Supervised Learning Strategy of Market Making

1. Supervised Learning Strategy of Market Making Presented by Ori Gil Supervisor : Gal Zahavi Winter 2011 Control and Robotics Laboratory

2. Project Overview • 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. Control and Robotics Laboratory

3. Basic Concepts Control and Robotics Laboratory

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

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

6. The Models Population Liquidty Control and Robotics Laboratory

7. Roll Model (1984) Control and Robotics Laboratory

8. Roll Model (1984) Control and Robotics Laboratory

9. GM Model (1985) • Market population Control and Robotics Laboratory

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

11. Analyzing GM Model: Finding The Bid-Ask spread Control and Robotics Laboratory

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

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

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

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

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

17. Market Making Algorithm – Supervised learning approach 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)} Running the learned function on the training set (Multi-linear regression) Producing optimal mm strategy (OLS) Next-step” forecast Control and Robotics Laboratory

18. Parameters Measure – GM+Roll Control and Robotics Laboratory

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

20. Supervised Learning Strategy Training Test Control and Robotics Laboratory

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

22. 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. Control and Robotics Laboratory

23. 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. Control and Robotics Laboratory

24. Thank You!Questions? Control and Robotics Laboratory