This Study is aimed to establish an analytical foundation for electronic market making strategy, by giving a probabilistic interpretation to the Bid-Ask spread. The suggested strategy will be optimized with on-line learning from the high frequency data of the TASE (Tel Aviv Stock Exchange) order book.

1. 1
GAL ZAHAVI, ORI GILL
TECHNION-ISRAEL INSTITUTE OF TECHNOLOGY
THE WILLIAM DAVIDSON FACULTY OF INDUSTRIAL ENGINEERING & MANAGEMENT

2. Liquidity and Market Makers
Liquidity and Market Makers
•
• Liquidity
Liquidity defined an asset's ability to be sold without
causing a significant movement in the price and with
minimum loss of value.
• A market maker
market maker is a company, or an individual, that
provides liquidity to the market by taking the
opposite side of a transaction. If an investor wants to
buy, the market-maker sells and vice versa. Market
maker makes his profit by the bid-ask spread.
2

3. Transaction Costs
Transaction Costs
3
Bid
Bid-
-Ask Spread
Ask Spread

4. Transaction Costs
Transaction Costs
Adverse Selection
Adverse Selection
Costs
Costs
5
Bid
Bid-
-Ask Spread
Ask Spread

5. Transaction Costs
Transaction Costs
Adverse Selection
Adverse Selection
Costs
Costs
Inventory Costs
Inventory Costs
5
Bid
Bid-
-Ask Spread
Ask Spread

6. The Models
The Models
5

7. Roll Model (1984)
Roll Model (1984)
• Initial assumptions
• Single market maker at the market.
• All fundamental information is known to all
players.
• Same probability for buy and sell transactions.
• Only fixed transaction cost.
• No new information – the stock value is stable.
6

8. Roll Model (1984)
Roll Model (1984)
7

9. Roll Model (1984)
Roll Model (1984)
8

10. GM Model (1985)
GM Model (1985)
9

11. GM Model (1985)
GM Model (1985)
10
The event tree for the first trade:

12. Analyzing GM Model: Finding The Bid-Ask spread
11

13. Analyzing GM Model: Finding The Bid-Ask spread
y
12

14. Analyzing GM Model: Finding The Bid-Ask spread
13

15. Extended GM Model (GM+Roll)
Extended GM Model (GM+Roll)
14

16. Market Making Algorithm
Market Making Algorithm –
–
Basic approach
Basic approach
15
Estimating µ from
Bid(t-1) and Ask(t-1)
[GM Model]

17. Market Making Algorithm
Market Making Algorithm –
–
Basic approach
Basic approach
15
Estimating µ from
Bid(t-1) and Ask(t-1)
[GM Model]
Comparing µ
with the chosen
M threshold
µ ? M

18. Market Making Algorithm
Market Making Algorithm –
–
Basic approach
Basic approach
15
Estimating µ from
Bid(t-1) and Ask(t-1)
[GM Model]
Comparing µ
with the chosen
M threshold
Submitting
bid and ask orders
:
Bid(t)=Bid(t-1)
Ask(t)=Ask(t-1)
µ ≤ M
µ ? M

19. Market Making Algorithm
Market Making Algorithm –
–
Basic approach
Basic approach
15
Estimating µ from
Bid(t-1) and Ask(t-1)
[GM Model]
Comparing µ
with the chosen
M threshold
Submitting
bid and ask orders
:
Bid(t)=Bid(t-1)
Ask(t)=Ask(t-1)
µ ≤ M
Waiting for
new order to
arrive at the
market
µ ? M

20. Market Making Algorithm
Market Making Algorithm –
–
Basic approach
Basic approach
15
Estimating µ from
Bid(t-1) and Ask(t-1)
[GM Model]
Comparing µ
with the chosen
M threshold
Submitting
bid and ask orders
:
Bid(t)=Bid(t-1)
Ask(t)=Ask(t-1)
µ ≤ M
µ M
Cancelling open
orders and holding
trade work until
new order arrives
Waiting for
new order to
arrive at the
market
µ ? M

21. Market Making Algorithm
Market Making Algorithm –
–
Online learning approach
Online learning approach
16
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}

