A Brief Review of recent Artificial Market Simulation(Agent-Based Model, ABM) Studies
for Financial Market Regulations and/or Rules
Takanobu Mizuta
SPARX Asset Management Co., Ltd.
This working review shows recent agent-based models (ABMs) for financial market (artificial market simulations)to discuss financial regulations and/or rules. This review aimed to introduce recent papers as many as possible.
See [Mizuta 20a] for more details of importance of discussion into design financial markets with artificial market
models, contribution to society and how to build and use such models. ([Mizuta 20a] has related materials, detailpresentation slides and a presentation movie on YouTube.)
It is very diﬃcult to discuss about changing financial market regulations and/or rules by only using results of
empirical studies. An artificial market, which is a kind of an agent-based model, can isolate the pure contributionof changing the regulations to the price formation and can treat situations that have never occurred. These arestrong points of the artificial market simulation study. Recently, some artificial market studies contributed to
discussion what financial regulations and rules should be, for example, price variation limits and short selling
regulation whether preventing bubbles and crushes or not, tick size, usage rate of dark pools, rules for investment
diversification, speed of order matching systems on financial exchanges, frequent batch auctions, how active funds
that trade infrequently make a market more eﬃcient, an interaction between leveraged ETF markets and underlying
markets and micro-foundation of price variation model using intelligence of artificial market simulation studies. I
will review those studies.

1.

Artificial Market Simulation

This working review shows recent agent-based models(ABMs) for financial market (artificial market simulations)to discuss financial regulations and/or rules. This review
aimed to introduce recent papers as many as possible. See[Mizuta 20a] for more details of importance of discussion
into design financial markets with artificial market models,
contribution to society and how to build and use such models. ( [Mizuta 20a] has related materials, detail presentation
slides and a presentation movie on YouTube.)[Mizuta 20a] described that ‘designing a financial market that works well is very important for developing andmaintaining an advanced economy, but is not easy becausechanging detailed rules, even ones that seem trivial, sometimes causes unexpected large impacts and side eﬀects. A
computer simulation using an agent-based model can directly treat and clearly explain such complex systems where
micro processes and macro phenomena interact.’
It is very diﬃcult to discuss about changing financial market regulations and/or rules only by results of empiricalstudies. Because so many factors cause price formation in
actual markets, an empirical study cannot isolate the pure
contribution of existing new type regulations or of changing rules to price formation. Furthermore, empirical studies
cannot investigate situations that have never occurred before in real financial markets.
We usually discuss whether regulations should bechanged or not on the basis of their eﬀects on price formation. An artificial market, which is a kind of a multi-agent
simulation (an agent-based model), can isolate the pure contribution of changing the regulations to the price formationand can treat situations that have never occurred [LeBaron
Contact: mizutata@gmail.com
https://mizutatakanobu.com

06, Chakraborti 11, Chen 12, Cristelli 14, Todd 16, Mizuta20a]. These are strong points of the artificial market simulation study.
Not only academies but also financial regulators andstock exchanges are recently interested in multi-agent simulations such artificial market models to investigate regulations and rules of financial markets. Indeed, the Science
article [Battiston 16] described that ‘since the 2008 crisis,
there has been increasing interest in using ideas from complexity theory (using network models, multi-agent models,and so on) to make sense of economic and financial markets’,and the Nature article [Farmer 09] described that ‘such(agent-based) economic models should be able to provide
an alternative tool to give insight into how government policies could aﬀect the broad characteristics of economic performance, by quantitatively exploring how the economy islikely to react under diﬀerent scenarios’. [Aruka 17, Mizuta
20a] also claimed importance of an artificial market simulation. [Segovia 22] analyzed bibliometric on artificial market
models.
Recently, some artificial market studies contributed to
discussion what financial regulations and rules should be[Todd 16, Mizuta 20a], for example, price variation limits
and/or short selling regulation whether preventing bubbles
and crushes or not [Yagi 10, Yeh 10, Mizuta 13b, Mizuta
15b, Mizuta 16c, Veld 16, Zhang 16, Llacay 19, Xiong 22],
the rule for investment diversification [Yagi 17], transaction taxes [Westerhoﬀ 08, Veryzhenko 17], financial leverages [Thurner 12, Veld 16], circuit breakers [Kobayashi
11, Muranaga 99], tick size [Darley 07, Mizuta 13a, Collver 17, Yang 20, Zhao 20, Mizuta 22a], frequent batch auctions [Mizuta 16a], usage rate of dark pools [Mo 13, Mizuta
14, Mizuta 15c], speed of order matching systems on financial exchanges [Mizuta 15a, Mizuta 16d], the eﬀects of dif-

