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Agent’s minimal intelligence calibration for
realistic market dynamics
Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
Abstract This paper investigates the question of the sophistication level, in the mean
of behavior and intelligence, one should endow artificial traders in order to obtain,
with realistic market microstructure, not only both qualitative and quantitative styl-
ized facts in an artificial market. For this purpose, we introduce an agent-based
simulation environment with an architecture close to the Euronext-NYSE Stock Ex-
change. Series of experiments with different kinds of agents’ behavior and trading
framework specifications where realized within this environment. The results in-
dicate that only special calibrations provide realistic stylized facts with coherent
quantitative levels. We introduce a new type of agents, called in this paper ”strongly
calibrated agents”, with their specific environment design, that provide price dynam-
ics in quantitative and qualitative accordance with real stock market characteristics.
1 Introduction
Agent-Based Finance, and specifically, Agent-Based Artificial Stock Markets (here-
after ABASM) is an ever-growing field that appears, in the aftermath of the recent
financial crisis, as a potential source for renewed analysis concerning the stability of
the whole financial system. For example, policy experiments with agent based plat-
forms become more realistic with the increasing sophistication of these softwares,
and topics like the assessment of Tobin Tax regarding financial markets liquidity and
volatility [9] or the analysis of the linkage market-microstructure and price dynam-
ics [11] can actually be undertaken. One strong argument pleading for an increasing
Iryna Veryzhenko
LEM, UMR CNRS 8174, e-mail: iryna.veryzhenko@univ-lille1.fr
Olivier BRANDOUY
Sorbonne Graduate Business School, e-mail: olivier.brandouy@univ-paris1.fr
Philippe MATHIEU
LIFL, UMR CNRS-USTL 8022, e-mail: philippe.mathieu@lifl.fr
1
2 Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
role of ABASM in the academics or policy-makers toolbox, is that these softwares
can duplicate the main stylized facts that can be observed on real-world stock ex-
changes (see for a detailed review of stylized facts [5], and for a work involving
ABASM in their emergence [6]). In this perspective, several research articles have
argued that Zero Intelligence Traders (ZIT, ”
`
a la” [7]) are sufficient to produce such
stylized facts (for instance [15]). Nevertheless, these stylized facts remain mainly
qualitatively congruent with real-world observations and the underlying price mo-
tions emerging from ZIT interaction remain, to our opinion, rather unrealistic. If
one wants to go beyond this mere qualitative approach, ABASM need some ”cal-
ibration” to deliver price dynamics that quantitatively correspond to real financial
markets motions on the one hand, and to produce more realistic price trajectories
on the other hand. Such ”calibration” must be done at the agents level and matched
against real-world data. Furthermore, this process must also be grounded on a real-
istic market microstructure. Thus, the following question is at the bottom line of the
present article : ”How basic artificial traders could be for realistic market simula-
tions ?”.
We show, using an asynchronous Agent-Based platform benchmarked against
a major European stock market, that pure ZIT cannot reproduce realistic price dy-
namics especially when one focus on their quantitative values. We introduce an aug-
mented intelligence specification that aim at delivering both qualitative and quanti-
tative stylized facts and discuss previous results that supported this minimalist spec-
ification in Agent’s artificial intelligence.
The article is organized as follows. In a first section, we briefly review the rele-
vant literature and point out the main results linking agents intelligence and financial
price dynamics. We then describe the agent-based platform used for the experiments
run in section 3, and the procedure that was used to verify the ability at mimicking its
benchmark real stock market. In a fourth section, we describe our empirical strategy
and present the main results we obtain.
2 Literature Review
2.1 Seminal contribution and initial controversy
The minimal agents intelligence calibration became controversial when the much
cited Gode and Sunder [7] model faced strong criticisms from Cliff and Bruten [4].
The main concern of this latter research was to evaluate how much intelligence
is actually needed in agent to achieve high-level trading performance. Cliff and
Bruten calibrated their system through agent’s ability to adjust their profits in order
to achieve a ”realistic market efficiency”. Other kinds of calibrations have appeared
afterwards. For example, some researchers tried to mix agents populations in their
models to get stylized facts from behavior heterogeneity (see for example [1]). Later
Maslov [10] improved an existing model using limit and market orders. This method
Agent’s minimal intelligence calibration for realistic market dynamics 3
has also been employed in the work of [12]. But their models reproduce only some
of generic features: namely, a congruent Hurst exponent and fat tails in the return
distribution. Challet and Stinchcombe [3] show that in continuous-double auction
setting the model of three processes (orders, executions, cancellations) is required
to produce the fat-tails and volatility clustering.
