high frequency market making yacine a t-sahalia mehmet saglam€¦ · lfts are randomly arriving...
TRANSCRIPT
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
1
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?
2
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.
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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...
15
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
16
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.
17
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.
18
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
19
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
20
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
21
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.
22
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.
23
6 CONCLUSIONS
• Details?
http://papers.ssrn.com/sol3/papers.cfm?abstract id=2331613
24