The Efficiency of an Artificial Double Auction Stock Market with Neural Learning Agents

1. The Efficiency of an Artificial Double Auction Stock Market with Neural Learning Agents Jing Yang Presentation at University of Essex

2. Agent-based simulation • Agent-based simulation models the economy from the bottom up rather than top down through the repeated interaction of heterogeneous agents channelled through trading institutions.

3. Road Map • Introduction of market institutions • Model • Assets • Traders • Trading institution • Experiment Design and Results • Conclusion and future research

4. Introduction of market institutions

5. Market Institutions • Market Institutions: Across developed economies, one observes two predominant types of markets: 1. order-driven markets (limit-order book) 2. quote-driven markets

6. Market Institutions • In an order-driven market, customers submit limit orders to buy or to sell from two sides of the market. Transactions occur when the bid and ask prices are equal. • In a dealership market, dealers stand ready to provide liquidity to the customers and charge a bid-ask spread for the service they provide.

7. Questions • Do the market dynamics under a double auction trading institution converge to the one under walrasian auction? • Can ANN be used to parameterize a agent’s strategy function?

8. Model • Assets • Types of traders • Trading institution

9. Basic framework • N traders with CARA utility function; • Traders choose between a risky asset and a risk free asset. • Each trader maximize next period wealth by optimizing the allocation between two assets; • The stock pays a stochastic dividend which follows a AR(1) process;

10. Model • Framework: • Max • subject to • The homogeneous rational expectation equilibrium (h.r.e.e) forecasting is

11. Value traders • Value trader: • each value trader possess a Feedforward neural networks ANN(1-3-1) model with one input, one hidden layer and one output.

12. Momentum traders • momentum traders compare the current market price with the average of the past 5 days denoted as MA(5) and responds as follows:

13. Momentum traders • If the market price > MA(5), they buy Q shares. • If the market price = MA(5), they hold current position. • If the market price < MA(5), they sell Q shares.

14. Model 3. Trading Institution

15. Double Auction • Double auction in reality • Path-dependent prices • Two-sided auction where buyers improve bid prices and seller improve ask prices until one of the buyers and one of the sellers reach agreement.

16. Double Auction • Scenario 1. If the best bid, b, and the best ask, a, exist on the market • If > a, he will post a market order, buy at this ask price. • If < b, he will post a market order, sell at this bid price. • If b< < a and <(a+b)/2, he will post a sell order at a price of • If b<< a and >(a+b)/2,he will post a buy order at a price of

17. Double Auction • Scenario 2. If only the best ask, a, exists • If > a, he will post a market order, buy at this ask price. • If < a, hewillpost a buy order at a price of

18. Double Auction • Scenario 3. If only the best bid, b, exist • If < b, he will post a market order, sell at this bid price; • If > b, he will post a sell order at a price of • Scenario 4. If no bid or ask exist, • he will has an equal chance to post a buy or a sell order at price of or respectively.

19. A Typical Trading Day • (1) Form reservation price or trading signals • ANN Traders • Momentum Traders • (2) Determine the sequence for traders to enter the market by a random mechanism. • (3) Traders submit orders according to this sequence. Under double auction mechanism, each trader can either submit bid/ask or accept the existing best bid/ask

20. A Typical Trading Day • (4) Transaction occurs when existing bid/ask orders are accepted or crossed and the transaction price is recorded accordingly. • (5) Repeat (3)-(4) for N times, N = # of traders • (6) Repeat (1)-(5) for i times, i = # trading rounds

21. A Typical Trading Day • (7) Market price is recorded as the last transaction price (closing price) • (8) Dividend is announced. • (9) Traders update their information set according to the revealed market price and dividend. • (10) ANN trader retrains his neural network and obtain updated ANN for next period learning. • (11) Repeat (1)-(10) for T periods.

22. Experiment Design and Computational Results

23. Experiment Design • Experiment 0 • 10 value traders in a Walrasian auction. • Experiment 1 • 10 experienced value traders in a double-auction market. • Experiment 2 • 10 inexperienced value traders in a double-auction market. • Experiment 3 • 10 value traders, 10 momentum traders, among them, 5 traders use MA(5) and 5 traders use MA(10).

24. Computational Results • H0: • Tests are performed for experiments 1, 2 and 3. • Results (Table 5)

25. Computational Results • H0: the MA technical indicators can explain the variations in prices. • Tests are performed for experiments 3. • Results (Table 6)

26. Figure 1. Experiment 0: Market Prices vs. REE Prices

27. Figure 2. Experiment 0: Rational vs. ANN Expectations

28. Figure 3. Experiment1: Market Prices vs. Price Deviations

29. Figure 4. Experiment 1: Market Prices vs. Trading Volume

30. Figure 5. Price Deviations in Experiment 1 and Experiment 2

31. Figure 6. Experiment 3: Market Prices and Price Deviations

32. Conclusion • Double auction trading institution can generate market dynamics which converge to REE. • The speed of the convergence varies in learning parameters and the heterogeneity of the agents. • The presence of the noise traders make the convergence unattainable.

33. Future work • Extensions in other trading institutions; • Extensions in learning algorithm • Other applications • —payment systems?