An Artificial Market Model of a Foreign Exchange Market

An Artificial Market Model
of a Foreign Exchange Market
Kiyoshi Izumi1
Department of General Systems Studies,
Graduate School of Arts and Sciences,
the University of Tokyo
1This research was partially supported by JSPS Research Fellowships for Young
Scientists.

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Abstract
In this study, we proposed a new approach to foreign exchange market
studies, an artificial market approach. The artificial market approach inte-
grated fieldwork studies and multiagent models in order to explain the micro
and macro relation in markets.
The artificial market approach has the three steps:
First, in order to investigate the learning patterns of actual dealers, we
carried out both interviews and questionnaires. These field data made it
clear that each dealer improved his or her prediction method by replacing (a
part of) his or her opinions about factors with other dealers’ opinion which
can forecast more accurately.
Second, we constructed a multiagent model of a foreign exchange market.
Considering the result of the analysis of the field data, the interaction of
agents’ learning is described with genetic algorithms in our model.
Finally, the emergent phenomena at the market level were analyzed on
the basis of the simulation results of the model. The results showed that rate
bubbles were caused by the interaction between the agents’ forecasts and the
relationship of demand and supply. The other emergent phenomena were
explained by the concept of the phase transition of forecast variety. The filed
data also supported this simulation results.
This approach therefore integrates the fieldwork and the multiagent mod-
el, and provides quantitative explanation of the micro-macro relation in mar-
kets.

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Contents
1
Introduction
9
2
Theoretical Background
13
2.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2
Macro Level Studies
. . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1
Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2
Rational Expectations Hypothesis (REH) . . . . . . . . 17
2.3
Micro Level Studies . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1
Fieldwork . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2
Game Theoretic Models and Experimental Markets . . 25
2.4
Multiagent models: Integration of Micro and Macro . . . . . . 26
3
Framework of the Artificial Market Approach
29
3.1
Outline of Procedure . . . . . . . . . . . . . . . . . . . . . . . 29
3.2
Advantages of the Approach . . . . . . . . . . . . . . . . . . . 31
4Hypotheses about Dealers’ Behavior
33
4.1
Observation at the Micro Level . . . . . . . . . . . . . . . . . 33
4.2
Interviews: Trace of Temporal Change . . . . . . . . . . . . . 35
4.2.1
Interview Methods . . . . . . . . . . . . . . . . . . . . 36
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4.2.2
Results: Features of Learning . . . . . . . . . . . . . . 36
4.2.3
Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3
Questionnaires: Snapshots of Distributed Patterns . . . . . . . 39
4.3.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.2
Results: verification of hypothesis . . . . . . . . . . . . 40
4.4
Discussion: Ecology of Dealers’ Beliefs . . . . . . . . . . . . . 42
5
Construction of a Multiagent Model
47
5.1
Framework of the Model . . . . . . . . . . . . . . . . . . . . . 47
5.1.1
Step 1: Perception . . . . . . . . . . . . . . . . . . . . 49
5.1.2
Step 2: Prediction
. . . . . . . . . . . . . . . . . . . . 51
5.1.3
Step 3: Strategy Making . . . . . . . . . . . . . . . . . 53
5.1.4
Step 4: Rate Determination . . . . . . . . . . . . . . . 55
5.1.5
Step 5: Adaptation . . . . . . . . . . . . . . . . . . . . 56
5.2
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6
Simulation and Evaluation of the Model
64
6.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2
Comparison with Other Models . . . . . . . . . . . . . . . . . 66
6.2.1
A Method of Comparison
. . . . . . . . . . . . . . . . 67
6.2.2
Results of Comparison . . . . . . . . . . . . . . . . . . 68
6.3
Rate Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3.1
Analysis of the Bubble in 1990 . . . . . . . . . . . . . . 71
6.3.2
Analysis of the Bubble in 1995 . . . . . . . . . . . . . . 74
6.3.3
Mechanism of the Rate Bubbles . . . . . . . . . . . . . 79
6.4
Phase Transition of Forecasts Variety . . . . . . . . . . . . . . 81
6.4.1
Flat Phase and Bubble Phase . . . . . . . . . . . . . . 81
2

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6.4.2
Data weights
. . . . . . . . . . . . . . . . . . . . . . . 86
6.4.3
Mechanism of Phase Transition . . . . . . . . . . . . . 99
6.5
Emergent Phenomena in Markets . . . . . . . . . . . . . . . . 100
6.5.1
Departure from normality . . . . . . . . . . . . . . . . 101
6.5.2
Volume and Fluctuation . . . . . . . . . . . . . . . . . 103
6.5.3
Contrary Opinions Phenomenon . . . . . . . . . . . . . 104
6.6
Comparison of the simulation results with the field data . . . . 104
6.6.1
Classification of weights . . . . . . . . . . . . . . . . . 105
6.6.2
Dynamics of weights . . . . . . . . . . . . . . . . . . . 107
6.6.3
Emergent phenomena . . . . . . . . . . . . . . . . . . . 108
7
Discussion
110
8
Conclusions
114
A Simple Genetic Algorithm
118
B Questionnaires
121
Bibliography
137
3

