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Internalisation by electronic FX Spot Dealers

Jim Gatheral’s 60th Birthday Conference �♩ �

NYU Courant, New York, October 14, 2017

Roel Oomen(joint work with Max Butz)

Motivation

I FX is traded OTC and makes up the world’s largest financial market. . . but often poorly understood /

I Traders obtain liquidity on a bi-lateral and bespoke basis from dealers

I The product is often standardised (e.g. spot) but the OTC nature liesin the delivery of liquidity

I There are a number of interesting topics here that have received limitedacademic interest thus far, e.g.

1. traders aggregate dealer liquidity: how to do this?

2. regulators are interested in “last look” : what is it (needed for)?

3. dealers act as principal and risk manage in different ways : how and why?

1 / 41

Risk management approach of principal dealers

Externalisation

Virtu Financial Inc (2014, p2) : “Our strategies are also designed to lock inreturns through precise and nearly instantaneous hedging, as we seek toeliminate the price risk in any positions held.”

Internalisation

Bank of England, H.M. Treasury, and Financial Conduct Authority (2014, p.59): “Market participants have indicated that some dealers with largeenough market share can now internalise up to 90% of their client orders inmajor currency pairs”

2 / 41

Question to a specialist audience of FX traders at majorindustry event

Question how long does it take a tier-1 LP to internalise a EURUSD ticketover the most active period of the day?

(a) seconds

(b) tens of seconds

(c) minutes

(d) tens of minutes

3 / 41

Fast markets . . .

. . . by “fast markets” I mean those markets where these trends have gonefurthest: most obviously major equity, foreign exchange (FX) and futuresmarkets. In these markets, there is less need for intermediaries to warehouserisk, due to the inherent liquidity characteristics that attract a wide range ofparticipants, making it easier to find a near-instant match between buyersand sellers.

Chris Salmon, “Keeping up with fast markets,” Speech at 13th Annual Central Bank Conference on theMicrostructure of Financial Markets, London 6 October 2017, www.bankofengland.co.uk/speeches

4 / 41

Contribution

Why is it important to understand internalisation?

I internalisation it is the process with which the majority (about 66%) ofFX liquidity is “generated”

I there is a polarisation amongst dealers into internalisers andexternalisers - how should traders evaluate this?

I the speed of internalisation (or externalisation) impacts transactioncosts and (should) influence a trader’s execution strategy

I there is virtually no data available on it (the BIS 2016 triennial surveynow includes a question on it)

Contribution of this paper is to provide a framework to analyse andunderstand the process

5 / 41

The model setup

I Let Xt , t ≥ 0 denote the position of a liquidity provider (LP) at time−t,defined as the accumulation of completed buy- and sell-transactions ofunit size:

Xt = N+t − N−t

where N+t and N−t count the number of buy and sell transactions up to

time−t

I X follows a compound Poisson process with position dependent arrivalrates of buys and sells, i.e. when Xt = n, then E (dN+

t ) = λ+n dt and

E (dN−t ) = λ−n dt

I The LP can control the arrival rate of buys and sells by skewing itsprices and does so in a manner that encourages risk reducing tradesonce the position exceeds some specified threshold n∗ ≥ 0, i.e.

λ+n < λ−n when n > n∗ and λ+

n > λ−n when n < −n∗.

6 / 41

The model setup

λ+n−1 λ+

n

λ−n λ−n+1

LP position X

n − 1 n n + 1

The global balance equation of a Markov chain (λ+n φn = λ−n+1φn+1) gives

the position distribution φn

φn = φ0

n∏k=1

λ+k−1

λ−kfor n > 0 and φn = φ0

n∏k=1

λ−1−kλ+−k

for n < 0.

7 / 41

Example - binary position skew

I Let λ+n + λ−n = 2λ0 with

λ+n =

λ0 |n| ≤ Rλ0(1− α) n > Rλ0(1 + α) n < −R

for some fixed threshold R ≥ 0 and 0 < α ≤ 1.

I The distribution of the LP’s position is stationary and given as:

φn = φ0 for |n| ≤ R and φn =φ0

1 + α

(1− α1 + α

)|n|−1−R

otherwise

where φ0 = (2R + 1 + α−1)−1.

8 / 41

Example - exponential position skew

I Let λ+n = λ−−n = λ0e

− 12 n/R

2

for R > 0.

