High Frequency Market Making Yacine A t-Sahalia Mehmet Saglam€¦ · LFTs are randomly arriving...

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High Frequency Market Making Yacine A¨ ıt-Sahalia Mehmet Saglam Princeton University and NBER Princeton University The Evolving Structure of the U.S. Treasury Market Federal Reserve Bank of New York October 20-21, 2015 1

Transcript of High Frequency Market Making Yacine A t-Sahalia Mehmet Saglam€¦ · LFTs are randomly arriving...

Page 1: High Frequency Market Making Yacine A t-Sahalia Mehmet Saglam€¦ · LFTs are randomly arriving noise traders submitting market orders. The HFMM posts quotes and aims to capture

High Frequency Market Making

Yacine Aıt-Sahalia Mehmet Saglam

Princeton University and NBER Princeton University

The Evolving Structure of the U.S. Treasury MarketFederal Reserve Bank of New York

October 20-21, 2015

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1 A MODEL OF HFMM

1. A Model of HFMM

• Premise: Compared to traditional market makers

– HFMMs are better informed than their counterparties: able to ex-

tract signals about the direction of the order flow

– And are faster

• What can we expect when HFMMs become the primary providers of

liquidity?

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1 A MODEL OF HFMM

• Inventory discipline is the primary means of risk control by the HFMM

who is risk-neutral, but penalized for holding inventory

• LFTs are randomly arriving noise traders submitting market orders.

• The HFMM posts quotes and aims to capture the spread as often as

possible.

• The HFMM receives a signal that is informative, but not perfect, about

the sign of the incoming market order from LFTs.

• Optimal Policy: HFMM always quote unless inventory thresholds are

exceeded.

• When deciding whether to quote or not, the HFMM is constantly

weighing the potential of capturing the spread vs. the cost of increas-

ing his inventory.

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2 PREDICTIONS OF THE MODEL

2. Predictions of the Model

• Objective value and optimal inventory limits as a function of model

parameters

– the arrival rate of the LFTs, λ

– the arrival rate of the HFMM’s signal, µ

– the accuracy of the signal, p

– the bid-offer spread, c

– the coefficient of inventory aversion, γ

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2.1 LFTs’ Market Orders Arrival Rate 2 PREDICTIONS OF THE MODEL

2.1. LFTs’ Market Orders Arrival Rate

Optimal value and inventory trading limits

50 100 150 200

2

4

6

8

10

12

14

16

18

Arrival rate of market orders (λ)

Ob

ject

ive

Val

ue

0 50 100 150 200

-15

-10

-5

0

5

10

Arrival rate of market orders (λ)C

riti

cal L

imit

s

UL

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2.2 HFMM’s Signal Arrival Rate (or Latency) 2 PREDICTIONS OF THE MODEL

2.2. HFMM’s Signal Arrival Rate (or Latency)

Optimal value and inventory trading limits

100 200 300 400 500 600 7004

4.5

5

5.5

6

6.5

7

7.5

8

8.5

Arrival rate of signals (μ)

Ob

ject

ive

Val

ue

0 100 200 300 400 500 600 700-15

-10

-5

0

5

Arrival rate of signals (μ)C

riti

cal L

imit

s

UL

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2.3 Signal Accuracy 2 PREDICTIONS OF THE MODEL

2.3. Signal Accuracy

Optimal value and inventory trading limits

0.5 0.6 0.7 0.8 0.9 10

0.005

0.01

0.015

0.02

0.025

Signal accuracy (p)

v(-1

,1)-

v(-1

,-1)

0.5 0.6 0.7 0.8 0.9 1-10

-8

-6

-4

-2

0

2

4

6

8

Signal accuracy (p)C

riti

cal L

imit

s

UL

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2.4 Bis-Ask Spread 2 PREDICTIONS OF THE MODEL

2.4. Bis-Ask Spread

Optimal value and inventory trading limits

0.05 0.1 0.15 0.2 0.25

4

6

8

10

12

14

16

18

20

22

Bid-Offer Spread (C)

Ob

ject

ive

Val

ue

0.05 0.1 0.15 0.2 0.25

-10

-5

0

5

10

Bid-Offer Spread (C)C

riti

cal L

imit

s

UL

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2.5 Inventory Aversion 2 PREDICTIONS OF THE MODEL

2.5. Inventory Aversion

Optimal value and inventory trading limits

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

6

6.5

7

7.5

8

Inventory Aversion (Γ)

Ob

ject

ive

Val

ue

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-10

-5

0

5

10

Inventory Aversion (Γ)C

riti

cal L

imit

s

UL

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2.6 Provision of Liquidity by the HFMM 2 PREDICTIONS OF THE MODEL

2.6. Provision of Liquidity by the HFMM

Long-run Probability of LFTs’ Orders Being Filled by the HFMM

0 200 400 600 800 10000.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

0.71

Average Time between HFT Decisions (ms)

Fill

Rat

e o

f M

arke

t O

rder

s

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2.7 Endogenous Cancellations by the HFMM 2 PREDICTIONS OF THE MODEL

2.7. Endogenous Cancellations by the HFMM

Long-run probability of an existing quote being canceled by the HFMM

0 200 400 600 800 10000.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

Average Time between HFT Decisions (ms)

Lo

ng

Ru

n C

ance

llati

on

Rat

es

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3 PRICE VOLATILITY

3. Price Volatility

• Add price variability in the form of jumps in the asset’s fundamental

value.

• The HFMM has no informational advantage regarding these price

movements; his only signal is about the likely direction of the order

flow.