ferent regulatory policies directed towards high frequency
traders (HFTs) [Leal 16], eﬀects of Basel and value atrisk [Cheng 17,Llacay 17], one-sided and two-sided markets[Zhou 17], settlement cycle [Xiong 17], extension of trading
hours [Miwa 18], maker-taker fees [Hoshino 22, Guan 24],short-selling limitation [Noritake 22], capital adequacy ratio (CAR) regulation in the Basel regulatory framework [Hirano 20], policy maker intervention to prevent bubbles andcrashes [Westphal 23] and so on.
Of course, many artificial market simulation studies investigated the nature of financial markets, detection offactors influencing market liquidity [Yagi 19], how active
funds that trade infrequently make a market more eﬃcient [Mizuta 17, Mizuta 19b], investigation of interaction
between leveraged ETF markets and underlying markets
to price formation using artificial market simulations [Yagi16, Yagi 20a, Mizuta 23], eﬀects of arbitrage in ETFs [Torii
15, Mizuta 19a, Shearer 21, Shearer 22], micro-foundationof price variation model using intelligence of artificial market simulation studies [Mizuta 16b], market eﬃciency [Immonen 17, Pruna 16, Tsao 17, El Oubani 21], market impacts [Cui 12, Oesch 14, Bouchaud 18], especially market
impacts of institutional investors [Luo 20], trading volume
and price distortion [Lespagnol 17], financial market bubble
and crush [Yagi 12,Paddrik 12,Torii 15,Schmitt 16,Benhammada 17, Lucas 18, Agliari 18, Shearer 21, Shearer 22, BEK
23, Zhu 23], market liquidities on the network of banks[Sakiyama 16], eﬀects of insider traders [Fuchen 18], immature markets [Krichene 16], interaction between option
markets and underlying markets [Kawakubo 14a,Kawakubo
14b], eﬀects of market makers for P2P market [Kuno 22], effects of market makers and passive funds [Braun-Munzinger16], eﬀects of HFTs [Gsell 09, Wang 13, Kusada 14, Xiong
15,Hanson 16,Mandes 19,Yagi 20b,Gao 22], eﬀects of HFTs
using an order book imbalance strategy [Yagi 23], eﬀects ofarbitrage trading between markets that have diﬀerent latencies [Wah 13,Wah 16,Wellman 17,Duﬃn 18], an information
diﬀusion on investors’ multi-later networks [Biondo 16, Alsulaiman 17,Zhang 17,Biondo 17], role of behavioral heterogeneity [Hessary 17,Masmoudi 21], an investor network andherding [Jiménez Bermúdez 16,Krichene 17,Wang 17], comparing behaviors of actual and simulated HFT traders [Hirano 19, Hirano 21a], optimizing HFT strategy in an artificial market simulation [Maeda 20], competition on analysts’ forecasts [Zhang 20], interaction between trades oflarge funds and those of individual investors [Shi 21], effect of increasing horizontal shareholding with index funds
on competition and market prices [Mizuta 18], information game [Ben Abdelaziz 21], a communication line withrelativistic delay [Lerner 21], impact of arbitrages [Zhou21], order cancellations [Yoshimura 20], spoofing orders[Mizuta 20c, Wang 21], the eﬀect of risk preferences andoptimal rebalancing frequency on performance [Veryzhenko21], information cascades [Benhammada 21], VaR forecasting [Tubbenhauer 21], essentially instability of financial
markets by optimizing investment strategies [Mizuta 22b],
manipulation of benchmark and closing price [Shearer 22],eﬀects of liquidation strategies [Luo 22], many learning

