optimisation strategy in a dvp model 1 securities ... · optimisation strategy in a dvp model 1 ......

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Optimisation strategy in aDvP model 1

Bank of Finland’s Sixth Seminar on Payment Systems SimulationHelsinki, August 2008

DvP model 1Securities Settlement System

Julien Loron & Fabien RenaultBanque de FranceThe views expressed in this presentation are those of the authors

only, and may not represent the views of Banque de France

Overview• Rationale for investigating SSS

optimisation• Objectives and toolsj• Research Questions

1. What are the best offsetting algorithms ?2. Mono ISIN Vs Multi ISIN approach3. Multi, Tri or Bilateral approach

2

4. Continuous Vs Batch approach

• Conclusions

2

Rationale for investigating SSS optimisationOversight of SSS systems• Efficient optimisation means lower liquidity needs (lower liquidity

costs), and/or lower settlement delay (potentially safer)• By studying optimisation, the overseers can better assess if the

operators have put in place efficient settlement procedures

Development of the T2S system• “On 17 July 2008, the Governing Council of the European Central

Bank decided to launch the TARGET2-Securities (T2S) project and to provide the resources required until its completion. It also decided to assign the development and operation of T2S to the Deutsche Bundesbank, the Banco de España, the Banque de France and the Banca d’Italia”. (Governing Council press release)

• As operator of T2S, the Eurosystem should be able to provide the

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As operator of T2S, the Eurosystem should be able to provide the market with an efficient system

Importance of optimisation in SSS and RTGS• SSS are often less liquid than RTGS. As a consequence

optimization plays a greater role in SSS...

Rationale for investigating SSS optimisationExample: We simulate the case of a generic SSS (random data)

– Full day, 20 000 transactions,100 participants, 30 ISIN– Real time settlement, optimisation every 1 hour– Liquidity level varied from 25% to 400%– Settlement delay is recorded

4Liquidity needed to settle all transactions

3

Rationale for investigating SSS optimisationComparing with similar results obtained on a real RTGS by Segendorff (2004)…

Zone of operation of RIX

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Liquidity needed to settle all transactions Taken from Segendorff, Sveriges Riksbank, 2004

Rationale for investigating SSS optimisationExample: We take the case of a generic SSS (random data)

– Full day, 20 000 transactions,100 participants, 30 ISIN– Real time settlement, optimisation every 1 hour– Liquidity level varied from 25% to 400%– Settlement delay is recorded

Typical zone of ti f RTGS

Typical zone of operation

of SSS

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operation of RTGS

Liquidity needed to settle all transactions

4


– Full day, 20 000 transactions,100 participants, 30 ISIN– Real time settlement, optimisation every 1 hour– Liquidity level varied from 25% to 400%– Settlement delay and end of day fail ratio are recorded



of SSS

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operation of RTGS



– Full day, 20 000 transactions,100 participants, 30 ISIN– Real time settlement, optimisation every 1 hour– Liquidity level varied from 25% to 400%– Settlement delay and end of day fail ratio are recorded



of SSS

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operation of RTGS


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Objectives and tools• Objectives of SSS optimization (alternatively):

– Lowest settlement delay in volume (number of transactions)– Lowest settlement delay in value– Lowest end-of-day fail ratio in volume– Lowest end-of-day fail ratio in valueLowest end of day fail ratio in value

• An adequate balance is to be found between these four (sometimes antinomic) objectives– “With respect to the level of priority of instructions and their intended

settlement dates, T2S should maximize the volume (number of instructions) and the overall value of settlements, by trying to find out an optimum balance between the two.” (T2S market consultation TG3, July 2007)

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• Available tools to increase SSS efficiency:– Self-collateralization (on stock and/or on flows)

– Partialization of the trades

– Offsetting mechanisms

RQ 1: What are the best algorithms?• We consider a batch of 200 DvP transactions bearing on a single

ISIN between 2 participants. We let the liquidity level vary

• Which algorithm will perform best (settle most in value and/or volume) in this bilateral Mono ISIN optimisation ?

