Agent-Based Models of Financial Markets : A Comparison with Experimental Markets

1. Agent-Based Models of Financial Markets : A Comparison with Experimental Markets Chan, Lebaron, Lo and Poggio 報告人 王淑卿 2001年6月15日

2. Highlight • Introduction • Review of the literature • Experimental design • Experiments • Results and discussion • Conclusions

3. Introduction(1)

4. Introduction(2) • Construct a computer simulation of a repeated double-auction market, to model complex interactions among AI traders endowed with varying degree of learning capabilities.

5. Introduction(3) • We investigate a number of features of our agent-based model： • the price efficiency of the market • The speed converge to the REE price • The dynamics of the distribution of wealth • Trading volume • Bid/ask spreads

6. Review of the literature • Market Microstructure • Experimental Markets • Simulated Markets

7. Market microstructure (1) • This literature provides important background and context for our experiments. • Several important papers that provides motivation and inspiration. 【Garman (1976), Cohen (1983), Hakansson (1990) 】 • The focus of this literature is primary the structure of markets and market-making activities.

8. Market microstructure (2) • We provide enough market structure to enable our agents to trade with each other. • We also specify the preference and learning heuristics of all market participants. • The interaction of these two sets of specifications that yields the rich implications that we shall describe later.

9. Experimental markets(1) • In much of this literature, the rational expectations (RE) model has been the main benchmark, and has mixed success in various studies. Insiders Uninformed agents Information dissemination ： Informational efficiency Information dissemination Partially informed agents ：

10. Even in heterogeneous preference (REE price) Experimental markets (2) • Conclude that markets disseminate information efficiently.【Plott & Sunder (1982) and Forsythe, Palfrey & Plott (1982)】 • Markets aggregate information efficiently only under：identical preferences, common knowledge of the dividend structure, and complete contingent claims. 【Plott & Sunder (1988) and Forsythe & Lundholm (1990)】 Information aggregation is a more complicated situation

11. Simulated markets • Computer simulations of markets populated by software agents extend the experimental approach by allowing the experimenter to test various theories of learning behavior and market microstructure in a controlled environment. • Agent-based model can easily accommodate complex learning behavior, asymmetric information, heterogeneous preferences, and ad hoc heuristics.

12. Experimental Design • Market Structure and Economic Environment • Trading Mechanism • Agents • Learning Mechanism

13. Market structure and Economic Environment • Simulation structure：double-auction market • Trading subject：single security (pays liquidating state-contingent dividend at the end of a trading period) • Each trading period contains 40 trading intervals. • 75 consecutive trading periods an epoch. • One epoch consists 100 trials. (6 experiments) (Figure 1)

14. Figure 1：experimental design

15. Market structure and Economic Environment(2) • Initialization：state of nature; endowments (cash、stock); private information. • State of nature is random and exogenously determined, and the underlying distribution of the state is common knowledge.【D=(0,1,2)】 • Homogeneous preference ： 【D=(0,1,2)】 • Heterogeneous preference： 【Da=(0,1,2)】 【Db=(2,0,1)】 One Motivation for trade

16. Market structure and Economic Environment(3) • Differences in information about the likely state of nature is the other motive for trade.

17. Trading Mechanism(1) • A simplified double-auction market. • Agents can either submit a bid ( > posted bid) or ask (< posted ask), or accept a posted bid or ask. • A transaction occurs when an existing bid or ask is accepted (a market order matches a limit order), or when the bid and ask cross( in which case the transaction price is set at the middle of the bid and ask).

18. Trading Mechanism(2) • Restriction：1.quantity traded to be one share, 2. no borrowing or short selling. • At the beginning of each interval, a specific ordering of all agents is drawn at random (uniformly). • Following this randomly selected ordering, each agent submits one limit or market order.

19. Agents (1) • Agents design：”zero-intelligence” (Gode and Sunder,1993) • All traders are risk neutral, and they max their end-of-period expected wealth by choosing between cash and stock. • Agents max the end-of-period expected value of their portfolios by forecasting the liquidating dividend (buy if market price < forecast, sell if market price > forecast)

20. Agents (2) • Agents differ in how they determine the expected value of the stock p* (base price). • Procedure of submitting orders. (table 2) • S: preset maximum spread.

21. Table 2：the order-submission algorithm

22. Agents (3) How they construct their forecasts

23. Learning mechanism • Empirical Bayesian trader • Momentum trader • Nearest-neighbor trader

24. Empirical Bayesian trader(1) • Condition their beliefs on market information. • Want to compute the expected dividend E(D p0,p1,…,pt). • Assume that most of the relevant information is embedded in the transaction prices of the last k trades.