traders interacting [Dicks 23,Lussange 24], eﬀects of switching trade-strategies [Bassi 23], short squeeze [Matei 22], effects of noise traders [Dai 23], market impact of financial literacy [Zhou 23], eﬀects of stop loss orders [Liston 24], eﬀects
of belief [Albers 24],over-the-counter (OTC) market [Vidler24], an investor structure [Zhao 24] and so on. [Kita 16]
reviewed the U-Mart project which is one of Japanese top
artificial market research projects in the 2000s. Recently,
PhalmJ∗1 that is a platform of an artificial market model isalso used. [Hirano 22a, Hirano 23] quantitatively fit parameters of artificial market models using machine learning.
There are studies of AI traders learning in artificial markets such as a execution algorithm AI divides the orders
and automatically places orders little by little [Karpe 20],
AI technical traders [Izumi 09] and an AI portfolio manager [Kuo 21].
[Hirano 22b] proposed a concept called the artificial market data mining platform in which a model designed to evaluate a trading strategy tuned up on data mining. The
model can fairly evaluate strategies without actual data
dependence. Further more, the model can change environment through changing its parameters and this study
showed that diﬀerent environment leads to be diﬀerent difficulty of prediction for returns. So, users can test a trading
strategy in the several environment on this model. Moreover, this study showed that parameters of an artificial market model should satisfy that the trading strategies should
not unrealistically perform and this shows a new way validating parameters of an artificial market model. There aresome studies to discuss for validation of an artificial market
model, e.g., [Faria 22].
Recently, who should be charged with responsibility for
an artificial intelligence performing market manipulation
have been discussed. [Mizuta 20b] constructed an artificial intelligence using a genetic algorithm that learns in
an artificial market simulation, and investigated whether
the artificial intelligence discovers market manipulation
through learning with an artificial market simulation despite a builder of artificial intelligence has no intention ofmarket manipulation. As a result, the artificial intelligence
discovered market manipulation as an optimal investment
strategy. This result suggests necessity of regulation, suchas obligating builders of artificial intelligence to prevent artificial intelligence from performing market manipulation.
[Zare 21] built an artificial market model to detect pricemanipulation. [Li 22] investigated impact of spoofing trades.
[Shearer 23] investigated manipulating a financial benchmark using an artificial market model.
Recently, artificial market models to test new automatedtrades, high frequency trades and market impacts by antrade-execution algorithm have been emerged, especially,[Li 20, Coletta 21, Hirano 21b, Hirano 22c, Kolm 22, Coletta
22,Nagy 23,Coletta 23] introduced a new approach of an artificial market model where they built generators of realistic
stock market order streams that are learning actual data oforders using machine learning models. It is very large meritthat the models can generate realistic order flows without∗1 https://github.com/plham/plhamJ2

assuming any agent strategies and are suitable to test new
automated high speed or high frequency strategies. [Potluru
23] is a great review for synthetic data applications in finance including synthetic and generative trades data using
an artificial market model.
By the way, [Mizuta 22b] showed financial markets are
essentially unstable by optimizing investment strategies.
Even if all other traders are fixed, only one investor will
use backtesting to optimize their strategy, which leads
to the time evolution of market prices becoming unstable. Optimization instability is one level higher than ”nonequilibrium of market prices.” Therefore, the time evolutionof market prices produced by investment strategies havingsuch unstable parameters is highly unlikely to be predicted
and have stable laws written by equations. This nature
makes us suspect that financial markets include the principle of natural uniformity and indicates the diﬃculty ofbuilding an equation model explaining the time evolutionof prices.
Recently, investigation on deep hedging sometimes uses
an artificial market [Kang Gao 23].
Macro-economics should also investigated by agent-basedmodels to discuss for financial and/or fiscal policy by central banks and government. There are many studies trying
such very important and diﬃcult investigation [Ogibayashi
14,Guerini 22,Guilmi 22,Reissl 22,Kopiec 22,Peters 22,Neuner 22,Chen 23,Knicker 23,Glielmo 23,Takashima 24,Bardoscia 24,Pallante 24]. [Noia 24] included bond market to a
macro-economics artificial market. The great review book
is [Gallegati 17, Ogibayashi 22, Farmer 22].
I will review some of those studies on the next section.
The artificial market simulation models simulate macro
processes such as investors and order matching on a computer. Artificial market studies observe macro phenomena
such as price variations as a result of the modeled macro
processes. Artificial market models only modelize the microprocesses and observe macro phenomena, therefore, artificial market models are fully micro-founded models. So, artificial market models have been gaining intelligence micromacro interaction mechanisms such as what micro processes
amplify price variations.
An artificial market can isolate the direct eﬀect of changes
the regulations to price formation, and can treat situations
that have never occurred. However, outputs of artificial
market simulations may not be accurate or credible forecasts in actual markets. It is an important for artificial
market simulations to show possible mechanisms aﬀecting
price formation through many runs and gain new knowledge; conversely, a limitation of artificial market simulations is that their outputs may, but not certainly, occur inactual financial markets.
Therefore, for more detailed discussions, they should
compare the simulation results to those from studies using other methods, e.g. empirical studies, would not showsuch possible mechanisms. Indeed, artificial markets should
replicate macro phenomena existing generally for any asset
and any time. Price variation, which is a kind of macro
phenomena, is not explicitly modeled in artificial markets.