I The distribution of the LP’s position is stationary and given as:

φn =1√

2πR2e−

12 n

2/R2

.

9 / 41

Position skewing and distribution

Panel A : probability of risk reducing trade Panel B : distribution of LP’s position

position-50 -40 -30 -20 -10 0 10 20 30 40 50

pro

bab

ility

ofrisk

-red

ucing

trade

50%

51%

52%

53%

54%

55%

56%

57%

58%

59%

60%

exponential skew binary skew (, = 2:5%) binary skew (, = 10%)

position-50 -40 -30 -20 -10 0 10 20 30 40 50

distr

ibution

exponential skew binary skew (, = 2:5%) binary skew (, = 10%)

10 / 41

Internalisation horizon – definition

We define the internalisation horizon as the length of time a given tradeforms part of the LP’s risk position before it is fully offset by another tradein the opposite direction.

11 / 41

Internalisation horizon – illustration

time

Last-in-first-out allocation

buy buy sell sell

wait = 5 wait = 2

time

First-in-first-out allocation

buy buy sell sell

wait = 3 wait = 4

time

Pro-rated-by-volume allocation

buy buy sell sell

50%

50%

50%

50%wait = 4 wait = 3

( 12· 3 + 1

2· 5) ( 1

2· 2 + 1

2· 4)

12 / 41

Internalisation horizon – illustration

Sample path of LP (risk) position Time to internalise risk increasing trades

time (HH:MM)00:00 00:05 00:10 00:15 00:20 00:25 00:30

position

Xt

-40

-30

-20

-10

0

10

20

30

40

position Xt

risk jXtj

time (HH:MM)00:00 00:05 00:10 00:15 00:20 00:25 00:30

tim

eto

inte

rnalise

0.0s

0.1s

0.2s

0.6s

2s

6s

19s

1m

3m

10m

32m

FIFO allocationLIFO allocationVPRO allocationaverage (sample)

Distribution depends on allocation methodology → intractable?

13 / 41

Queuing theory

14 / 41

Little’s Law

The average number of customers in a queuing system, denoted L, equals theaverage arrival rate of customers to the system, λ, multiplied by the averagewaiting time of a customer in the system, W , or L = λW (Little, 1961)

15 / 41

Internalisation as a queuing theory problem

I Reformulate buy/sell trades → risk increasing/decreasing trades

I Reformulate the dealer’s long/short position → (absolute) risk position

I The time it takes for a risk increasing trade (the “customer”) to beinternalised by a risk decreasing trade (“serviced”) once it has enteredthe dealer’s risk position (the “queue”) is what defines theinternalisation horizon (“queuing time”).

I Dealer uses position skewing to encourage risk-reducing flow (“deployingadditional staff when restaurant is busy”) to control the build-up of risk

16 / 41

Internalisation as a queuing theory problem

I Arrival rate of risk increasing trades (“customers”):

λ =∑n≥0

φnλ+n +

∑n≤0

φnλ−n .

I Dealer’s risk position (“length of the queue”)

L =∑n∈N

φn|n|

17 / 41

Internalisation horizon

With a binary position skew as specified in Example 1, the LP’s averageinternalisation horizon of a trade is:

W =R

λ0

cR4

(1)

where cR = 2α2R+2α(1+α)+(1+α)/R2α2R+α(1+α) →R 1.

With an exponential position skew as specified in Example 2, the LP’saverage internalisation horizon of a trade is:

W ≈ R

λ0

cR√2π

(2)

where cR = 2(1− Φ( 12R−1))e1/(8R2) + 1/

√2πR2 →R 1.

18 / 41

Internalisation horizon

Panel C : cumulative internalisation time Panel D : distribution of internalisation time

time (HH:MM)00:00 00:05 00:10 00:15 00:20 00:25 00:30

cum

ula

tive

tim

eto

inte

rnal

ise

(in

hours

)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

FIFO allocationLIFO allocationVPRO allocation

time to internalisation (seconds)0 10 20 30 40 50 60

distr

ibution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FIFO allocationLIFO allocationVPRO allocationaverage (theory)

19 / 41

The size of the FX market

EURUSD JPY

GBP CHF

AUD CAD

CNH MXN

OTHER

spotcomponentofFXmarket$5,100,000,000,000ADV

customerflows

electronicsegmentbycurrencypair

byOmeinterval

bydealer

I FX is the world’s largest financial market, ADV of $5,067bn (BIS, 2016) but . . .

