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(1)
market microstructure
theoretical analysis
experimental-market
approach
the use of AI agent
only handle the
simplest stylized
models
can't control the
motives and
information-processing
ability of the agents
agents' preferences and
learning algorithms
can be carefully cntroled
and modified
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.
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
Review of the literature
Market Microstructure
Experimental Markets
Simulated Markets
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.
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.
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.
Informational
efficiency
Information
dissemination
Information
dissemination
Insiders
：
Uninformed agents
：
Partially informed
agents
Experimental markets (2)
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
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
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)
Differences in information about the likely
state of nature is the other motive for trade.
trader
insider
partially informed trader
uninformed trader
D=(-,1,-)
D=(0,1,-)
D=(0,1,2)
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)
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)
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)
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
empirical Bayesian trader
momentum trader
nearest-neighbor trader
use market information
to update their belef
about the state of
the economy
their forecast of
tomorrow's return
is today's return
attempt to exploit
any pattern to
predict market price
by using NN learning
using these belief
to form
their base price
reinforce and magnify
the ups and downs
of price movements
they learn and
adapt to changing
market conditions
Learning mechanism
Empirical Bayesian trader
Momentum trader
Nearest-neighbor trader
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.
Empirical Bayesian trader(2)
A k-period moving average of prices mt is
used to summarize market information at
time t：(k=10)
t
1
mt 
p

k  t  k 1
Empirical Bayesian trader(3)
Given mk,mk+1,……mt and the realized
dividend Di,
P( Di m) 
P(m Di ) P( Di )

N
j 1
Posterior Distribution
P( m D j ) P( D j )
N
E ( D m)   P( Di m) Di
i 1
Posterior Mean
THEN
= p*
TABLE2
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
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)
In each period i they from a sequence of ntuples from the prices: xni , xni 1,...., xTi
i
N=5
xt  ( pt n1, pt n2 ,......, pt )
The market
price at time t
,
t  k , k  1,....T
The number of
transactions
in the period
Nearest-neighbor trader(2)
( xni , Di ), ( xni 1, Di ),..., ( xTi i , Di ), ( xni 1, Di 1 ),... 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)
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, 10U
10 PI
10 PI
5 I, 5U
5 I, 5U
PI
PI
Results and discussion
Focus
Homogeneous preference
Heterogeneous preference
Momentum traders
Nearest-neighbor traders
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.
1 T
 p   pt  D
T t 1
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)
The difference in wealth between two types of
traders provides an indication of the economic
impact of the differences among the traders.
 w (i , j ) 
Wi  W j
The value of insider
information
Wj
 100
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.
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.
Homogeneous preference
The results from our simulation are similar
to those in the human-based experimental
markets literature.
Figure 2a & 2b：Prices,bid-ask spreads, and
volume of experiment 4.1(I A, P homo)
Early periods
later periods
Figure 2c：Absolute price-deviations of markets prices from
the REE price, average over 100repetitions of experiments 4.1
Market efficiency
clearly improves
substantially over the
epoch
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
Figure 3a & 3b：Prices,bid-ask spreads, and
volume of experiment 4.2 (I D, P homo)
Early periods
later periods
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
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.
Figure 3d：Empirical distribution of moving-average prices,
conditioned on the state of nature S, in experiments 4.2
Figure 3e：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)
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 4a & 4b：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?
average absolute
price-deviation
allocative efficiency
Is it influenced by the traders’
initial cash endowments
Figure 4c：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 4d：Allocative efficiency, average over 100 repetitions
of each of two runs of experiments 4.3
Close to 100%
allocative
efficiency
Figure 4e：Empirical distribution of moving-average prices,
conditioned on the state of nature S, in experiments 4.3
Figure 5a & 5b：Prices,bid-ask spreads, and
volume of experiment 4.4 (I D, P hetero)
Early periods
later periods
Figure 5c：Absolute price-deviations of markets prices from
the REE price, average over 100 repetitions of each of two runs
of experiments 4.4
Figure 5d：Allocative efficiency, average over 100 repetitions
of each of two runs of experiments 4.4
Figure 5e：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
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 6a：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 6b： 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 6c：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 6d：Deciles of percentage wealth differences between
empirical Bayesian and momentum traders in 100 repetitions
of experiments 4.5
+：median
5
Nearest-neighbor traders
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 7a：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 7b： 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)
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)
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)
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
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




Advantages and Disadvantages of the
Agent-Based Model
Model with agents using different learning
schemes
Dividend Processes
Noisy Traders


Here, you see a perfect example on how to
bring different learning schemes into the
model.
Learning schemes incorporated into this
paper includes:



Bayesian Learning
Momentum
Nearest Neighborhood


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




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