Only micro processes, agents (general investors), and pricedetermination mechanisms (financial exchanges) are explicitly modeled in artificial markets. Macro phenomena are
emerging as the outcome interactions of micro processes.
Therefore, the simulation outputs should replicate generalmacro phenomena at least to show that simulation models
are probable in actual markets.
However, it is not a primary purpose for the artificial
market to replicate specific macro phenomena only for a
specific asset or a specific period. An unnecessary replication of macro phenomena leads to models that are overfitted and too complex. Such models would prevent our understanding and discovering mechanisms aﬀecting the priceformation because of related factors increasing.
Indeed, artificial market models that are too complex
are often criticized because they are very diﬃcult to evaluate [Chen 12]. A too complex model not only would prevent
our understanding mechanisms but also could output arbitrary results by over-fitting too many parameters. Simpler
models harder obtain arbitrary results, and are easier evaluated.
As Weisberg mentioned [Weisberg 12], “Modeling, (is)the indirect study of real-world systems via the construction
and analysis of models.” “Modeling is not always aimed at
purely veridical representation. Rather, they worked hard
to identify the features of these systems that were mostsalient to their investigations.” Therefore, under diﬀerent
phenomena to focus on, good models are diﬀerent. Thus,
a model is good only for the purpose of study and may be
not good for other purposes.
Therefore, previous studies constructed an artificial market models that are as simple as possible and do not intentionally implement agents to cover all the investors who
would exist in actual financial markets.
The next section, I review some of recent artificial market
studies for financial market regulations and/or rules.

2.

Recent Studies for Financial Market
Regulations and/or Rules

2.1

Bubble, Crash, Price Variation Limit andShort Selling Regulation[Mizuta 13b] built an artificial market model, based on
the model of [Chiarella 02], implementing a learning process
to replicate bubbles and investigated a price variation limit
whether preventing bubbles and crush or not. The pricevariation limits are expected to be an especially eﬀective
way to prevent bubbles, so the model should be able toreplicate bubbles.
When they gave a bubble-inducing trigger, which is a
rapid increment of the fundamental value, a bubble occurred in the case with the model implementing the learning
process but did not occur in the case without the process.
They also showed that a hazard rate enables validation ofwhether the models can replicate a bubble process or not.
[Mizuta 15b] built an artificial market model, based on
the model of [Chiarella 02], and compared eﬀects of pricevariation limits, short selling regulations and up-tick rules.

3

In the case without the regulations, the price fell to below a fundamental value when an economic crush occurred.
On the other hand, in the case with the regulations, thisovershooting did not occur. However, the short selling regulation and the up-tick rule caused the trading prices to behigher than the fundamental value.
They also surveyed an adequate limitation price range
and an adequate limitation time span for the price variation limit and found a parameters’ condition of the pricevariation limit to prevent the over-shorts. They also showed
the limitation price range should be bigger than a volatility
calculated by the limitation time span.
[Mizuta 16c] investigated eﬀects of price variation limits and up-tick rules in large price fluctuation turbulencecaused by large erroneous orders, and investigated whether
dark pools stabilize markets or not.
They found that the amount of erroneous orders decided
ranges of price falls. They also found that the limited timespan of price variation limits should be shorter than thetime of erroneous orders existing to prevent large turbulence. For the eﬀects of up-tick rules adopting a trigger
method they found that in the cases with time unlock, effect time of the up-tick rule is not very diﬀerent from thetime of erroneous orders existing, and this prevents large
turbulence. In the case with price unlock, the rules prevent
large turbulence in all cases.
Because we cannot forecast how long an investor would
erroneous order in actual financial markets, it is impliedthat actual stock markets should employ several price variation limits that have diﬀerent limited time spans. Tokyo
Stock Exchange employs two kinds of price variation limits
that adopt diﬀerent time spans: one is daily price limit,
300 minutes and the other is special quote, 3 minutes. It is
implied that Tokyo Stock Exchange should employ anotherprice variation limit having shorter limited time spans than
one minute because HFTs (High Frequency Trading) are
increasing recently.
The results investigating the up-tick rules suggest thatthe price unlock is a better unlock method than time unlock, which the Japan Financial Services Agency adopted
on November 2013. However, more detail discussion would
be future study.

2.2

follow the rule for investment diversification, when the fundamental price of one asset collapsed and its market pricealso collapsed, the other asset market price also fell [Yagi17]. They also found that the possibility that when the fundamental price of one asset collapses and its market pricealso collapses, some asset market prices also fall, whereas
other asset market prices rise for a market in which investors
follow the rule for investment diversification [Nozaki 17].