In this research we also focus attention on price dynamics itself : this point is usu-
ally ignored by authors although we believe it is an important validation instrument
for market simulator success : amazingly, one can obtain stylized facts that match
”at a qualitative level”, real world dynamics with an underlying price series that is
totally unrealistic at a first glance. Thus, even if one can observe stylized facts from
the return series delivered by the simulator, he/she can easily face a problem of (un-
realistic) highly volatile price series for example. Therefore, computer simulations
that provide realistic stable price dynamics are particularly interesting to our opin-
ion. The Minimal Market Model (MMM) [2] is, with respect to the latter criterion,
particularly promising. These authors claim that this simple model can reproduce
real market features in both price and return terms. Voit [13] also programed this
model and tried to calibrate it. Simulations end up with very volatile price series.
All simplifications failed at stabilizing this highly sensitive system.
One can notice that many research claim that stylized facts, like volatility clus-
tering, positive correlation in order types or shape of the order book, are not di-
rectly driven by strategic behavior : the necessary and sufficient ingredients to gen-
erate these statistical properties could be a specific market microstructure and zero-
intelligence agents. For instance, an exhaustive investigation has been done by Li-
Calzi, Pellizzari and Dal Forno ([8], [11]), who show that the choice of a protocol
may have a substantial impact on the allocative effectiveness, and other criteria such
as excess volume or price dispersion. Nevertheless, and to the best of our knowl-
edge, no paper focuses on the calibration of ABASM such to obtain quantitative
stylized facts and non-volatile price dynamic in line with real markets. Our target
is to fill this gap and to propose simple parametric methods to calibrate agents be-
havior to provide realistic price and return dynamics in the ArTificial Open Market
API (here-after ATOM, see http://atom.univ-lille1.fr). Moving from
non-strategic behavior to simple intelligence elements we show that any assumption
about any kind of intelligence has an impact to stylized facts. We first present the
ATOM API, then introduce agents behavior specification within this environment.
3 ATOM and Real World Market
ATOM is a general environment for Agent-Based simulations of stock markets. It is
based on an architecture close to the Euronext-NYSE Stock Exchange one. Agent-
Based artificial stock markets aim at matching orders sent by virtual traders to fix
quotation prices. Price formation is ruled by a negotiation system between sellers
and buyers based on an asynchronous, double auction mechanism structured in an
order book. Using this API, one can generate, play or replay order flows (what-
4 Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
ever the origin of these order flows, real world or virtual agents population). One
of the main advantages of ATOM consists in its modularity. This means that it can
be viewed as a system where three interacting main components interact: i) Agents,
and their behaviors, ii) Markets defined in terms of microstructure and iii) the Ar-
tificial Economic World (including an information engine and, potentially, several
economic institutions such as banks, brokers, dealers...). The two first components
can be used independently or together. Depending upon the researcher targets, the
Artificial Economic World can be plugged or not in the simulations. For example,
one can use the system for the evaluation of new regulation policies or market pro-
cedures, for assessing potential effects of taxes or new trading strategies in a sophis-
ticated artificial financial environment. Thanks to its high modularity and its ability
to mimic real-world environments, it can also serve as a research tool in Portfo-
lio Management, Algorithmic Trading or Risk Management among others. From a
pure technological point of view, ATOM can also be viewed as an order-flow replay
engine. This means that bankers can test their algorithmic-trading strategies using
historical data without modifying the existing price series or backtest the impact of
their trading-agents in totally new price motions or market regimes generated by
artificial traders. Several distinctive aspects of ATOM can be highlighted:
1. It can be used without any agent. One can directly send orders written in a text
file (for example, a set of orders as it arrived on a given day, for a given real-
world stock market) to each order-book implemented in the simulation. In this
case, ATOM serves as a ”replay-engine” and simulations merely rely on market
microstructure. It therefore runs really fast (an entire day of trading in less than
5 seconds).
