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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
Highlight Introduction Review of the literature Experimental design Experiments Results and discussion Conclusions
Introduction(2) n Construct a computer simulation of a repeated double-auction market, to model complex interactions among AI traders endowed with varying degree of learning capabilities.
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 n
Review of the literature Market Microstructure Experimental Markets Simulated Markets
Market microstructure (1) n n n 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.
Market microstructure (2) n n n 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.
Experimental markets(1) n In much of this literature, the rational expectations (RE) model has been the main benchmark, and has mixed success in various studies. Informational efficiency Information dissemination Insiders ： Uninformed agents ： Partially informed agents
Experimental markets (2) n n Even in heterogeneous preference (REE price) 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
Simulated markets n n 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.
Experimental Design n n Market Structure and Economic Environment Trading Mechanism Agents Learning Mechanism
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)
Figure 1：experimental design
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
Market structure and Economic Environment(3) n Differences in information about the likely state of nature is the other motive for trade.
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).
Trading Mechanism(2) n n n 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.
Agents (1) n n n 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)
Agents (2) n n n 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.
Table 2：the order-submission algorithm
Agents (3) How they construct their forecasts
Learning mechanism n n n Empirical Bayesian trader Momentum trader Nearest-neighbor trader
Empirical Bayesian trader(1) n n n Condition their beliefs on market information. Want to compute the expected dividend E(D p 0, p 1, …, pt). Assume that most of the relevant information is embedded in the transaction prices of the last k trades.
Empirical Bayesian trader(2) n A k-period moving average of prices mt is used to summarize market information at time t：(k=10)
Empirical Bayesian trader(3) n Given mk, mk+1, ……mt and the realized dividend Di, Posterior Distribution Posterior Mean THEN = p* TABLE 2
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.
Momentum trader n n 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 pt and pt-1, then a momentum trader’s forecast of next transaction price is simple pt × ( pt / pt-1 ).
Nearest-neighbor trader(1) n In each period i they from a sequence of ntuples from the prices: N=5 The market price at time t The number of transactions in the period
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.
Nearest-neighbor trader(3) n n r controls the robustness of the prediction by governing the trade-off between bias and variance of the estimate. If r 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.
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)
table 1：summary of six experiments PI：partially informed； I：insider； U：uninformed 20 PI 10 I, 10 U 10 PI 5 I, 5 U PI PI
Results and discussion n n Focus Homogeneous preference Heterogeneous preference Momentum traders Nearest-neighbor traders
Focus(1) n n 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.
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.
Focus(3) n 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
Focus(4) n n 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.
Focus(5) n n 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.
Homogeneous preference n The results from our simulation are similar to those in the human-based experimental markets literature.
Figure 2 a & 2 b：Prices, bid-ask spreads, and volume of experiment 4. 1(I A, P homo) Early periods later periods
Figure 2 c：Absolute price-deviations of markets prices from the REE price, average over 100 repetitions of experiments 4. 1 Market efficiency clearly improves substantially over the epoch
Figure 2 d：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
Figure 3 a & 3 b：Prices, bid-ask spreads, and volume of experiment 4. 2 (I D, P homo) Early periods later periods
Figure 3 c：Absolute price-deviations of markets prices from the REE price, average over 100 repetitions of experiments 4. 2 Prices converges faster (than ex. 4. 1) and closer to the REE price
Reasons for difference in ex 4. 1 & ex 4. 2 n n 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.