2.3

Tick Size[Mizuta 13a, Mizuta 22a] investigated competition, in
terms of taking market share of trading volume between
two artificial financial markets that had exactly the same
specifications except tick size and initial trading volumeusing multi-agents simulations.
When the tick size of market A, ∆PA , was larger thanapproximately the standard deviation of tick by tick return,
σt , if the tick size of market B, ∆PB , was enough smaller
than ∆PA , much trading occurred in market B inside ∆PA .
Therefore, market B took market share of the trading volume from market A.
On the other hand, when ∆PA was smaller than approximately σt , even if ∆PB was very small, price fluctuations
cross many widths of ∆PA and enough price formations occurred only in market A. Therefore, market B could rarely
take market share of trading volume from market A.
They also compared these simulation results with empirical data from the Tokyo Stock Exchange. They argued that
this investigation will enable discussion about the adequate
tick sizes markets should adopt.
After [Mizuta 13a] be published, [Nagumo 16, Nagumo
17] built a simple model and introduced general analyticalsolutions explaining moving speed of trading volume sharein competing financial markets due to tick size diﬀerences.
The general analytical solutions showed that share is shiftedfrom a market with a larger tick size to a market with asmaller tick size, and that the size of share-shift is determined by diﬀerence between tick sizes, not ratio between
tick sizes.
[Yang 20] investigated more details than [Mizuta 13a,Mizuta 22a] espesically about market quality(market liquidity).
They investigated the way that minimum tick size aﬀects
market quality based on an artificial market. The simulation results indicated that stepwise and combination systems can promote market quality in certain aspects, compared with a uniform system. A minimal combination system performed the best to improve market quality. These
results implied that a minimal combination system could
be considered a new direction for market policy reform to
improve market quality.

Rule for Investment Diversification

As financial products have grown in complexity and levelof risk compounding in recent years, investors have come tofind it diﬃcult to assess investment risk. Furthermore, companies managing mutual funds are increasingly expected toperform risk control and thus prevent assumption of unforeseen risk by investors. A related revision to the mutual fundlegal system in Japan led to establishing what is known as“the rule for investment diversification” in December 2014,
without a clear discussion of its expected eﬀects on market price formation having taken place. [Yagi 17,Nozaki 17]
used an artificial market to investigate its eﬀects on priceformation in financial markets where investors must follow
the rule at the time of a market crash that was caused by
the collapse of the asset fundamental price. As results, theyfound that, in a two-asset market where investors had to

2.4

Frequent Batch Auctions[Mizuta 16a] implemented a price mechanism that ischangeable between a comparable continuance double auction (CDA, δt = 1) and a frequent batch auction (FBA,
δt > 1) continuously introducing a new parameter, a batch
auction interval δt. And then, they analyzed profits/losses
and risks of market maker strategies (MM) and investigated4whether MM can continue to provide liquidity even on FBA
by using an artificial market model.
Their simulation results showed that δt is larger, execution rates of MM is smaller and this causes to reduce liquidity supply by MM. Furthermore, they suggested that whenδt is larger (FBA), MM cannot avoid both an overnight risk
and a price variation risk intraday. Furthermore, they alsosuggested that when δt > 1 (FBA) it is very diﬃcult that
MM is rewarded for risks and continue to provide liquidity.
Only the case of δt = 1 (CDA) MM is rewarded for risks
and continue to provide liquidity.
These suggestions implies that MM that can provide liquidity on CDA cannot continue to provide liquidity on FBA
and then many MM retire, and finally liquidity will be reduced. This implication is consistent with the argument
by [Otsuka 14, Melton 17].

2.5

derived indicate that whether D > 1/2 or D < 1/2 is intrinsically important to whether markets become eﬃcient orineﬃcient. Therefore, this suggests that the optimal usage
rate of the dark pool for the market eﬃciency is D = 1/2
and that a trading volume amount in dark pools higher
than that in lit markets makes markets ineﬃcient. They
also compared results of the equations with those of simulations and found similar tendencies.
They also derived an equation showing the boundary ofa buy-sell imbalance at which dark pools destroy the pricediscovery function. They also discussed that when the usage rate of dark pools is low, for example D = 20%, theequation suggests that dark pools rarely destroy the pricediscovery function even though a large buy-sell imbalanceoccurs. On the other hand, when the usage rate of darkpools is very high, for example D = 90%, this equation suggests that dark pools very easily destroy the price-discovery
function by a very slight buy-sell imbalance.
A future study is to investigate more details of the optimal usage rate of dark pools for the market eﬃciency.
Our results suggested the optimal usage rate was around
50% − 70%, which is much higher than about 8%, whichis the cap level of dark pools that European regulators are
discussing. However, they could not determine the precise
level of the optimal usage rate of dark pools for the market
eﬃciency.
Another future study is comparing the simulation resultswith empirical data. Indeed, they cannot observe Mie ofreal markets by empirical data because they cannot findfundamental prices in real markets. On the other hand,
they can observe an execution rate, depth of limit orders
and a bid ask spread of each stock in real lit markets fromempirical data. In addition, they can estimate D of eachstock from some statistics. D are diﬀerent from one stock
to another. Therefore they can draw figures from empirical data plotting each stock having diﬀerent D, execution
rates and so on. To compare these figures with simulation
results, they can compare the simulation results with empirical data.
They also observe buy-sell imbalances in real lit markets
from empirical data. They can discuss how much D may
destroy the price-discovery function in real financial markets.