I $1,652bn of this is spot

I $1,047bn of this is customer flow

I $692bn of this is executed electronically

I further break-down by currency, time-period, and then individual dealer

20 / 41

Illustration of FX market flow rates in e-spot

I The EURUSD accounts for 23.1% of trading volumes which translatesinto

23.1%× $692bn/day = $159, 852mn/1440min = $111mn/min.

I Individual tier-1 dealer captures a fraction of this. Euromoney (2016)estimates that top 10 dealers hold 66% marketshare . . .

1

2× $111mn/min× 6.6% = 3.66mn/min of each type.

21 / 41

Illustration of internalisation horizons in practice

I Assume dealer adopts exponential price skewing and sets her risk limitso that the absolute risk position is within a $25mn corridor 95% of thetime, i.e. R = $25mn/Φ−1(97.5%) = $12.75mn.

I This yields a top-down measurement of the average internalisationhorizon of a tier-1 dealer in EURUSD as:

$25mn/1.9612 × $111mn/min× 6.6%

× 1.00√2π

=$12.75mn

3.66$mn/min×1.00

2.51= 1.39 minutes.

22 / 41

Illustration of internalisation horizons in practice

EURUSD JPY GBP CAD CHF AUD CNH MXN SEK NOK INR TRY RUB NZD HKD SGD ZAR PLN

inte

rnal

isat

ion

hor

izon

inm

inute

s

0

5

10

15

20

25

G10 Asia Emerging Markets

23 / 41

Illustration of internalisation horizons in practice

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00

London local time

0

100

200

300

400

500

600

mar

ket t

radi

ng v

olum

e pe

r m

inut

e in

$m

illio

ns

28

148

267

67

market volumeAsia sessionLondon sessionLondon-New York cross overNew York session

24 / 41

Illustration of internalisation horizons in practice

per minute trade flow rate (in $mn) average internalisation horizon (in mins)market by trading session by trading session

currency share avg APAC LON NYLON NY min avg APAC LON NYLON NYPanel A: G10 currencies (73.3% market share)EURUSD 23.1% 111 28 148 267 67 1 1 5 1 1 2JPY 19.3% 93 86 103 140 47 1 2 2 1 1 3GBP 11.2% 54 13 84 119 32 1 3 12 2 1 5CHF 4.4% 21 4 31 49 14 3 7 40 5 3 11AUD 5.5% 26 23 32 40 13 4 6 7 5 4 12CAD 4.6% 22 6 17 56 23 3 7 27 9 3 7NZD 1.5% 7 6 9 12 4 13 21 26 18 13 40SEK 2.0% 10 1 19 23 3 7 16 60+ 8 7 48NOK 1.5% 7 1 14 17 3 9 21 60+ 11 9 60+

Panel B: Asian currencies (8.1% market share)CNH 3.8% 18 20 33 14 5 5 8 8 5 11 34SGD 1.6% 8 7 11 10 3 14 20 21 14 16 59HKD 1.5% 7 6 11 9 3 14 21 26 14 17 46INR 1.1% 5 5 15 1 0 10 29 29 10 60+ 60+

Panel C: Emerging markets currencies (5.6% market share)MXN 1.8% 9 1 5 24 11 6 18 60+ 34 6 14TRY 1.3% 6 1 13 14 2 11 25 60+ 12 11 60+

RUB 1.1% 5 0 8 12 5 13 29 60+ 18 13 34ZAR 0.8% 4 0 6 10 2 16 40 60+ 24 16 60+

PLN 0.6% 3 0 6 7 1 21 53 60+ 28 21 60+

25 / 41

Internalisation horizon for non-unit trade sizes . . .

trade size1k 10k 50k 250k 1mn 5mn 10mn 25mn

aver

age

inte

rnal

isat

ion

hor

izon

(norm

alise

dat1m

n)

0

1

2

3

4

5

6

FIFO allocation LIFO allocation VPRO allocation

26 / 41

What are the costs of position skewing / internalisation?Let’s start with an informal 3-step approach to build intuition . . .