22. Market Making Algorithm
Market Making Algorithm –
–
Online learning approach
Online learning approach
16
Bid price
Ask price
Informed proportion
Vlow probability
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}

23. Market Making Algorithm
Market Making Algorithm –
–
Online learning approach
Online learning approach
16
Gathering training
set D(t)={X(t),Y(t)}
from TASE quotes
characterize the structure
of our learned function
(Multi-linear Regression)
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}

24. Market Making Algorithm
Market Making Algorithm –
–
Online learning approach
Online learning approach
characterize the structure
of our learned function
(Multi-linear Regression)
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}
16

25. Market Making Algorithm
Market Making Algorithm –
–
Online learning approach
Online learning approach
characterize the structure
of our learned function
(Multi-linear Regression)
Running the
regression on the
training set +
learning regression
coefficients
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}
16

26. Market Making Algorithm
Market Making Algorithm –
–
Online learning approach
Online learning approach
characterize the structure
of our learned function
(Multi-linear Regression)
Running the
regression on the
training set +
learning regression
coefficients
Evaluating
our market making
strategy on the test
set against
historical data
Gathering training
set
from TASE quotes
D(t)={X(t),Y(t)}
“In the money” forecast
“Next-step” forecast
16

27. TASE Trading System
TASE Trading System
17

28. Order Book Dynamics
Order Book Dynamics
Ask Side
Ask Side
Bid Side
Bid Side
18

29. 25
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

30. 12
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

31. 34
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

32. 31
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

33. -10
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

34. -31
9
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

35. -34
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

36. -15
Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

37. Ask Side
Ask Side
Bid Side
Bid Side
Order Book Dynamics
Order Book Dynamics
18

38. Leumi
Leumi’
’s share (03/01/2010)
s share (03/01/2010)
Price Process
Price Process
0 1 2 3 4 5 6 7
1730
1735
1740
1745
1750
1755
1760
1765
t [hours]
Share
Price
[0.01
NIS]
Ask
Bid
Price
Empirical Results (Matlab)
Empirical Results (Matlab)
19

39. Leumi
Leumi’
’s share (03/01/2010)
s share (03/01/2010)
Price Process
Price Process
0 1 2 3 4 5 6 7
1730
1735
1740
1745
1750
1755
1760
1765
t [hours]
Share
Price
[0.01
NIS]
Ask
Bid
Price
Empirical Results
Empirical Results
19

40. Leumi
Leumi’
’s share (03/01/2010)
s share (03/01/2010)
Price Process
Price Process
0 1 2 3 4 5 6 7
1730
1735
1740
1745
1750
1755
1760
1765
t [hours]
Share
Price
[0.01
NIS]
Ask
Bid
Price
2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5
1751.5
1752
1752.5
1753
1753.5
1754
1754.5
1755
t [hours]
Share
Price
[0.01
NIS]
Ask
Bid
Price
Empirical Results
Empirical Results
19

41. Order Book Statistics
Order Book Statistics
0 1 2 3 4 5 6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
# ticks
Percentage
of
spreads
[%]
1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
# level
Percentage
of
transactions
[%]
0 1 2 3 4 5 6 7
0
2
4
6
Bid-Ask Spread
t [hours]
B
id
-
A
s
k
S
p
r
e
a
d
[0
.0
1
N
IS
]
0 1 2 3 4 5 6 7
1
1.5
2
2.5
3
transactions in order book levels
t [hours]
#
le
v
e
l
0 1 2 3 4 5 6 7
0
5
10
15
x 10
4 Best Ask Volume
t [hours]
V
o
lu
m
e
[S
h
a
re
s
]
0 1 2 3 4 5 6 7
0
2
4
6
x 10
4 Best Bid Volume
t [hours]
V
o
lu
m
e
[S
h
a
r
e
s
]
20

42. Roll Model
Roll Model
0 1 2 3 4 5 6 7
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
t [hours]
Share
Price
[0.01
NIS]
Quoted Bid-Ask Spread
Expected Bid-Ask Spread
Roll Bid-Ask Spread
21