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List of Figures
2.1
Overview of exchange market studies. . . . . . . . . . . . . . . 14
2.2
Framework of macro studies . . . . . . . . . . . . . . . . . . . 16
2.3
equilibrium of the market
. . . . . . . . . . . . . . . . . . . . 17
2.4
Steps of dealers’ process . . . . . . . . . . . . . . . . . . . . . 23
2.5
Framework of multiagent models
. . . . . . . . . . . . . . . . 27
3.1
Framework of the artificial market approach . . . . . . . . . . 30
4.1
Overview of observation at the micro level . . . . . . . . . . . 34
5.1
Framework of model. . . . . . . . . . . . . . . . . . . . . . . . 48
5.2
Time structure of AGEDASI TOF. . . . . . . . . . . . . . . . 50
5.3
Genetic algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.1
Comparison with Other Models. . . . . . . . . . . . . . . . . . 66
6.2
Out-of-sample forecast . . . . . . . . . . . . . . . . . . . . . . 67
6.3
RMSE under different parameter sets. (The forecast horizon
is 1 week.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.4
RMSE under different parameter sets. (The forecast horizon
is 13 weeks.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
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6.5
Distribution of simulated paths: the paths move in the dotted
areas.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.6
Rate paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.7
Market Average of External Data Weights . . . . . . . . . . . 74
6.8
Market Average of Internal Data Weights . . . . . . . . . . . . 75
6.9
Supply and Demand Curves and Quantity . . . . . . . . . . . 76
6.10 Distribution of simulation paths.
. . . . . . . . . . . . . . . . 77
6.11 Rate change and demand-supply curves. . . . . . . . . . . . . 80
6.12 Rate dynamics of the simulation path . . . . . . . . . . . . . . 82
6.13 Percentages of agents’ forecasts . . . . . . . . . . . . . . . . . 83
6.14 Supply and demand . . . . . . . . . . . . . . . . . . . . . . . . 84
6.15 Temporal change of Econometrics category . . . . . . . . . . . 91
6.16 Distribution of scores of Econometric category . . . . . . . . . 91
6.17 Market averages of component data of Econometric category . 92
6.18 Temporal change of News category . . . . . . . . . . . . . . . 93
6.19 Distribution of scores of News category . . . . . . . . . . . . . 94
6.20 Market averages of component data of News category . . . . . 95
6.21 Frequency of minus weights
. . . . . . . . . . . . . . . . . . . 96
6.22 Means of trend factors . . . . . . . . . . . . . . . . . . . . . . 97
6.23 Scores of trend factors . . . . . . . . . . . . . . . . . . . . . . 97
6.24 Market averages of component data of Trend category . . . . . 98
6.25 Distribution of rate change. . . . . . . . . . . . . . . . . . . . 102
6.26 Mechanism of departure from normality
. . . . . . . . . . . . 103
A.1 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A.2 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5

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A.3 Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6

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List of Tables
4.1
Results of interview with dealer X.
. . . . . . . . . . . . . . . 37
4.2
Results of interview with dealer Y.
. . . . . . . . . . . . . . . 37
4.3
Correlation between differences
. . . . . . . . . . . . . . . . . 42
4.4
Analogy between genetics and a market . . . . . . . . . . . . . 45
5.1
Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.1
Comparison of models
. . . . . . . . . . . . . . . . . . . . . . 70
6.2
Numbers of simulation paths in each trend. . . . . . . . . . . . 77
6.3
Comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4
Difference of trading amounts . . . . . . . . . . . . . . . . . . 85
6.5
Difference of fluctuation . . . . . . . . . . . . . . . . . . . . . 85
6.6
Features of flat and Bubble phase . . . . . . . . . . . . . . . . 85
6.7
Loading value . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.8
Categories of factors . . . . . . . . . . . . . . . . . . . . . . . 88
6.9
Correlation coefficients between the Econometric category and
the rate change . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.10 Correlation coefficients between the News category and the
rate change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
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6.11 Correlation coefficients between the Trend category and the
rate change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.12 Kurtsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.13 Loadings of factors . . . . . . . . . . . . . . . . . . . . . . . . 106
7.1
Analogies between Ising model and artificial markets . . . . . 112
8

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