Supervised Learning Strategy

of Market Making

Presented byOri Gil

Supervisor : Gal Zahavi

Control and Robotics Laboratory

Winter 2011

Introduce to basic concepts. 

Display the main models in the project:Roll model (1984).Glosten-Milgron model (1985).

Implement a profitable automated market maker

in TASE:Basic strategy – trading threshold.Supervised learning strategy – training set and test set.

Simulation on TASE data and conclusions.

Project Overview

Control and Robotics Laboratory 2

Basic Concepts

3Control and Robotics Laboratory

Market Liquidity

Market Making

Bid-Ask Spread

Control and Robotics Laboratory

Price Process

0 1 2 3 4 5 6 71730

1735

1740

1745

1750

1755

1760

1765

t [hours]

Sha

re P

rice

[0.0

1 N

IS]

AskBidPrice

Leumi’s share (03/01/2010)

5

Price Process

Control and Robotics Laboratory

Price Process

0 1 2 3 4 5 6 71730

1735

1740

1745

1750

1755

1760

1765

t [hours]

Sha

re P

rice

[0.0

1 N

IS]

AskBidPrice

Leumi’s share (03/01/2010)

5

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]

Sha

re P

rice

[0.0

1 N

IS]

Ask

BidPrice

The Models

6Control and Robotics Laboratory

ExtendedGM Model

Roll Model (1984)

Glosten-Milgrom Model (1985)

Liquidty Population

Roll Model (1984)

Control and Robotics Laboratory 7

Roll Model (1984)

Control and Robotics Laboratory 8

GM Model (1985)

Control and Robotics Laboratory 9

Market Makers (uninforme

d)

Uninformed Traders

Informed

Traders

Market population

GM Model (1985)

Control and Robotics Laboratory

The event tree of a trade:

11

Analyzing GM Model: Finding The Bid-Ask spread

Control and Robotics Laboratory 12

Market Making Algorithm – Basic approach

13

Control and Robotics Laboratory

Estimating μ from Bid(t-1) and Ask(t-

1)[GM Model]

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

14

Control and Robotics Laboratory

Gathering training set

from TASE quotesD(t)={X(t),Y(t)}

Market Making Algorithm – Supervised learning approach

14

Control and Robotics Laboratory

Bid priceAsk price

Informed proportion µV probability δ

Gathering training set

from TASE quotesD(t)={X(t),Y(t)}

Gathering training set

from TASE quotesD(t)={X(t),Y(t)}

Market Making Algorithm – Supervised learning approach

14

Control and Robotics Laboratory

Gathering training set

D(t)={X(t),Y(t)}from TASE quotes

Gathering training set

from TASE quotesD(t)={X(t),Y(t)}

Running the learned function on the

training set (Multi-linear regression)

Market Making Algorithm – Supervised learning approach

Control and Robotics Laboratory

Gathering training set

from TASE quotesD(t)={X(t),Y(t)}

14

Running the learned function on the

training set (Multi-linear regression)

Market Making Algorithm – Supervised learning approach

Market Making Algorithm – Supervised learning approach

Control and Robotics Laboratory

Running our mm strategy on test set and compare results against historical data

Gathering training set

from TASE quotesD(t)={X(t),Y(t)}

Next-step” forecast

14

Running the learned function on the

training set (Multi-linear regression)

Producing optimal mm

strategy (OLS)

Control and Robotics Laboratory

0 1 2 3 4 5 6 71730

1735

1740

1745

1750

1755

1760

1765

1770

t [hours]

Pric

e [0

.01

NIS

]

PriceV

high

Vlow

0 1 2 3 4 5 6 70

20

40

60

80

t [hours]

[%

]

Proportion of informed traders

0 1 2 3 4 5 6 720

40

60

80

100

t [hours]

1-

[%]

probabilty of Vhigh

15

Parameters Measure – GM+Roll

Market Making - Basic Strategy

Control and Robotics Laboratory 16

“Next-step” Forecast

Control and Robotics Laboratory

Training

0 0.2 0.4 0.6 0.8 1 1.2 1.41732

1734

1736

1738

1740

1742

1744

1746

1748

1750Bid Regression

t [hours]

Price [

0.0

1 N

IS]

Training output

Training predicted

0 0.2 0.4 0.6 0.8 1 1.2 1.41735

1740

1745

1750Ask Regression

t [hours]

Price [

0.0

1 N

IS]

Training output

Training predicted

Test

1 2 3 4 5 6 71744

1746

1748

1750

1752

1754

1756

1758

1760

1762

1764Bid Regression

t [hours]

Price [

0.0

1 N

IS]

Test output

Test predicted

1 2 3 4 5 6 71746

1748

1750

1752

1754

1756

1758

1760

1762

1764

1766Ask Regression

t [hours]

Price [

0.0

1 N

IS]

Test output

Test predicted

17

Supervised Learning Strategy

Control and Robotics Laboratory 18

“Next-step” Forecast

Supervised Learning Strategy

ConclusionsKnowing informed traders population at the market

improves our market making performance.

Adding supervised learning solution to the model showed even better performance.

The project has shown success in bringing learning techniques to building market-making algorithms.

Future extensions of this study may include the refinement of the learning techniques.

19Control and Robotics Laboratory

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.

TASE website, http://www.tase.co.il/TASEEng/Homepage.htm.

20Control and Robotics Laboratory

Thank You!

Questions?

Control and Robotics Laboratory