43. Extended GM
Extended GM-
-Roll Model
Roll Model
0 1 2 3 4 5 6 7
1730
1735
1740
1745
1750
1755
1760
1765
1770
t [hours]
Price
[0.01
NIS]
Price
Vhigh
Vlow
0 1 2 3 4 5 6 7
0
20
40
60
80
t [hours]
µ
[%]
Proportion of informed traders
0 1 2 3 4 5 6 7
20
40
60
80
100
t [hours]
1-
δ
[%]
probabilty of Vhigh
22

44. Market Making
Market Making -
- Basic Strategy
Basic Strategy
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
75
80
85
90
95
µ barrier
In
market
forecast
Basic strategy
Strategy
Trivial
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
74
76
78
80
82
84
µ barrier
Bid
Ask
forecast
Basic strategy
Strategy
Trivial
23

45. 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
94.1
94.15
94.2
94.25
94.3
94.35
δ barrier
In
market
forecast
Basic strategy
Strategy
Trivial
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
80.5
81
81.5
82
δ barrier
Bid
Ask
forecast
Basic strategy
Strategy
Trivial
Market Making
Market Making -
- Basic Strategy
Basic Strategy
24

46. Online Learning Strategy
Online Learning Strategy
Training
Training
0 0.2 0.4 0.6 0.8 1 1.2 1.4
1732
1734
1736
1738
1740
1742
1744
1746
1748
1750
Bid Regression
t [hours]
Price
[0.01
NIS]
Training output
Training predicted
0 0.2 0.4 0.6 0.8 1 1.2 1.4
1735
1740
1745
1750
Ask Regression
t [hours]
Price
[0.01
NIS]
Training output
Training predicted
Test
Test
1 2 3 4 5 6 7
1744
1746
1748
1750
1752
1754
1756
1758
1760
1762
1764
Bid Regression
t [hours]
Price
[0.01
NIS]
Test output
Test predicted
1 2 3 4 5 6 7
1746
1748
1750
1752
1754
1756
1758
1760
1762
1764
1766
Ask Regression
t [hours]
Price
[0.01
NIS]
Test output
Test predicted
25

47. Online Learning Strategy
Online Learning Strategy
10 20 30 40 50 60 70 80 90
92.5
93
93.5
94
94.5
95
95.5
Training Set Proportion
In
market
forecast
Learning strategy
Strategy
Trivial
10 20 30 40 50 60 70 80 90
76
77
78
79
80
81
82
83
84
Training Set Proportion
Bid
Ask
forecast
Basic strategy
Strategy
Trivial
26

48. Conclusions
Conclusions
Authorized market maker takes a major role in TASE trading system.
These privileged market makers provide high liquidity on the market.
Estimating informed traders proportion does not provide significant
advantage over other traders in TASE.
Bid-Ask spread changes due to arrival of large orders on the market, and
not because any market making strategy.
The expectation of the bid-ask spread is lower than the minimal private
transaction fee (0.07%) in TASE.
We can not perform as a profitable private market makers in Tel
We can not perform as a profitable private market makers in Tel-
-
Aviv exchange.
Aviv exchange.
27

49. BIBLIOGRAPHY
BIBLIOGRAPHY
Cont R., Stoikov S. and Talreja R., 2010, A Stochastic Model for Order Book
Dynamics, Operations Research, 58, pp. 549–563.
Das, S., 2005. A Learning Market-Maker in the Glosten-Milgrom Model
Quantitative Finance, 5, 169-180.
Glosten L. R., and P. R. Milgrom, 1985, “Bid, Ask and Transaction Prices in a
Specialist Market with Heterogeneously Informed Traders,” Journal of Financial
Economics, 14, 71–100.
Huang, R.D. and H. R. Stoll, 1997, “The components of the bid-ask spread: A
General approach”, Review of Financial Studies 10, 995-1034.
Roll, R., 1984, “A Simple Implicit Measure of the Effective Bid-Ask Spread in an
Efficient Market”, Journal of Finance, 39, 1127–1139.
28

50. Thank You!
Thank You!
Questions?
Questions?