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

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

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

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  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?