Impact on Financial Markets of Dark Pools,
Large Investor, and HFT
Shin Nishioka1 , Kiyoshi Izumi1 , Wataru Matsumoto2 , Takashi Shimada1 ,Hiroki Sakaji1 , and Hiroyasu Matushima1
1

Graduate School of Engineering, The University of Tokyo,
7-3-1 Hongo, Bunkyo, Tokyo, Japan
2
Nomura Securities Co., Ltd.⋆izumi@sys.t.u-tokyo.ac.jp

Abstract. In this research, we expanded an artificial market model including the lit market, the dark pools, the large investor, and the market
maker (HFT). Using the model, we investigated their influences on themarket eﬃciency and liquidity. We found that dark pools may improvethe market eﬃciency if their usage rate were under some threshold. Especially, It is desirable that the main users of the dark pool are large
investors. A certain kind of HFT such as the market making strategy
may provide the market liquidity if their usage rate were under somethreshold.
Keywords: Artificial Market · Dark pool · Large investor.

1

Introduction

Dark pools, private financial forums for trading securities, are becoming widelyused in finance especially by institutional investors [15]. Dark pools allow investors to trade without showing their orders to anyone else.
One of the main advantages of dark pools is their function to significantly
reduce the market impact of large orders. Large investors have to constantly
struggle with the problem that the market price moves adversely when they buy
or sell large blocks of securities. Such market impacts are considered as trading
costs for large investors. Hiding the information of large orders in dark pools
may decrease market impacts. Moreover, from the viewpoint of a whole market,
dark pools may stabilize financial markets by reducing market impacts[7].
On the other hand, one of the main disadvantages of dark pools is the lack oftransparency of their market information. The lack of transparency could resultin the damage of price discovery function of the lit markets, a public exchangethat provide all order books to investors. That may cause market instability andineﬃciency[4, 17]. Therefore, for example in Europe, regulators are discussing
introducing a volume cap regulation for dark pools, which means that theyshould be subject to limits on what volume of orders can be traded in them[16].
⋆It should be noted that the opinions contained herein are solely those of the authorsand do not necessarily reflect those of Nomura Securities Co., Ltd.

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S. Nishioka et al.

High frequency trading (HFT) is another trend in fiance. HFT is a type ofelectronic program trading that uses computers to transact a large number oforders at high speeds. In 2014, HFT in the United States is expected to accountfor approximately 48.5% of exchange trading volume [1]. Dark pools account for
13.7% of the total trading volume[14]. HFT firms participate in both lit markets
and dark pools.
The eﬀect of interaction between HFT and dark pools on market stability
and eﬃciency is becoming increasingly important issue. Some researchers areconcerned the issue that the heavily use of dark pools by HFT firms causes thedivergence of dark pools from lit markets. Then, the price discovery process canbegin to erode[10]. It is however very diﬃcult to discuss what are caused by
the interaction of HFT and dark pools by using only results of empirical studies
because some situations have never occurred before in real financial markets.
An artificial market, which is a kind of a multi-agent simulation, will help us
to discuss situations that have never occurred before in real financial markets[9,2]. Using artificial market simulations, many studies have investigated eﬀects
of market segmentation and changing regulations[18, 12]. A previous study[13]investigated dark pools using artificial market simulations. However, because
they also use historical real financial stock prices, they have not investigatedsituations that have never occurred before, such as usage rates of dark poolsthat are much higher than those at present.
We built a simple artificial market model on the basis of the model of Mizuta
et al. [11] including one lit market and one dark pool. Using the model, we introduced algorithm agents and investigated whether dark pools stabilize markets
or not by observing market impacts of these agents. We emphasize that theseinvestigations included cases in which usage rates of dark pools are much higher
than those of present financial markets.

2

Artificial market model

The artificial market model of this study is based on Mizuta et al. [11] andChiarella et al. [3]. Chiarella et al. modeled only a lit market and Mizuta et al.
added a dark pool to [3]. Our model added HFT firms and large investors to
Mizuta et al. [11]. Those preceding models succeeded at replicating stylized facts
that are the statistical nature of long-term returns that stably exist in almost
all financial markets. The model of Mizuta et al. succeed at replicating highfrequency micro structures such as the trade rate, cancel rate, one tick volatility,
and so on, which were not replicated by the model of Chiarella et al.
2.1

Markets

Figure 1 shows the overall view of the model of this study. The model treats only
one risk asset and non-risk asset (cash). In the model, there are three markets:
One lit market, which provides all order books to investors, and two dark pools,