1. Assume linear approximation to exponential skewing, i.e. when Xt = n

Probability of risk reducing trade Pn ≈1

2+|n|

4R2

2. Assume simplest Oomen (2017) model with two LPs competing foruninformed trader’s flow

Required price skew θn ∝ −n

R2

3. Cost of skewing is then the sum of . . .3.1 cost when skewing “in”

C−S ∝

∑n

|θn|Pnφn ≈κ−

2R+

√2πκ−

8R2

3.2 minus revenues when skewing “out”

C+S ∝

∑n

|θn|(1− Pn)φn ≈κ−

2R−√

2πκ−

8R2.

27 / 41

What are the costs of position skewing / internalisation?

Heuristic approach shows:

(a) costs increase with re-duction in LP’s willingness tohold risk

(b) skew components O(R−1)

(c) net skew costs O(R−2)

LP risk limit R1 2 3 4 5 7 10 20 30 40 50 70 100

spre

ad/

cost

s

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

sacri-ced spread C!S additional spread C+

S skew costs CS

28 / 41

What are the costs of position skewing / internalisation?

There are a number of deficiencies with this approach

I adverse selection (set of deals won) is affected by the act of skewing

I trader’s actions may depend on price (skew) shown

I dealer may skew prices “asymmetrically”

29 / 41

What are the costs of position skewing / internalisation?

Starting point model by Oomen (2017) where LPs compete on best price fora trader’s flow

I True price process is unobserved

p∗t = p∗t−1 + εt

I LPs make independent assessment of true price:

p(i)t = p∗t + d

(i)t where d

(i)t ∼ i.i.d. N (0, ω2)

for i ∈ {1, 2} and corr(d(1)t , d

(2)t ) = ρd

I LPs charge a nominal spread around this price:

b(i)t = p

(i)t −

1

2s and a

(i)t = p

(i)t +

1

2s

30 / 41

Two extensions

1. Explicit decomposition of “true price deviation” into dt = mt + θtwhere

I mt is the measurement error, random i.i.d. (0,κ2)

I θt is the LP’s position skew, known and deterministic to the LP, butrandom to others.

2. The trader is “informed” to the extent that her order placementdepends on the LPs prices as follows:

I trader gets a signal on true price that is i.i.d. (p∗t , ω

2T )

I they sells to LP–i when:

LP–i shows best bid b(i)tj> b

(6=i)tj

Selling is more attractive than buying p(0)tj− b

(i)tj< min(a

(i)tj− p

(0)tj, a

( 6=i)tj− p

(0)tj

)

I trader fully informed when ωT = 0, noise trader when ωT =∞.

31 / 41

Spread metrics

Assume two identical LPs and absence of position skewing (i.e. θ = 0).

The expected observed spread is defined as S = E (mini a(i)t −maxi b

(i)t ) and

equal to:S = s − κ−

√2/π, (3)

where κ2± = 2κ2(1± ρm).

The expected effective spread is defined as S = 2E (|xtj − p∗tj |) and equal to:

S = S − ξ−1κ2+

√2/π, (4)

where ξ2 = κ2+ + 4ω2

T .

The equilibrium spread at which neither LP can profit by unilaterally makinga change to their own spread is equal to:

s∗ =4κ2 + πξκ−ξ + κ−

√2/π. (5)

32 / 41

Spread metrics

Trader's informedness (!T )0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

spre

adm

easu

res

0.2

0.4

0.6

0.8

1

1.2

1.4

equilibrium spread s$ observed spread S e,ective spread S

33 / 41

LP’s position skewing rule

Symmetric price skewing θ(i)t = −γX (i)

t

Asymmetric generalisation

b(i)t = m

(i)t −

1

2s − γin min(X

(i)t , 0)− γout max(X

(i)t , 0),

a(i)t = m

(i)t +

1

2s − γin max(X

(i)t , 0)− γout min(X

(i)t , 0),

34 / 41

Cost of skewing

Assume LP–2 does not control position via skewing.

LP–1 compares revenues with (Rγ) and without (R0) position skewing →difference is cost of skewing where . . .

Rc = E(a(1)tj− p∗

tj | γ = c, trader buys from LP-1) · Pr(trader buys from LP-1| γ = c)

+E(p∗tj − b

(1)tj| γ = c, trader sells to LP-1) · Pr(trader sells to LP-1| γ = c)

Note that R0 = S.

35 / 41

Internalisation metrics (first order)

Costs of position skewing for LP–1 is:

Cγ = ϑ (s∗ − s)γin − γout

4πR +OC

(R−2

).