2. ATOM can use various kind of sophisticated agents with their own behaviors
and intelligence. Thousands of these agents can evolve simultaneously, creating
a truly heterogeneous population. Once designed, agents evolve by themselves,
learning and adapting to their (financial) environment.
3. ATOM can mix human-beings and artificial traders in a single market using its
network capabilities. This allows for a wide variety of configurations, from ”ex-
perimental finance” classrooms with students, to competing strategies run inde-
pendently. The scheduler can be set so to allow human agents to freeze the market
during their decision process or not.
4. ATOM has been tested rigorously. It has the ability to replay perfectly an order
flow actually sent to a given market with the same microstructure. The result-
ing price series (on the one hand, the ”real-world” one and on the other hand,
the ”artificial” one) overlap perfectly. Moreover, given a population of agents,
ATOM can generate stylized facts qualitatively similar to the market it is geared
at mimicking.
Simulations in ATOM are organized as ”round table discussions” and are based
on an equitably random scheduler. Within every ”round table discussion”, agents
are randomly interrogated using a uniformly distributed order. This latter feature en-
sures that each of them has an equal possibility of expressing its intentions. Notice
Agent’s minimal intelligence calibration for realistic market dynamics 5
that the API offers a random generator that is shared by all agents. The reproducibil-
ity of experiments is therefore guaranteed.
In real life, investors do not share the same attitudes. Some will be more reactive
than others, or will implement more complex strategies leading to a higher rate of
activity. In ATOM having the possibility to express an intention does not necessarily
imply that a new order is issued. Since agents are autonomous, they always have the
possibility to decline this opportunity.
Moreover, if an agent had been allowed to send several orders when interrogated,
this would have led to an equality problem similar to the one described above. To
overcome this issue, agents are just allowed to send at most one single order to a
given order book (i.e. one order at most per stock) within the same ”round table
discussion”. However, if an agent plans to issue several orders concerning the same
stock (thus, the same order book), she must act as a finite state automata.
ATOM can include human-beings in the simulation loop. A human agent is an
interface allowing for human-machine interaction. Through this interface one can
create and send orders. Notice that human agents do not have any artificial intelli-
gence : they just embed human intelligence in a formalism that is accepted by the
system. To allow the introduction of human in the loop, ATOM has been designed
to deal with communications over the network.
4 Empirical strategy and results
4.1 Data description
Our data consist in intraday prices observed in the Euronext Paris Stock Exchange.
The sampling of these observations is based on intervals of about 1 minute. We use
37 stocks for January 1st 2001 - January 31th 2001 and August 1st 2002 - August
31th 2002 (in total 1628 assets’ price lists). Each day has from 1000 to 5000 records
for different assets, depending on the market activity. Our goal is to compare, using
price and return series, the results delivered by the ATOM platform under some
set of Artificial Intelligence specifications, and real data. For this reason, we first
present some general elements, then how agents behavior is progressively modified
moving in the direction of growing intelligence.
4.2 Calibration elements: agent’s behavior
This section illustrates how we create different agents behavior and how to specify
a general environment within the ATOM framework. We first start from a simple
model (inspired by [10]), then step by step additional constraints are introduced in
order to observe the appearance of nontrivial stylized facts and more realistic price
6 Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
dynamics. Some initial settings, that are implemented in the Market component of
ATOM, are detailed below.
· Buy and Sell orders arouse with equal probability.
· Each agent can submit both orders, Buy and Sell.
· There are three possible order types: limit, market and cancel. We use also a
proportion between different order types, such as 80% of limit orders, 15% of
market orders and 5% of cancel orders. These proportions are equal to those
observed for one specific asset within one specific day. This initial calibration
is geared at imposing realistic market conditions, where both market and limit
orders come in different sizes and exist for various time frame.
· Transactions are realized for a single asset.
· There are two types of traders regarding the volume that they are able to set
up in the orders. A first subset, in which ”Big fish” traders send orders with
a volume close to the maximum possible value (initialization parameter), and
”Small fish” agents, respectively with a volume close to the minimum.
· Budget constraints are implemented: traders cannot make a trade that will yield
a negative profit, i.e., buyers cannot buy at a price higher than their buyer value
(reservation price) and sellers cannot sell for a price below their seller cost.
· Parameters for setting initialization are calculated based on the real market data.
These parameters are measured for each stock within each day.