• Algorithm1 : Greedy• Algorithm 2: One By One• Algorithm 3 : FIFO• Algorithm 4: Robin Hood• Algorithm 5: Las Vegas Greedy• Algorithm 6 : Greedy2 / Greedy4

10

6





14€10€7€7€

A

0 €

B

0 €

Greedy Reselection

Greedy Algorithm

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14€10€7€7€

A

0 €B

0 €





14€10€7€7€

A

0 €

B

0 €

OneByOne

Deselection

Lack = -10€

One By One Deselect Algorithm

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14€10€7€7€

A

0 €B

0 €

7





14€10€7€7€

A

0 €

B

0 €

FIFO Deselection

08:01

08:0208:0308:04

FIFO Algorithm

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14€10€7€7€

A

0 €B

0 €

08:0108:02

08:0308:04





A

B C

Participant able to pay an important transaction in cash

O

Robin Hood Algorithm

14

A D

F E G

H

« driving belts »

Participants able to pay transactions in securities

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14€10€7€7€

A

0 €

B

0 €

Lack = -10€

Selected with a probability of 10/14

Las Vegas Greedy Algorithm

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14€10€7€7€

A

0 €B

0 €





1410

7 7

Greedy selection

Greedy2 Algorithm

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10

4

7 7

Greedy2 Algorithm• First step: Greedy selection on initial set

• Second step: Greedy launched on subset

• « Sub-Greedy » finds a solution

• Third step: Transactions are exchanged in the initial set

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Settlement rate in VALUE

60

80

100

120

emen

t Rat

e va

lue

in %

GreedyOneByOneFIFORobinHoodLasVegasGreedy-Power-2Greedy-Power-4

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Standings in Value1. Las Vegas Greedy2. Greedy2 / Greedy4

3. Greedy4. One By One

Liquidity available0 20 40 60 80 1000

20

40

Set

tle





Settlement rate in VOLUME

50

60

70

80

90

100

nt R

ate

valu

e in

%

G d

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Standings in Volume1. One By One2. Las Vegas Greedy3. Robin Hood4. FIFO

Liquidity available0 20 40 60 80 100

0

10

20

30

40

Set

tlem

en

GreedyOneByOneFIFORobinHoodLasVegasGreedy-Power-2Greedy-Power-4

10




200

250

300

350

400

450

calc

ulat

ion

(s)

GreedyOneByOneFIFORobinHoodLasVegas-GreedyGreedy-Power-2


Computational time

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0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

Tim

e of

c

Standings in Speed1. One By One2. FIFO3. Greedy4. Robin Hood

Liquidity available

RQ 1: What are the best algorithms?• Some algorithms complement each other in an efficient

manner

• Launching them alternatively may provide an edge over a monoculture approach

40

50

60

70

80

90

100 GreedyOneByOneDeselect

40

60

80

100

120GreedyOneByOneDeselect

Settlement rate in VOLUMESettlement rate in VALUE

20

-20 0 20 40 60 80 100 1200

10

20

30

-20 0 20 40 60 80 100 1200

20

40

Liquidity available Liquidity available

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RQ 2: Mono ISIN Vs Multi ISIN approach• We consider a batch of 200 DvP transactions bearing on 3 different

ISIN between 2 participants (averaged over 500 draws)

• Bilateral OneByOne is used, Cash-poor (securities rich) system

• Which approach will settle the most transactions ?Approach 1 : Optimisation Multi ISIN only

Cash-poor system

• Multi ISIN better

– Approach 1 : Optimisation Multi-ISIN only– Approach 2 : Optimisation Mono-ISIN only– Approach 3 : Optimisation Multi-ISIN first then Mono-ISIN– Approach 4 : Optimisation Mono-ISIN first then Multi-ISIN