Impact on Financial Markets of Dark Pools, Large Investor, and HFT

3

Fig. 1. Framework of Artificial Market

which provide no order books. One dark pool accepts orders from HFT firms,
but the other dark pool does not accept.
This model consists of three types of agents: 100 stylized traders (normal
traders), one large investor, and one HFT agent. In each time step t, one stylized
trader j is randomly selected (Fig. 2). This stylized trader places an order tobuy or sell the risk asset: For each time, each agent j determines its bid or ask
limit price Po,j (t). Stylized traders always order only one share and can short-sell
freely. The quantity of holding positions is not limited, so agents can take any
shares for both long and short positions to infinity. After the stylized trader’sorder, the larger investor and HFT agent place their orders with their respective
probabilities. This cycle is repeated. Note that time t passes even if no deals aredone.
Lit market The lit market adopts a continuous double auction to determine
a market price of the risk asset. A continuous double auction is an auction
mechanism where multiple buyers and sellers compete to buy and sell somefinancial assets in the market, and where transactions can occur at any time
whenever an oﬀer to buy and an oﬀer to sell match [5, 6]. In the lit market,
transactions are made by matching against relative orders according to priceand time priority principle (Fig. 3).
All agents can acquire the information of the lit market: Transaction pricesof the lit market Plit (t); best bid prices Pbb (t); best ask prices Pba (t); mid prices
Pmid (t) = (Pbb (t) + Pba (t))/2. The minimum unit, a tick size, of the lit market
price Plit (t)’s change is δP = 0.1. The buy order price is rounded oﬀ to thenearest fraction, and the sell order price is rounded up to the nearest fraction.
When an agent orders to buy (sell), if there is a lower price sell order (a higher
price buy order) than the agent’s order, dealing is immediately done, we call thisa market order. If there is not, the agent’s order remains in the order book, wecall this a limit order. The remaining order is canceled tc after the order time.

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S. Nishioka et al.

Fig. 2. Order processing

Dark pools Contrary to the lit market, agents can not get the information suchas transaction prices and order prices in the dark pools. There are many ways todetermine trade prices in dark pools. In the model, the dark pool adopts a mid
price of the lit market Pmid (t), an average price of the best bit and oﬀer in the lit
market, as its trade price (Fig. 3). This method is adopted by many dark pools inreal financial markets [2]. Agents do not specify an order price in the dark pool.
When the agent orders one unit buy (sell) order, trading is done immediately ifthere are opposite sell (buy) orders. If there are no opposite orders, the orderremains and waits for opposite orders to come. In the dark pool, therefore, only
either buy or sell orders remain. The same as in a lit market, the remaining orderis canceled tc after the order time.
2.2

AgentsAn agent of an artificial market is a virtual trader that places its buying or
selling orders to financial markets in the model. There are 3 types of agents in
our model: 100 stylized traders (normal traders), one large investor, and one
HFT agent.
Stylized trader Stylized traders (normal agents) in the model are the sameas agents in the model of Mizuta et al.[11]. Stylized traders need to replicate
characteristics of price formations in real financial markets, stylized facts, andmarket micro structures.
A stylized trader j determines an order price Po,j (t) and buys or sells by thefollowing process. It uses a combination of fundamental value and technical rules
to form expectations on a risk asset returns re,j (t).

Impact on Financial Markets of Dark Pools, Large Investor, and HFT

5

Fig. 3. Lit Market and Dark Poolre,j (t) =1
w1,j + w2,j + w3,j(
w1,j log)
Pf (t)+ w2,j rh,j (t) + w3,j ϵj (t) ,Plit (t)(1)

where wi,j is a weight of term i of the agent j and is determined by randomvariables uniformly distributed in the interval (0, wi,max ) at the start of thesimulation independently for each agent. Pf (t) is a fundamental value that isconstant. Plit (t) is a lit market price of the risk asset at time t. When thedealing is not done at t, Plit (t) remains at the last market price Plit (t − 1), andat t = 1, Plit (t) = Pf (t). ϵj (t) is a noise determined by random variables ofnormal distribution with an average 0 and a variance σ. rh,j is a historical pricereturn inside an agent’s time interval τj , and rh,j = log (Plit (t)/Plit (t − τj )). τj isdetermined by random variables uniformly distributed in the interval [τmin , τmax ]at the start of the simulation independently for each agent. The first term of Eq.
1 represents a fundamental strategy: an agent expects a positive return whenthe market price is lower than the fundamental value, and vice verse. The second
term of Eq. 1 represents a technical strategy: an agent expects a positive return
when the historical market return is positive, and vice verse. After the expected
log return re,j (t) has been determined by the equation 1, an expected pricePo,j (t) is determined as follows.
Po,j (t) = Plit (t) · exp (re,j (t))(2)

We modeled an order price by random variables of normal distributed in an
average Po,j (t), a standard deviation Pσ , where Pσ is a constant. A minimum
unit of a price change (tick size) is δP , we round oﬀ a fraction of less than δP .