Dark Pool[Mizuta 15c] investigated how a dark pool, in which noorder books are provided, aﬀects financial markets’ eﬃciency and price-discovery function by using the artificial
market model. This is a very important investigation into
financial systemic risk because making a market ineﬃcientand losing the price-discovery function may make the market unstable and increase financial systemic risk. In thisstudy, they additionally implemented a smart order routing(SOR) to treat actual market selection of investors. They
discussed quantitatively how spreading of dark pools beyond our experience could aﬀect the price-discovery function. They also aimed to clarify the mechanism of a darkpool that makes a market eﬃcient or ineﬃcient.
They found that market ineﬃciently (Mie ) was decreased
sharply by raising the share of the trading value amountof the dark pool (D) in D ≲ 70%. On the other hand,in D ≳ 70%, Mie increased significantly. This indicatesthat there is an optimal usage rate of the dark pool for themarket eﬃciency.
The reason Mie decreased in D ≲ 70% is that the execution rates in the lit market are reduced by more market
orders being sent to the dark pool by the SOR than limit
orders increasing D. This leads the depth of limit orders
to become thicker, these thicker limit orders absorb market
orders, and thus the market price is still stable near thefundamental price.
The reason Mie increased significantly in D ≳ 70% is asfollows. When a market price (P t ) becomes much higher
than the fundamental price (Pf ), many waiting buy orders
are stored in the dark pool and averaged estimated returnst(re,j) for all agents are negative, which means that agents
make market sell orders. These market sell orders could
have made P t converge to Pf , but many waiting buy orders stored in the dark pool absorb these market sell orders
and prevent P t converging to Pf . Therefore, P t maintains
a much higher price than Pf , and the lit market is madeineﬃcient. When P t becomes much lower than Pf , the opposite occurs.
They also discussed mechanisms by which a dark poolmakes a market eﬃcient or ineﬃcient by a simple equation model. The equations about an execution rate they

2.6

Increasing Speed of Order Matching Systems on Financial Exchanges[Mizuta 15a, Mizuta 16d] constructed a simple artificial
market model in which the latency was implemented andinvestigated price formations and market eﬃciency for various latencies. They clarify the mechanisms of the direct
eﬀects of latency on financial market eﬃciency and discuss
how much of an increase in speed is needed for market eﬃciency.
If the latency is large, agents cannot quickly change
their estimated prices when the market trend has finished.
Agents then make unnecessary market orders, and suchmarket orders increase the execution rate. They argued
that increasing the execution rate reduces limit orders tonear the market price, widens the bid ask spread, and makes5the market becomes less eﬃcient. This indicates that latency should be suﬃciently smaller than the average orderinterval for a market to be eﬃcient.
The largest contribution of this study was the possiblythat a large latency (too slow of a matching system) would
directly make market price formation ineﬃcient. Therefore,
too slow of a matching system might destabilize a market.
This implication is generally opposite to that in which theincrease in the speed of matching systems might destabilizefinancial markets.
They also analyzed empirical data of the Tokyo Stock Exchange and compared the results with simulation results. It
is possible that the market was chronically ineﬃcient during a large portion of trading time due to the latency before
the introduction of new trading system, “arrowhead”, from2010 in the Tokyo Stock Exchange. On the other hand, themarket is not chronically ineﬃcient due to the latency atleast for a time scale of minutes after the introduction ofarrowhead.
For future work, they will investigate the case of a large
amount of orders for less than one minute after very important news. They did not consider this case for specific andvery short spans in the simulations of this study. They implemented only normal agents replicating general investors;
however, latency was more important, especially for HFTs
whose investment strategies are market maker, arbitrage,
and so on. They should discuss the latencies for diﬀerent
types of agents for future work.