60

70

80

90

100Settlement Rate of OneByOne in Volume in Bilateral - Approach 1-2-3-4

lum

e in

%

60

70

80

90

100Settlement Rate of OneByOne in Value in Bilateral - Approach 1-2-3-4

alue

in %

21

better

• Combining both approaches does not improve much 0 20 40 60 80 100

0

10

20

30

40

50

60

α = 0.1 *β in %

Set

tlem

ent R

ate

vo

Approach 1Approach 2Approach 3Approach 4

0 20 40 60 80 1000

10

20

30

40

50

60

α = 0.1 *β in %

Set

tlem

ent R

ate

va


RQ 2: Mono ISIN Vs Multi ISIN approach• We consider a batch of 200 DvP transactions bearing on 3 different

ISIN between 2 participants (averaged over 500 draws)

• Bilateral OneByOne is used, Cash-rich (securities poor) system

• Which approach will settle the most transactions ?Approach 1 : Optimisation Multi ISIN only

Cash-rich system

• Mono ISIN li htl b tt

– Approach 1 : Optimisation Multi-ISIN only– Approach 2 : Optimisation Mono-ISIN only– Approach 3 : Optimisation Multi-ISIN first then Mono-ISIN– Approach 4 : Optimisation Mono-ISIN first then Multi-ISIN

70

80

90

100Settlement Rate of OneByOne in Value in Bilateral - Approach 1-2-3-4

e in

%

70

80

90

100Settlement Rate of OneByOne in Volume in Bilateral - Approach 1-2-3-4

e in

%

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slightly better

• Combining both approaches does not improve much

0 20 40 60 80 1000

10

20

30

40

50

60

α = 10 *β in %

Set

tlem

ent R

ate

valu

e


0 20 40 60 80 1000

10

20

30

40

50

60

α = 10 *β in %

Set

tlem

ent R

ate

volu

m


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RQ3: Multi, tri or bilateral approach• We consider a batch of 1000 transactions between 10

participants that we optimize using a Greedy Mono ISIN algorithm (results averaged over 100 draws)

• What is the best approach to lower the fail ratio (value and volume) ?– Multilateral: the algorithm is launched once on the set of all

participants

– Trilateral: the algorithm is launched for each triplet of participants (120 triplets)

– Bilateral: the algorithm is launched for each pair of participants

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Bilateral: the algorithm is launched for each pair of participants (45 pairs)

• …depending on the topology of the transactions

RQ3: Multi, tri or bilateral approach

Importance of the core of central participants, in %

• Variation of the topology is investigated on a 11x11 matrix, where the relative importance of the core of central participants and of the central pair is varied

40

50

60

70

80

90

100

Heavy core

Heavy Pair

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10

20

30

40

0

Relative importance of the two biggest participants with regards to the core of central participants, in %

0 10 20 30 40 50 60 70 80 90 100

Dispersed

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RQ3: Multi, tri or bilateral approach• Results in VALUE settled

Single Pair Bilateral is bestImportance of the core of

central participants, in %

Heavy core: Trilateral is best

40

50

60

70

80

90

100

25

Dispersed: Multilateral is best


0 10 20 30 40 50 60 70 80 90 100

10

20

30

40

0

RQ3: Multi, tri or bilateral approach• Results in VOLUME settled

Single Pair Bilateral is bestImportance of the core of

central participants, in %

Heavy core and dispersed:

40

50

60

70

80

90

100

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Trilateral is best


0 10 20 30 40 50 60 70 80 90 100

10

20

30

40

0

14

RQ4: Continuous Vs Batch approach• We want to assess the pros and cons of

continuous settlement and batch settlement – Continuous settlement: Each incoming transaction is

immediately attempted for settlement

– Batch settlement: Incoming transactions are directly sent to optimisation

– In both cases an optimisation algorithm (multilateral multi ISIN One By One) is launched on the bulk of unsettled transactions

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• Simulations performed on a generic SSS– 20 000 transactions with 30 ISIN and 100 participants

RQ4: Continuous Vs Batch approach• Settlement delay and end of day fail ratio in volume