• Volatility introduces adverse selection: the HFMM may get stuck with

stale quotes that can be sniped by another HFT

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3 PRICE VOLATILITY

Example: A Simulated Path with Volatility

0 59.95

10

10.05

10.1

τµ,s1 τζ,up2 τλ,s3 τµ,b4

Loss

Time (s)

Price

Bid Quote Ask Quote Price Trade Signal Jump

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3 PRICE VOLATILITY

Long-run probability of quoting as a function of the price jump arrival

rates

0 20 40 60 80 1000.6

0.62

0.64

0.66

0.68

0.7

0.72

Rate of jumps (/min)

Fill

Rat

e o

f M

arke

t O

rder

s

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3 PRICE VOLATILITY

• When the price is more volatile, the likelihood that the HFMM will

provide liquidity decreases.

• This is because this volatility introduces a new source of risk for the

HFMM (excess inventory) that is not compensated for and for which

he holds no advantage (no signal).

• So while the HFMM provides plenty liquidity in normal times, it is op-

timal for the HFMM to withdraw when the market needs that liquidity

the most...

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4 COMPETITION AMONG HFMMS

4. Competition Among HFMMs

• Duopoly: Splitting the Rent

Optimal value achieved by the HFMM: Monopoly vs. Duopoly

0 100 200 300 400 500 600 700 8004

4.5

5

5.5

6

6.5

7

7.5

Average Time between HFT Decisions (ms)

Ob

ject

ive

Val

ue

MonopolyDuopoly

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4 COMPETITION AMONG HFMMS

• The rent extracted from LFTs gets split between the two market mak-

ers.

• The faster the HFMM, the more of the rent he is able to capture:

there are benefits to becoming faster among HFMMs.

• LFTs are better off when market makers compete compared to the

monopolistic HFMM situation.

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5 COMPARING DIFFERENT HFT REGULATIONS

5. Comparing Different HFT Regulations

• Three policies in the context of the model: imposing a transaction tax

on each trade, setting minimum rest times on limit orders and taxing

cancellations of limit orders.

• Objective: induce the HFMM to provide liquidity that is more resilient

to increases in volatility = procyclical with respect to volatility

– We find that none of the three policies result in an improvement

compared to doing nothing.

– Transaction taxes result in less liquidity both in low and high volatil-

ity environments.

– Both minimum rest times and a cancellation tax result in more

liquidity in good (low volatility) environments but less in bad (high

volatility) environments = countercyclical.

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5.1 Tobin Tax: Taxing Transactions 5 COMPARING DIFFERENT HFT REGULATIONS

5.1. Tobin Tax: Taxing Transactions

• Equivalent to a reduction in the spread. Transaction taxes reduce the

incentive to quote.

0 5 10 15 20 25 30

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Transaction Tax (bps)

Lo

ng

-ru

n P

rob

abili

ty o

f Q

uo

tin

g

0 5 10 15 200.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

Rate of jumps (/min)

Lo

ng

Ru

n F

ill R

ate

of

Mar

ket

Ord

ers

Tax = 0 bpsTax = 10 bpsTax = 20 bps

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5.2 Minimum Rest Time 5 COMPARING DIFFERENT HFT REGULATIONS

5.2. Minimum Rest Time

• Mandatory rest times increase the provision of liquidity when volatility

is low, but decrease it when volatility is high

0 200 400 600 800 1000 1200 1400 16000.575

0.58

0.585

0.59

0.595

0.6

Rest Time (ms)

Lo

ng

-ru

n P

rob

abili

ty o

f Q

uo

tin

g

0 5 10 15 200.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

0.78

0.8

Rate of jumps (/min)

Lo

ng

Ru

n F

ill R

ate

of

Mar

ket

Ord

ers

Rest time = 0 msRest time = 50 msRest time = 500 ms

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5.3 Taxing Order Cancellations 5 COMPARING DIFFERENT HFT REGULATIONS

5.3. Taxing Order Cancellations

• Tax the HFMM whenever an existing quote is cancelled.

• Cancellation taxes encourage the HFT to quote more when volatility

is low but less when it is high.

0 0.02 0.04 0.06 0.08 0.10.575

0.58

0.585

0.59

0.595

0.6

Cancellation Tax (bps)

Lo

ng

-ru

n P

rob

abili

ty o

f Q

uo

tin

g

0 5 10 15 20

0.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

0.78

0.8

Rate of jumps (/min)

Lo

ng

Ru

n F

ill R

ate

of

Mar

ket

Ord

ers

Tax = 0 bpsTax = 0.02 bpsTax = 0.1 bps

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6 CONCLUSIONS

6. Conclusions

• The latency advantage of a HFT can be quantified in a fully optimizing

model.

• Predictions of the model:

– The HFMM trades often, carries little inventory, captures the spread

from LFTs.

– Lower latency is beneficial to the HFMM.

– Order cancellations occur endogenously in the model.

– In good times, the HFMM improves liquidity. But when price

volatility increases, the HFMM decreases his liquidity provision.

– Competition among HFMMs lead to splitting the rent and benefits

LFTs.

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Page 23: High Frequency Market Making Yacine A t-Sahalia Mehmet Saglam€¦ · LFTs are randomly arriving noise traders submitting market orders. The HFMM posts quotes and aims to capture

6 CONCLUSIONS

• Regulations?

– Taxing transactions is ineffective: it uniformly reduces the provision

of liquidity

– Mandatory rest times and cancellation taxes increase the provision

of liquidity when volatility is low

– But decrease it when volatility is high

– So both fail to encourage countercyclical liquidity provision.

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6 CONCLUSIONS

• Details?

http://papers.ssrn.com/sol3/papers.cfm?abstract id=2331613

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