Figure 3 d：Empirical distribution of moving-average prices, conditioned on the state of nature S, in experiments 4. 2
Figure 3 e：Deciles of percentage wealth differences between insiders and uninformed traders in 100 repetitions of experiments 4. 2 +：median The value of insider information is diminishing over the epoch as uninformed traders learn 【～Sunder(1992) 】
Heterogeneous preference(1) n n 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
Figure 4 a & 4 b：Prices, bid-ask spreads, and volume of experiment 4. 3 (I A, P hetero) Early periods later periods
Heterogeneous preference(2) How to measure the degree of market efficiency? Is it influenced by the traders’ initial cash endowments
Figure 4 c：Absolute price-deviations of markets prices from the REE price, average over 100 repetitions of each of two runs of experiments 4. 3 No convergence Some convergence
Figure 4 d：Allocative efficiency, average over 100 repetitions of each of two runs of experiments 4. 3 Close to 100% allocative efficiency
Figure 4 e：Empirical distribution of moving-average prices, conditioned on the state of nature S, in experiments 4. 3
Figure 5 a & 5 b：Prices, bid-ask spreads, and volume of experiment 4. 4 (I D, P hetero) Early periods later periods
Figure 5 c：Absolute price-deviations of markets prices from the REE price, average over 100 repetitions of each of two runs of experiments 4. 4
Figure 5 d：Allocative efficiency, average over 100 repetitions of each of two runs of experiments 4. 4
Figure 5 e：Empirical distribution of moving-average prices, conditioned on the state of nature S, in experiments 4. 4
Heterogeneous preference(3) Information dissemination in a market with diverse dividends (ex 4. 4) is unsuccessful 【contrast with Plott & Sunder (1982) 】 Information aggregation in a market with diverse dividends (ex 4. 3) is unsuccessful 【consistent with Plott & Sunder (1982) 】 Information aggregation in a market with diverse dividends is successful if traders know the existence of heterogeneous preference 【Forsythe & Lundholm (1990) 】
Momentum traders n We add momentum traders to the market to introduce extra noise and volatility to the “signal” perceived by the partially informed empirical Bayesian traders.
Figure 6 a：Absolute price-deviations of markets prices from the REE price in periods 30, 40, 50 and 75, average over 100 repetitions as a function of the number of momentum traders present in experiments 4. 5 (I A, P homo) The market becomes more efficient over time as agents learn 5 25
Figure 6 b： Absolute price-deviations of markets prices from the REE price, average over 100 repetitions, over the epoch for 0, 25, and 50 momentum traders in experiments 4. 5
Figure 6 c：Empirical distribution of moving-average prices, conditioned on the state of nature S, in experiments 4. 5 20 momentum traders, 20 E. B. traders
Figure 6 d：Deciles of percentage wealth differences between empirical Bayesian and momentum traders in 100 repetitions of experiments 4. 5 +：median 5
Nearest-neighbor traders n n Nearest-neighbor traders attempt to uncover and exploit predictabilities in past prices. Our hypothesis is that if market prices are informationally efficient and do fully reveal all available information, then nearestneighbor traders will perform poorly against empirical Bayesians.
Figure 7 a：Absolute price-deviations of markets prices from the REE price, average over 100 repetitions of experiments 4. 6 (I A, P homo) The nearest-neighbor traders do not hinder the process of information aggregation
Figure 7 b： Deciles of percentage wealth differences between empirical Bayesian and nearest-neighbor traders in 100 repetitions of experiments 4. 6 +：median N. N. > E. B. 4 almost N. N. ～ E. B.
Conclusions(1) n n Our simulation results accord well with human-based experimental market studies in many cases. In small number of cases our market behave differently from human-based experimental markets (experiment 4. 3, information dissemination under heterogeneous preference).
Conclusions(2) n n We shows that adding momentum traders to a population of empirical Bayesian has an adverse impact on market performance and the momentum traders do poorly overall. (diminishes over time) Nearest-neighbor traders are relatively successful free riders, not only matching the performance of empirical Bayesian in the long run, but outperforming the Bayesian in the short run.
Conclusions(3) n We conjecture that this advantage comes from the nearest-neighbor traders’ ability to exploit short-term predictabilities more efficiently, and such predictabilities are more readily available in the early periods of trading.
Future research n n n What are the relative merits of a monopolistic market maker versus multiple dealers? What are the likely effects of decimalization on the bid-ask spreads and volume? Do “circuit breakers” ameliorate or exacerbate market volatility?
Discussion n n Advantages and Disadvantages of the Agent-Based Model with agents using different learning schemes Dividend Processes Noisy Traders
n n Here, you see a perfect example on how to bring different learning schemes into the model. Learning schemes incorporated into this paper includes: n n n Bayesian Learning Momentum Nearest Neighborhood
n n This provides us an opportunity to exam whether GA has monopoly power on its capability of replicating human experiments. If the answer is no, as it seems to be, we are ready to ask what are the common features shared by the GA and other learning schemes
Noisy Traders n n Noisy traders was characterized as momentum traders. Why were momentum traders treated as noisy traders? What is the justification? Would it be possible to show the emergence of momentum traders? Here, we see the main difference in using or not using John Holland’s Legacy in agent-based modeling.
Agent-Based Models of Artificial Markets With explicit reference to John Holland’s Legacy With no explicit reference to John Holland’s Legacy Providing a foundation for emergence of behavior Behavior are arbitrarily assumed