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RQ4: Continuous Vs Batch approach• Settlement delay and end of day fail ratio in volume

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RQ4: Continuous Vs Batch approach• Settlement delay and end of day fail ratio in value

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RQ4: Continuous Vs Batch approach• Settlement delay and end of day fail ratio in value

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Conclusions (provisional)RQ1 What are the best offsetting algorithms ?– OneByOne is well balanced– If value matters most, Greedy is most adequate– More advanced algorithms (LV Greedy or Greedy4) can

improve especially in a batch optimisation but at a certainimprove, especially in a batch optimisation, but at a certain CPU cost

– Combining various algorithms should allow for a robust and efficient optimisation

RQ2 Mono ISIN Vs Multi ISIN approach– Multi ISIN is more suited for cash poor (securities rich)

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systems– Mono ISIN is more suited for cash rich (securities poor)

systems– Usually, Mono ISIN performs best for very low liquidity

levels (especially true for Greedy algorithms, not shown here)

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Conclusions (provisional)RQ3 Multi, tri or bilateral approach– Results (on Greedy and OneByOne, not shown) tend to

confirm intuition that • Trilateral is best in value in case of “heavy core”• Multilateral is best in value when “dispersed”

– Trilateral is also best in terms of volume (Greedy)– Multilateral is fastest. Trilateral slowest– Results probably very dependent on topology

RQ4 Continuous Vs Batch approach– A batch approach can win an edge over a continuous

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batc app oac ca a edge o e a co t uousapproach with regards to the end-of-day fail ratio in value (Threefold reduction)… at the expense of the settlement delay

– Batch approach can be advised for night settlement

Conclusions (provisional)Best answers depend – on the situation (level of liquidity, cash/securities rich,

topology…)– on the objectives (fail ratio vs delays, value vs volume)

Options for a complete engine– Build a robust engine

• Supposed to be efficient in every situation

– Build a configurable engine• To be fitted by system operators periodically

Build a smart engine

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– Build a smart engine• “Understand” the situation and launch the adequate strategies

The different RQ are entangled

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Annex: details on the algorithms used– Robin Hood Algorithm

– Select the most important transaction that doesn’t create any lack for the resource considered.

– Create a tree of redistribution of the resource.

– Check if it has not created any lack for the counter-resource.

A

O100 eu0 sec

0 eu0 sec

100

5050

A

Participant able to pay an important transaction in cash

O

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B C

A D

F E G

H

0 eu0 sec

0 eu10 sec

0 eu0 sec

0 eu0 sec 0 eu

40 sec

0 eu10 sec

20 30

20 2010

40

0 eu20 sec 0 eu

20 sec

B C

A D

F E G

H

« driving belts »

Participants able to pay transactions in securities

Annex: details on the algorithms used– The Greedy power algorithm

– Recursive Algorithm: Greedy2 calls Greedy on a smaller subset of transactions. Similarly, Greedy3 calls Greedy2

on a smaller subset of transactions…

It h l t l th bl h th i f t– It helps to solve the problem when the series of amounts are not super-increasing

14€10€7€7€

A

0 €

B

0 €

Greedy

10€7€7€

X

4 €Y

0 €

The results obtained on the smaller subset help improve

We call Greedy on a smaller Subset

36

14€10€7€7€

A

0 €B

0 €

Reselection The results obtained on the smaller subset help improve the situation on the initial problem

10€7€7€

A

0 €B

0€

14€

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Annex: details on the algorithms used– The Las Vegas Greedy algorithm

– When reselecting transactions on a lack, and if we don’t have a super-increasing series of amounts, we reselect the transactions according to a certain probability

L hi th l ith l ti ll f– Launching the algorithm several times allows for an increased efficiency

stock

LasVegas

LasVegas

LasVegas

LasVegas

LasVegas

LasVegasNew

stockFinal stock

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Selection of the “best”

set of transactions

LasVegas LasVegas

Selection of the “best”

set of transactions

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