We now introduce a detailed description of agents behavior, moving from uncal-
ibrated to strongly calibrated agents, in other words the agents in growing intelli-
gence. These agents are realized in the Agents component of the ATOM API.
• Uncalibrated agents should be considered in the above predefined framework
design. They pick a log-normally distributed price α(t) ∼ Log − N(P
mean
, P
sd
),
where P
mean
and P
sd
are respectively mean value and standard deviation of real
market data (initialization parameters). Volume is an integer drawn normally
within the predefined (as parameters) ranges.
• Statistically calibrated agents have ranges within which they are able to setup
orders’ price and volume. Let [P
min
, P
max
] be respectively the minimum and max-
imum real market intraday prices, and [V
min
,V
max
] the minimum and maximum
experienced trading volume for one specific asset. If the agent is willing to send
an Ask order, he/she should respect a sellers’ range [P
A
min
, P
A
max
]; respectively,
in case of a Bid order, the price will be within the limits [P
B
min
, P
B
max
], where
P
min
5 P
B
min
5 P
A
min
5 P
B
max
5 P
A
max
5 P
max
. The price is described in the follow-
ing expressions:
α(t) = P
A
min
+ 4
α
β (t) = P
B
min
+ 4
β
where 4
α
∼ N(P
A
max
− P
A
min
+1, 1), 4
β
∼ N(P
B
max
− P
B
min
+1, 1), α(t) and β(t)
are prices sent at the moment t by the Seller and the Buyer respectively. In a
similar manner, volume is normally distributed within the limits, that are defined
as follow: V
min
= V
A
min
= V
B
min
and V
max
= V
A
max
= V
B
max
.
Agent’s minimal intelligence calibration for realistic market dynamics 7
• Strongly calibrated agents pick a price generated with two major parameters. One
parameter γ reproduces series’ tendency, for instance, slow decay from maximum
to minimum price during one day. The other parameter δ , normally distributed
in N(0, 1), delivers a generic price fluctuation. An example of price formation,
characterized by a slow decay, can be described as follow:
γ(0) = 1 δ (t) ∼ N(0, 1)
γ(t) = γ(t − 1) − 0.001 × t
P(t) = P
min
+ (P
max
− P
min
+ 1) × γ(t) × δ(t)
More complex price dynamics require a modification of γ parameter description.
Volume, as in the previous cases, is a normally distributed value within the given
range.
Using this environment and behavior calibration, we show that Uncalibrated agents
fail at delivering both realistic prices and quantitative stylized facts. Thus a mini-
mum level of calibration is necessary in the system, which directly question the fact
that ”zero is enough”. In other terms, we show that agents actually should have non-
zero intelligence, in order to perform results that are qualitatively and quantitatively
congruent with empirically observed motions in real stock markets.
4.3 One single stock detailed results
This section demonstrates the simulations using BNP PARIBAS intraday price se-
ries 1
st
August 2002 as a benchmark. The following list sums up the initial settings
in the simulations: P
min
= 46.25, P
max
= 48, P
mean
= 47.26, P
sd
= 0.35, V
min
= 1,
V
max
= 54000, V
mean
= 876.05, V
sd
= 2016.19, Number of fixed prices = 4000. Their
applications for each calibration method are described in the following items:
• Uncalibrated agents pick a log-normally distributed price α(t) ∼ Log−N(47.26, 0.35)
and volume v(t) = Log−N(876.05, 2016.19) and randomly set transaction direc-
tion (buy/sell). There are three order types, the possibility to send a limit order is
80%, market order - 15%, cancel order - 5%.
• Statistically calibrated agents pick a normally distributed price within the ranges:
[45, 48] for Ask order and [46.25, 50] for Bid. Transaction volume is normally
distributed value between 1 and 54000. These ranges correspond to reality. These
agents send the same proportion of order types as the uncalibrated agents.
• Strongly calibrated agents pick a price generated by the two parameters evoked
previously that provide a price tendency and generic fluctuations. In addition, if
we need to get three extreme maximum points in the price series, parameter γ
should be coded as illustrated in the Algorithm 1.
