1. Presented by Ori Gil Supervisor : Gal Zahavi Control and Robotics Laboratory Winter 2011

2. 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 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 Laboratory2

3. Basic Concepts 3Control and Robotics Laboratory Market Liquidity Market Making Bid-Ask Spread

4. 4Control and Robotics Laboratory Bid-Ask Spread

5. Control and Robotics Laboratory Price Process Leumi’s share (03/01/2010) 5 Price Process

6. Control and Robotics Laboratory Price Process Leumi’s share (03/01/2010) 5

7. The Models 6Control and Robotics Laboratory Extended GM Model Roll Model (1984) Glosten- Milgrom Model (1985) Liquidty Population

8. Roll Model (1984) Control and Robotics Laboratory7

9. Roll Model (1984) Control and Robotics Laboratory8

10. GM Model (1985) Control and Robotics Laboratory9 Market population

11. GM Model (1985) Control and Robotics Laboratory10

12. GM Model (1985) Control and Robotics Laboratory The event tree of a trade: 11

13. Analyzing GM Model: Finding The Bid-Ask spread Control and Robotics Laboratory12

14. 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

15. 14 Control and Robotics Laboratory Gathering training set from TASE quotes D(t)={X(t),Y(t)} Market Making Algorithm – Supervised learning approach

16. 14 Control and Robotics Laboratory Bid price Ask price Informed proportion µ V probability δ Gathering training set from TASE quotes D(t)={X(t),Y(t)} Gathering training set from TASE quotes D(t)={X(t),Y(t)} Market Making Algorithm – Supervised learning approach

17. 14 Control and Robotics Laboratory Gathering training set D(t)={X(t),Y(t)} from TASE quotes Gathering training set from TASE quotes D(t)={X(t),Y(t)} Running the learned function on the training set (Multi-linear regression) Market Making Algorithm – Supervised learning approach

18. Control and Robotics Laboratory Gathering training set from TASE quotes D(t)={X(t),Y(t)} 14 Running the learned function on the training set (Multi-linear regression) Market Making Algorithm – Supervised learning approach

19. Control and Robotics Laboratory Running our mm strategy on test set and compare results against historical data Gathering training set from TASE quotes D(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)

20. Control and Robotics Laboratory 15 Parameters Measure – GM+Roll

21. Market Making - Basic Strategy Control and Robotics Laboratory 16 “Next-step”Forecast

22. Control and Robotics Laboratory Training Test 17 Supervised Learning Strategy

23. Control and Robotics Laboratory 18 “Next-step”Forecast Supervised Learning Strategy

24. Conclusions Knowing 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. 19 Control and Robotics Laboratory

25. 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. 20 Control and Robotics Laboratory

26. Thank You! Questions? Control and Robotics Laboratory