Liquidity saving mechanisms and bank behaviour

Liquidity saving mechanisms andbank behaviour

Marco Galbiati – BoEKimmo Soramäki – VerticeTree

ABM-BaFTorino - 10 February 2009

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)

• Pool internal queues!

Aims

1. Model a system with internal queues (LMM)

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

3. Look at how banks would use a LSM

An ‘agent-based’ model

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

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Low urgency? RTGS

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Low urgency? RTGS

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High urgency? QueueA

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High urgency? QueueA

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high u

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End of day Cost = delay cost + liquidity costs

= _ uk • (tk - tk’) + _ • a

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Very low liquidity

% routed to RTGS

costIllustration of costs

Liquidity cost

Illustration of costs

Delay cost

Very low liquidity

% routed to RTGS

cost

Total cost

Very low liquidity

% routed to RTGS

Illustration of costsco

st

Total cost

Very low liquidity

Total cost

Very high liquidity

% routed to RTGS % routed to RTGS

Illustration of costsco

st

• Banks choose–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

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Agent-based modelling

Liquidity flows very complex

simulate the settlement process

to compute costs,

and hence equilibria

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

1Model with internal queues

(LMM)

1

Delay costs with LMM

Del

ay c

osts

Increase “your” threshold

1

Del

ay c

osts


2



Del

ay c

osts

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Del

ay c

osts

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Del

ay c

osts

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Del

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ay c

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ay c

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osts

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Del

ay c

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Delay costs with LMMsystem level

Equilibria - LMM

Equilibria - LMMIncrease liquidity price a







Cos

tLi

quid

ity

Equil.

* Planner

Too little liquidity,too much queueing

Equilibria - LMM

2Potential savings from a LSM

(‘LSM mechanics’)

RTGS + LMM

RTGS + LSM

Savings in liquidity

All in RTGS All queued

RTGS + LMM

RTGS + LSM

Savings in liquidity

Savings in delay costs

3How would banks

use the LSM ?

Delay costs with LSM

Increasing “your” threshold

Delay costs with LSM

UAD

Delay costs with LSMIncreasing “your” threshold








_ - equilibria with LSM


Increase liquidity price





























At high liquidity costthis is the onlyequilibrium









At very highliquidity costplanner andbanks choose thesame











liquidity

thresh.

costs

LMM vs LSM (good) equilibria

liquidity

thresh.

costs


costs


cost ratio

costs


LMM vs LSM (bad) equilibria

liquidity

thresh.

costs

Conclusions

In the hands of a ‘planner’,

LSM can save substantial amounts of liquidity,

and largely improve settlement speed

Conclusions



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

Conclusions



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 113 (!)

~ _ ~

Many thanks

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Liquidity saving mechanisms and bank behaviour

Economy & Finance