This code defines the curve dynamics and stick price from tour to tour (tick by
tick). The fluctuation, typical for real market, is provided by the parameter δ (t) ∼
8 Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
if t < 50 then
γ = 1 − t × 0.02
else if t >= 50 and t < 100 then
γ = 1.2 − t × 0.01
else if t >= 100 and t < 200 then
γ = 0.7 − t × 0.001
else if t >= 200 then
γ = 1 − t × 0.0001
Algorithm 1: Strong calibration
N(0, 1). Finally, the price is defined as P(t) = 46.25 +(48− 46.25+1)×γ(t)× δ (t).
The volume is defined as in the statistical calibration case. Order types proportion
remains the same. In these experiments we use 20 ”big fishes”, that set the orders
with volume from 1 to 54000 units, and 100 ”small fishes” agents, that set the orders
with volume from 1 to 54 units. Figure 1 shows the price plot, performed by different
types of agents. As one can notice, no one can confuse price series of uncalibrated
0 1000 2000 3000 4000
46.5 47.0 47.5 48.0
(a) Human Traders
0 1000 2000 3000 4000
46.5 47.0 47.5 48.0
(b) Strongly Calibrated Traders
0 1000 2000 3000 4000 5000
46.0 46.2 46.4 46.6
(c) Statisticaly Calibrated Traders
0 1000 2000 3000 4000 5000
44.5 45.0 45.5 46.0 46.5 47.0 47.5
(d) Uncalibrated Traders
Fig. 1: Intraday price series
agent (even with budget constrains) with real world data. We use a Wilcoxon non-
parametric test to estimate the difference in the median of generated data. According
to the p − value = 2.2e− 16 of the Wilcoxon Test hypothesis (H
0
: ATOM generated
prices series are similar to real data) the Null should be rejected. Nevertheless, our
target is not to exactly duplicate real price series, but to obtain a not-so-high volatile
price series, with statistical characteristics close to the real ones. Table 1 present the
statistical properties of this experiment. Quantitative characteristics coming from
uncalibrated agents are far from real one. As expected, prices performed by strongly
calibrated agent are much more realistic.
Agent’s minimal intelligence calibration for realistic market dynamics 9
Real Strong Statistical Uncalibrated
Mean 47.2550 47.3195 46.2435 45.9331
Median 47.2300 47.3200 46.2600 45.9400
Variance 0.1218 0.0771 0.0198 0.4262
Stdev 0.3491 0.2777 0.1407 0.6529
Skewness -0.2885 -0.3099 -0.0247 0.0108
Kurtosis -0.0148 -0.0028 -0.8709 -0.9180
Table 1: Basic statistics for price series
Quantitative properties of ATOM generated price series are far from being real.
We now move to consider the properties of the return series (figure 2). According to
p − value
strong
= 0.9751 , p − value
statistical
= 0.644, p − value
uncalibrated
= 0.4138
of Wilcoxon Test, the series generated by the strongly calibrated agents are close to
the real one.
0 1000 2000 3000 4000
−0.008 −0.006 −0.004 −0.002 0.000 0.002 0.004
(a) Human Traders
0 1000 2000 3000 4000
−0.005 0.000 0.005 0.010
(b) Strongly Calibrated Traders
0 1000 2000 3000 4000 5000
−0.010 −0.005 0.000 0.005 0.010
(c) Statisticaly Calibrated Traders
0 1000 2000 3000 4000 5000
−0.06 −0.04 −0.02 0.00 0.02 0.04 0.06
(d) Uncalibrated Traders
Fig. 2: Intraday return
Even if uncalibrated agents are able to reproduce some of the main stylized facts
such as the non Gaussian return distribution (in all cases the Shapiro-Wilk test re-
jects the Normality hypothesis), positive autocorrelation in absolute returns (Ljung-
Box test allows for the rejection of the Null ”independence in a given time series”),
slow decay of autocorrelation in absolute returns, the corresponding quantitative
characteristics do not fit real ones (see table 2).
Uncalibrated agents’ returns show high variance and standard deviation compar-
ing with other time series, and at the same time, a very low level of kurtosis (which
is not typical for real market data), pretty close to normal one, hence high pick is not
really observed in return distribution of uncalibrated agents’ series. Table 2 reports
the facts, that even the lack of specific strategies with simple calibration mechanisms
may provide an approach of quantitative characteristics to the real ones.