The market share of LP–1 is:

Mγ =1

2+ ϑ

γin − γout2π

R +OM

(R−2

).

The average spread shown by LP–1, i.e. E (a(1)t − b

(1)t ), is:

sγ = s − γin − γout√π/2

R +Os

(R−2

).

36 / 41

Internalisation metrics – illustration of skewing costs

target position volatility R1 2 3 4 5 6 7 8 9 10

skew

ing

cost

s

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

symmetric skewasymmetric skew-inasymmetric skew-outanalytical approximation

Note: parameters set as ωT = 12κ, and s = 1

2s∗ , i.e. a scenario with a highly informed trader and LPs that charge a tight nominal spread.

37 / 41

Internalisation metrics – illustration of market share

target position volatility R1 2 3 4 5 6 7 8 9 10

LP-1

mark

etsh

are

35%

40%

45%

50%

55%

60%

65%

70%

symmetric skewasymmetric skew-inasymmetric skew-outanalytical approximation

Note: parameters set as ωT = 12κ, and s = 1

2s∗ , i.e. a scenario with a highly informed trader and LPs that charge a tight nominal spread.

38 / 41

Cost of internalisation

Nominal spread s = equilibrium spread s∗

Trader perfect high medium noneinformedness (ωT = 0) (ωT = κ) (ωT = 2κ) (ωT =∞)

Panel A: spread metrics in absence of position skewing (×100)Nominal half-spread ( 1

2 s) 68.9 67.4 65.9 62.7Observed half-spread ( 1

2 S) 49.0 47.4 45.9 42.7Effective half-spread ( 1

2 S) 14.4 24.8 32.2 42.7

Panel B: cost of symmetric position skewing (×100)Low risk (R = 1) 2.0 3.1 4.1 6.1Medium risk (R = 5) 0.1 0.1 0.2 0.3High risk (R = 10) 0.0 0.0 0.0 0.1

Panel C: cost of asymmetric-in position skewing (×100)Low risk (R = 1) 9.1 12.1 15.2 30.0Medium risk (R = 5) 0.3 0.4 0.5 0.6High risk (R = 10) 0.1 0.1 0.1 0.1

Panel D: cost of asymmetric-out position skewing (×100)Low risk (R = 1) 1.5 2.6 3.5 5.0Medium risk (R = 5) 0.1 0.2 0.3 0.4High risk (R = 10) 0.0 0.1 0.1 0.1

39 / 41

Cost of internalisation

Nominal spread s = 12 equilibrium spread s∗

Trader perfect high medium noneinformedness (ωT = 0) (ωT = κ) (ωT = 2κ) (ωT =∞)

Panel A: spread metrics in absence of position skewing (×100)Nominal half-spread ( 1

2 s) 34.5 33.7 32.9 31.3Observed half-spread ( 1

2 S) 14.5 13.7 13.0 11.4Effective half-spread ( 1

2 S) −20.0 −8.9 −0.7 11.4

Panel B: cost of symmetric position skewing (×100)Low risk (R = 1) 3.0 3.9 4.7 6.0Medium risk (R = 5) 0.1 0.1 0.2 0.2High risk (R = 10) 0.0 0.0 0.0 0.1

Panel C: cost of asymmetric-in position skewing (×100)Low risk (R = 1) 14.6 17.4 20.4 34.8Medium risk (R = 5) 1.7 1.7 1.8 1.8High risk (R = 10) 0.8 0.8 0.7 0.8

Panel D: cost of asymmetric-out position skewing (×100)Low risk (R = 1) −3.3 −2.2 −1.2 0.4Medium risk (R = 5) −1.2 −1.1 −1.0 −0.8High risk (R = 10) −0.6 −0.6 −0.6 −0.5

40 / 41

Concluding remarks

I In the world’s largest financial market of FX, where the majority of spottransactions are conducted electronically at a pace approaching thespeed of light, the popular perception is that dealers tend to hold riskpositions for only a matter of seconds. We show this is not the case.

Liquidity is finite and takes time to “produce” . . .(Jim – of course – already knew that long time ago!)

I Efficient execution requires the execution objectives of the trader andthe hedging approach of the LPs to be aligned

I more LPs not always better

I execution style of the trader impacts the liquidity they can access

I polarisation between internalisers and externalisers overly simplistic

I direct trade-off between urgency and costs

(note: big difference between efficient execution and “best execution”)

41 / 41

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