2.7of the impact of circuit breakers, and in particular explain
why ex-post circuit breakers have no eﬀect on volatility andhave a negative impact on the duration of flash crashes. In
contrast, they found that ex-ante circuit breakers are very
eﬀective, as they markedly reduce price volatility and completely remove flash crashes.
Overall, simulation results suggest that regulatory policies can have quite complex eﬀects on markets populated
by normal investors and HFTs. From the viewpoint of policy design, our analysis highlights in particular the importance of understanding the diﬀerent transmission mechanisms through which the eﬀects of regulatory policies unfold. Moreover, it points out the need of taking into account the fundamental dual role played by HFTs. On the
one hand, HFTs can be the source of extreme events like
flash crashes by placing aggressive sell orders and removing
liquidity from the market. On the other hand, it can playa leading role in the recovery from the crash, by quickly
restoring liquidity.

3.

Some Recent Studies for the Natureof Financial Markets

3.1

Detection of Factors Influencing Market
Liquidity[Yagi 19, Yagi 20b] investigated which market factors affect major liquidity indicators, including Volume, Tightness, Resiliency, and Depth, using an artificial market,
which is a type of agent-based simulation system. As aresult, market liquidity based on Volume is completely opposite to market liquidity based on Tightness, Resiliency,or Depth. Moreover, they confirmed the price decline ratefrom the fundamental price and the price convergence periods to the fundamental price as a measure of the convergence speed, which is the original meaning of Resiliency,from the price level, which has been brought about by random price changes. Therefore, the trades of fundamentalists have the eﬀect of shortening the convergence period,i.e., causing market liquidity to increase.

Eﬀects of several Regulations directed towards HFTs

[Leal 16] constructed an agent-based model to analyze
the eﬀectiveness of a set of regulatory policies on market
volatility, and on the occurrence and the duration of flash
crashes. analyzed the impact of policies trading halt facilities (both ex-post and ex-ante designs), minimum restingtimes, order cancellation fees, and transaction taxes. These
policies have been proposed and implemented in many developed countries to prevent flash crashes.
Simulations results showed that, policies slowing down
the order cancellation of HFTs, like the implementation ofminimum resting times or cancellation fees lead to significant improvements in terms of lower market volatility andincidence of flash crashes. Also the introduction of a financial transaction tax, by discouraging HFTs, can improve
market stability, although the eﬀectiveness of such a measure is much lower compared to policies targeting order cancellation, and eﬀects are relevant only for high values of thetax.
At the same time, all these policies are characterized by atrade-oﬀ between market stability (in terms of lower volatility and number of flash crashes) and market resilience (interms of longer recoveries from a crash). This trade-oﬀ
emerges because of the positive role played by HFTs inquickly restoring good liquidity conditions after a crash.
Regulatory policies introduce important distortions in sucha process, thereby contributing to lengthen the duration ofprice-recoveries. The beneficial impact of HFTs on priceresilience also underlies the results concerning the study

3.2

How active funds that trade infrequently
make a market more eﬃcient

Since managers of active funds choose stocks that are expected to raise their prices on the basis of the fundamental
value, many argue that active funds discover the fundamental value and make a market more eﬃcient. However,it has not been clear whether actual active funds make amarket more eﬃcient or not. It has been shown that active
funds that trade infrequently earn more. At first glance,
infrequent trades seem to not impact and change market
prices and this leads to market prices not converging withthe fundamental price. Therefore, it is important to discuss
whether active funds that trade infrequently make a market
more eﬃcient or not, and if so, we should investigate themechanism of how they do so.
[Mizuta 17, Mizuta 19b] built a model of investors who
trade infrequently in an artificial market model, and they
investigated eﬀects of these investors on market prices andwhether they make a market more eﬃcient by using the6model.
The results indicated that such active investors trade frequently in the rare situation that the market becomes unstable and ineﬃcient due to the market price moving awayfrom the fundamental price. These trades, occurring only
at a necessary time, impact the market prices and lead themconverging with the fundamental price. This leads preventing the market from becoming more unstable and less eﬃcient.
Though the trading volume of fundamental investors is
low throughout whole period, the volume increases greatly
only when a market becomes less eﬃcient, and these trades
then make the market eﬃcient. An increasing market
volatility makes the order prices of speculators (technicalinvestors) move further away from the fundamental price,and this leads to amplifying market volatility more excessively.
It is possible that the orders of active investors prevent
this amplification. This also implies that money movingfrom active funds to passive funds leads a market to becomeless eﬃcient.

3.3

There are two future works. One is an empirical study
validating our model. Another one is more detail discussionof our assumptions that are too strong assumptions for real
financial markets.

4.