10 Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
Real Strong Statistical Uncalibrated
Mean -0.000002 -0.000004 -0.0000006 -0.000006
Variance 0.000000 0.000001 0.000006 0.000255
Stdev 0.000573 0.000993 0.002377 0.015963
Skewness -0.974680 0.462673 -0.003997 0.007360
Kurtosis 21.324362 12.751463 2.987817 0.574427
Table 2: Basic statistics of return
4.4 Population statistics
We now consider a population statistics or sampling distribution approach to inves-
tigate the return properties delivered by ATOM. This technique is not widely used
in current financial data analysis. One example of such approach can be found in
[14], who demonstrate that the sampling distribution of mean values is Student − t,
standard deviations - χ
2
and kurtosis - Weilbull distribution.
In this research, we show that even if the statistics calculated with the ATOM
generated data differ from real-world ones, once considered as population statistics,
they follow the similar distributions with different parametrization (see figures 3, 4,
5). For this experiment, 37 assets per 22 days (a total of 814 intraday trading series)
were modeled using calibration approaches described in the section 4.2.
0 100 200 300
0 50 100 150 200 250
(a) Human Traders
0 20 40 60 80 100
0 20 40 60 80 100 120 140
(b) Strongly Calibrated Traders
0 5 10 15 20 25
0 20 40 60 80 100 120
(c) Statisticaly Calibrated Traders
0 1 2 3 4 5
0 50 100 150
(d) Uncalibrated Traders
Fig. 3: Histogram - distribution of kurtosis; Solid curve - Weilbull distribution
Agent’s minimal intelligence calibration for realistic market dynamics 11
0.0005 0.0010 0.0015 0.0020 0.0025 0.0030
0 5 10 15 20 25
(a) Human Traders
0.000 0.001 0.002 0.003 0.004 0.005
0 5 10 15 20 25 30 35
(b) Strongly Calibrated Traders
0.000 0.002 0.004 0.006 0.008
0 10 20 30 40 50 60 70
(c) Statisticaly Calibrated Traders
0.00 0.02 0.04 0.06
0 20 40 60 80
(d) Uncalibrated Traders
Fig. 4: Histogram - distribution of standard deviations; Solid curve - χ
2
distribution
−0.00015 −0.00010 −0.00005 0.00000 0.00005 0.00010
0 20 40 60 80 100 120 140
(a) Human Traders
−4e−05 −2e−05 0e+00 2e−05 4e−05
0 10 20 30 40 50 60 70
(b) Strongly Calibrated Traders
−2e−05 −1e−05 0e+00 1e−05 2e−05
0 20 40 60 80
(c) Statisticaly Calibrated Traders
−6e−05 −4e−05 −2e−05 0e+00 2e−05 4e−05 6e−05 8e−05
0 50 100 150
(d) Uncalibrated Traders
Fig. 5: Histogram - distribution of mean values; Solid curve - Student − t distribution
Conclusion
In this paper we first present our simulation environment, that allows any kind of
agents behavior and artificial intelligence specification. This platform can easily be
calibrated to match specific features judged as central with regards to a given real-
world stock market. In this article, we use this calibration facility to investigate the
following question: ”What is the minimal level of artificial agents intelligence to
get simulated, realistic market prices ?” Based on the simulations, we show that
there are significant number of important features of real markets that are not suffi-
ciently delivered by basic artificial intelligence designs. Only with a series of speci-
fications concerning agents’ behavior realistic quantitative stylized facts can be ob-
tained. Among other results, we show that strongly calibrated agents are definitely
12 Iryna VERYZHENKO and Olivier BRANDOUY and Philippe MATHIEU
much less complex than human beings, and much more complex than uncalibrated
(ZIT) ones. Nevertheless, results, performed by strongly calibrated agents, are in
qualitative and quantitative agreement with empirically observed behavior of prices
on real stock markets. We therefore discuss the ”zero is enough” result that states
that sophisticated behaviors are useless to understand how market motions emerge,
even at the intraday level. We present an extensive empirical analysis to support this
statements. From a practical point of view, this research suggests that if one wants to
conduct policy-oriented experiments focusing on technical features of the market-
microstructure (for example, to investigate the impact of the tick size on market
liquidity and volatility), a minimal calibration of agents population is clearly neces-
sary. Although this calibration is clearly necessary with regard to the desired prop-
erties of return series generated with agents population, a special attention should
also be put on the price motions themselves.
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