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

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Basic Concepts

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Market Liquidity

Market Making

Bid-Ask Spread

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Price Process

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AskBidPrice

Leumi’s share (03/01/2010)

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Price Process

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Price Process

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Leumi’s share (03/01/2010)

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2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

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The Models

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ExtendedGM Model

Roll Model (1984)

Glosten-Milgrom Model (1985)

Liquidty Population

Roll Model (1984)

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Roll Model (1984)

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GM Model (1985)

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Market Makers (uninformed)Uninformed TradersInformed Traders

Market population

GM Model (1985)

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The event tree of a trade:

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Analyzing GM Model: Finding The Bid-Ask spread

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Market Making Algorithm – Basic approach

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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

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Gathering training set

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

Market Making Algorithm – Supervised learning approach

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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

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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)}

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Running the learned function on the

training set (Multi-linear regression)

Market Making Algorithm – Supervised learning approach

Market Making Algorithm – Supervised learning approach

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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

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Running the learned function on the

training set (Multi-linear regression)

Producing optimal mm

strategy (OLS)

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PriceVhigh

Vlow

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t [hours]

[%

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Proportion of informed traders

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t [hours]

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[%]

probabilty of Vhigh

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Parameters Measure – GM+Roll

Market Making - Basic Strategy

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“Next-step” Forecast

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Training

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Training outputTraining predicted

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Training outputTraining predicted

Test

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Test outputTest predicted

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Test outputTest predicted

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Supervised Learning Strategy

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“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.

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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.

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Thank You!

Questions?

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