The ACM International Conference on AI in Finance∗2
had been held from 2020 sponsored by JP Morgan Chase &Co., the conference featured many presentations on artificial
market studies, especially, artificial market models to test
new automated trades, high frequency trades and market
impacts by an trade-execution algorithm.
When buying or selling a large amount of a particular
stock, investors should place only a few orders at a time because placing them all at once would impact market prices
significantly. A trade-execution algorithm divides the orders and automatically places orders a few at a time. A better trade-execution algorithm enables an investor to trade alarge amount with better prices; therefore, the performanceof the algorithm is very important especially for larger investors like as institutional investors.
[Byrd 19] built an artificial market simulation platform,
ABIDES, an Agent-Based Interactive Discrete Event Simulation environment, to test such automated trades. The
platform implemented many and deeply detailed components; for instance, the agent repeated the orders of actual
financial markets and replicated the latency, which is delayof order information between investors and exchanges.
[Karpe 20] build an trade-execution algorithm using AI
that learns in the artificial market on AIBIDES. An artificial market model for investigating a trade-execution algorithm should replicate stylized facts of high-frequency
micro structures like an order book because the performance of trade-execution algorithm would depend on the
structures. [Vyetrenko 20] investigated whether such models could replicate the stylized facts of the micro structure
and indicated many problems.
[Li 20, Coletta 21, Hirano 21b, Hirano 22c, Kolm 22] built
generators of realistic stock market order streams that arelearning actual data of orders. [Coletta 21] investigatedmarket impacts of an trade-execution algorithm using an
artificial market model based on ABIDES including only
two agents the trade-execution algorithm agent and realistic
order streams generator agent that uses generative adversarial networks (GANs), a kind of deep learnings. [Hirano21b] implemented realistic order streams generator agent
only focused on the high-frequency-trader market-making(HFT-MM) strategy. It is possible that fixing strategy willlead to decrease fitting ability on an in-sample but to increase generalization ability on an out-sample.
[Coletta 22] proposed to learn a unique “world” agent
from historical data. It was intended to emulate the overall trader population, without the need of making assumptions about individual market agent strategies. They implemented their world agent simulator models as a Conditional

Interaction between a Leveraged ETF andan Underlying[Yagi 16] built an artificial market model, based on themodel of [Yagi 10], implementing rebalancing trades of aleveraged ETF, and investigated impact of the rebalancing
trades on the price formation of future index (underlying
asset) market. They found that a market impact (MI) pera volatility (V) is very important key parameter, when MI< V the index future market becomes stable, on the other
hand when MI > V the index future market becomes unstable. They also showed the possible mechanism of suchdestabilizing market.
[Yagi 20a] compared diﬀerent strategies of trading of aleveraged ETF for a proposed trading model in a continuous
double auction market using an agent-based simulation, andreport how best to suppress an increase in market volatility.
As a result, it was found that as the minimum number oforders in a rebalancing trade increases, the impact on themarket price formation decreases.

3.4

Micro-Foundation
Model

of

Price

Variation[Mizuta 16b] tried micro-foundation of the ARCH(1)model, which is a kind of financial risk asset price variation model, using intelligence of artificial market simulation
studies. That is they tried to clarify which micro processes
determine each coeﬃcient of the ARCH(1) model. Thenthey obtained,l 2.
σt2 = ρ2 k2 + 2ρ2 k2 rt−1αTesting new automated trades in an
artificial market(1)

The dispersion of investors’ estimated prices(ρ) is larger orthe orders by the buy-sell imbalance taking liquidity(k) islarger, the volatility is larger. The ration of the normal
investors taking liquidity to the normal traders providing
liquidity(l) is higher or the measure of risk aversion of thenormal investors(α) is lower, the magnitude of volatility
clustering is larger.

∗2 https://ai-finance.org/

7

how to do so as an optimal investment strategy in an artificial market simulation in which it automatically learns theimpact of its trades on market prices. However, the results
also indicates the possibility that an AI trader cannot discover how to manipulate a market manipulation when thelearning employs backtesting in which there are no impact
on market prices.
The results suggest the need for regulation, such as obligating AI developers to prevent AIs from performing market manipulation. Another suggestion is that developers
should limit trades performed by AI to avoid impacting
market prices.

Generative Adversarial Network (CGAN), as well as a mixture of parametric distributions, and they compared theirmodels against previous work.
We can say these are a new approach of an artificial market model. Actually, because the model cannot start a simulation without actual order data not only when the model
learns but also when the model simulate on an out sample, the models are not suitable to investigate new rules
and regulations that have never implemented before. And,overtraining and overtraining for financial market data thatis lacking principle of the uniformity of nature are worried.
However, it is very large merit that the models can generaterealistic order flows without assuming any agent strategies
and are suitable to test new automated high speed or highfrequency strategies.

5.

Disclaimer
Note that the opinions contained herein are solely those of theauthors and do not necessarily reflect those of SPARX Asset Management Co., Ltd.

Who responsible when AIs perform
illegal trades

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