25. Empirical Bayesian trader(2) • A k-period moving average of prices mtis used to summarize market information at time t：(k=10)

26. Empirical Bayesian trader(3) • Given mk,mk+1,……mt and the realized dividend Di, Posterior Distribution Posterior Mean THEN = p* TABLE2

27. Empirical Bayesian trader(4) • In the actual implementation, the empirical Bayesian traders estimate the conditional density functions by constructing histograms with series of moving-average prices. • Each histogram corresponds to a dividend state. • These histograms give a picture of how well the agents discern different states gives market data.

28. Momentum trader • Momentum traders are simple technical analysis traders whose forecast of tomorrow’s return is today’s return. • If at time t the two most recent transaction prices are ptand pt-1, then a momentum trader’s forecast of next transaction price is simple pt× ( pt /pt-1 ).

29. Nearest-neighbor trader(1) • In each period i they from a sequence of n-tuples from the prices: N=5 The number of transactions in the period The market price at time t

30. Nearest-neighbor trader(2) • and so on represent the “memory” of a nearest-neighbor trader. • Predict the dividend by first observing the most recent n-tuple in the current market, xjt , then finding its r nearest neighbors in terms of Euclidean distance from memory. • The forecast is defined to be the mean of the associated dividends of the r nearest neighbors.

31. Nearest-neighbor trader(3) • r controls the robustness of the prediction by governing the trade-off between bias and variance of the estimate. • Ifr is too large the estimate is inaccurate. • If r is too small the estimate is noisy and sensitive to individual data points. • Simple trial-and-error r = 10.

32. Six experiments • Information aggregation and identical preference • Information dissemination and identical preference • Information aggregation and heterogeneous preference • Information dissemination and heterogeneous preference • Empirical Bayesian and momentum traders • Empirical Bayesian and nearest-neighbor traders (Table 1)

33. table 1：summary of six experiments PI：partially informed； I：insider； U：uninformed 20 PI 10 I, 10U 10 PI 10 PI 5 I, 5U 5 I, 5U PI PI

34. Results and discussion • Focus • Homogeneous preference • Heterogeneous preference • Momentum traders • Nearest-neighbor traders

35. Focus(1) • Do prices fully reflect all available information ? • We compare market prices to their REE counterpart by measuring their average absolute price-deviation, and by considering the rate of convergence of pt to D over the epoch.

36. Focus(2) • In addition, we investigate bid-ask spreads, trading volume, and the wealth distribution across the different types of traders. • Narrowing bid-ask spreads show that prices are converging, implying that buyers and sellers are reaching a common price. • Diminishing volume suggests that the market is approaching its equilibrium.

37. Focus(3) • The difference in wealth between two types of traders provides an indication of the economic impact of the differences among the traders. The value of insider information

38. Focus(4) • We also investigate the expectations formed by the agents by examining their empirical conditional density functions of moving-average price given the states. • The agents uses these density functions to distinguish one state from another.

39. Focus(5) • We define allocative efficiency as the ratio between total dividends earns by all traders and the total maximum dividends that can possibly be extracted from the market. • 100% allocative efficiency implies that all shares are held by traders in the group that receives the highest dividend in the realized states.

40. Homogeneous preference • The results from our simulation are similar to those in the human-based experimental markets literature.

41. Figure 2a & 2b：Prices,bid-ask spreads, and volume of experiment 4.1(I A, P homo) Early periods later periods

42. Figure 2c：Absolute price-deviations of markets prices from the REE price, average over 100repetitions of experiments 4.1 Market efficiency clearly improvessubstantially over the epoch

43. Figure 2d：Empirical distribution of moving-average prices, conditioned on the state of nature S, in experiments 4.1 3 states are clearly distinguishable by the agents

44. Figure 3a & 3b：Prices,bid-ask spreads, and volume of experiment 4.2 (I D, P homo) Early periods later periods

45. Figure 3c：Absolute price-deviations of markets prices from the REE price, average over 100repetitions of experiments 4.2 Prices converges faster (than ex. 4.1) and closer to the REE price

46. Reasons for difference in ex4.1 & ex4.2 • In ex 4.1 traders must trade with each other to “pool” their information to determine the correct price, whereas in ex 4.2 the insiders know the correct price. • In the former case the distribution of information to the traders is random.

47. Figure 3d：Empirical distribution of moving-average prices, conditioned on the state of nature S, in experiments 4.2

48. Figure 3e：Deciles of percentage wealth differences between insiders and uninformed traders in 100 repetitions of experiments 4.2 The value of insider information is diminishing over the epoch as uninformed traders learn 【～Sunder(1992) 】 +：median

49. Heterogeneous preference(1) • In contrast to the identical-preference cases, the prices in experiments involving diverse preferences do not seem to converge to the REE price. • Because our agents attempt to recover the state of nature from market information alone, and not from the preferences of other agents. REE model fails

50. Figure 4a & 4b：Prices,bid-ask spreads, and volume of experiment 4.3 (I A, P hetero) Early periods later periods