs with LSM
Increasing “your” threshold
SLIDE 71 Delay costs with LSM
Increasing “your” threshold
SLIDE 72 Delay costs with LSM
Increasing “your” threshold
SLIDE 73 Delay costs with LSM
Increasing “your” threshold
SLIDE 74 Delay costs with LSM
Increasing “your” threshold
SLIDE 75 Delay costs with LSM
Increasing “your” threshold
SLIDE 76 Delay costs with LSM
Increasing “your” threshold
SLIDE 77 Delay costs with LSM
Increasing “your” threshold
SLIDE 78
_ - equilibria with LSM
SLIDE 79 _ - equilibria with LSM
Increase liquidity price
SLIDE 80 _ - equilibria with LSM
Increase liquidity price
SLIDE 81 _ - equilibria with LSM
Increase liquidity price
SLIDE 82 _ - equilibria with LSM
Increase liquidity price
SLIDE 83 _ - equilibria with LSM
Increase liquidity price
SLIDE 84 _ - equilibria with LSM
Increase liquidity price
SLIDE 85 _ - equilibria with LSM
Increase liquidity price
SLIDE 86 _ - equilibria with LSM
Increase liquidity price
SLIDE 87 _ - equilibria with LSM
Increase liquidity price
SLIDE 88 _ - equilibria with LSM
Increase liquidity price
SLIDE 89 _ - equilibria with LSM
Increase liquidity price
SLIDE 90 _ - equilibria with LSM
Increase liquidity price
SLIDE 91 _ - equilibria with LSM
Increase liquidity price
SLIDE 92 _ - equilibria with LSM
Increase liquidity price
SLIDE 93 _ - equilibria with LSM
Increase liquidity price
SLIDE 94 At high liquidity cost this is the only equilibrium
_ - equilibria with LSM
Increase liquidity price
SLIDE 95 _ - equilibria with LSM
Increase liquidity price
SLIDE 96 _ - equilibria with LSM
Increase liquidity price
SLIDE 97 _ - equilibria with LSM
Increase liquidity price
SLIDE 98 At very high liquidity cost planner and banks choose the same
_ - equilibria with LSM
Increase liquidity price
SLIDE 99 _ - equilibria with LSM
Increase liquidity price
SLIDE 100 _ - equilibria with LSM
Increase liquidity price
SLIDE 101 _ - equilibria with LSM
Increase liquidity price
SLIDE 102 _ - equilibria with LSM
Increase liquidity price
SLIDE 103
SLIDE 104 liquidity thresh. costs
LMM vs LSM (good) equilibria
SLIDE 105 liquidity thresh. costs
LMM vs LSM (good) equilibria
SLIDE 106 costs
LMM vs LSM (good) equilibria
SLIDE 107 cost ratio costs
LMM vs LSM (good) equilibria
SLIDE 108 LMM vs LSM (bad) equilibria
liquidity thresh. costs
SLIDE 109
Conclusions
In the hands of a ‘planner’, LSM can save substantial amounts of liquidity, and largely improve settlement speed
SLIDE 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
SLIDE 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
SLIDE 112
Slide 112
SLIDE 113
Slide 113 (!) ~ _ ~ Many thanks