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S. Nishioka et al.

Buy or sell is determined by a magnitude relationship between the expect pricePe,j (t) and the order price Po,j (t) , that is,When Pe,j (t) > Po,j (t), the agent orders to buy one share.
When Pe,j (t) < Po,j (t), the agent orders to sell one share.
The stylized traders order in the lit market with a probability 1 − ds , in thedark pool with HFT with a probability 0.5ds , and in the dark pool without HFT
with a probability 0.5ds . An order of a stylized trader is canceled if the order is
not executed within the tst
c steps.
Large investor A large investor determine similarly its order price and direction to buy or sell as a stylized trader. However, it diﬀers from the stylized
trader in the way of ordering: Slicing of large orders. After the expectation, thelarge investor start to place orders in µ units with a possibility p and continues
to place µ units’ orders in k time steps. The order prices, the direction (buy orsell), and the selected market do not change in those k steps. The order volumeof the large investor is µ × k times larger than that of the stylized trader. In thisstudy, the parameters are set as (p, µ, k) = (0.05, 5, 5). The large investor orders
in the lit market with a probability 1 − dL , in the dark pool with HFT with aprobability 0.5dL , and in the dark pool without HFT with a probability 0.5dL .
HFT agent (market maker, MM) In this model, we introduced a market
maker (MM)[8], an agent with a market making strategy that is one of major
trading strategies of HFT. HFT, although not strictly defined at present, hasroughly the following characteristics. It is a trading strategy that aims for small
profits by placing orders automatically by a computer program to utilize theprice diﬀerence in a very short time such as milliseconds and microseconds.
There are some kinds of the trading strategy of HFT, and a market-making
strategy occupies a large percentage of them. A market-making strategy places
both buying and selling orders near a middle price by high frequency. Although
it can provide the liquidity of trading, it may distort price formation.
MM can place its order just after each stylized trader placed its order in every
time steps. That is, MM has much higher speed of ordering than the stylized
trader. The trading strategy of MM consists of the following steps. Firstly if there
is MM’s own order in the markets, MM cancels them. Secondly, MM places one
unit of buying order at a lower price Pbuy,M M (t) and one unit of selling order at
a higher price Psell,M M (t) simultaneously (Fig. 4).
(Pf air,M M (t) ≥ Pbb (t) + 0.5Pf θ) Pba (t)Pbuy,M M (t) = Pf air,M M (t) − 0.5Pf θ (others)
Pbb (t) − Pf θ
(Pf air,M M (t) ≤ Pba (t) − 0.5Pf θ)(Pf air,M M (t) ≥ Pbb (t) + 0.5Pf θ) Pba (t) + Pf θ
Psell,M M (t) = Pf air,M M (t) + 0.5Pf θ (others)
Pbb (t)(Pf air,M M (t) ≤ Pba (t) − 0.5Pf θ)

(3)

(4)

Impact on Financial Markets of Dark Pools, Large Investor, and HFT

7

Fig. 4. Order price of MM

Pf air,M M (t) is a fair price, a price level where MM can agree to buy or sell theasset. It is decided by the position size of MM’s asset s(t) and the mid price ofthe lit market Pmid (t). θ is a spread rate (the ratio of diﬀerence between bid andask prices in comparison to the fundamental price Pf ).
Pf air,M M (t) = (1 − wM M · s(t)3 )Pmid (t)(5)

The equations 3-4 means the position control of MM. That is, MM is willing tosell (buy) at a lower selling price Psell,M M (t) (higher buying price Pbuy,M M (t))
when it has larger positive (negative) position s(t) respectively. In this study,
the value of wM M is set to 2.0 × 10−6 .
MM usually uses the lit market for its orders. It however uses the HFTaccepted dark pool when the following two conditions are satisfied:
1. The selling price Psell,M M (t) (buying price Pbuy,M M (t)) reaches the minimum price Pbb (t) (the maximum price Pba (t)) because of its large positive(negative) position respectively.
2. There are orders on the opposite side and MM’s order can be transacted in
the dark pool.

3

Simulation results

Using our model, we examined the influence on the market of the interaction
among the dark pools, the large investor, and HFT.
3.1

Market eﬃciency and liquidity

We used the market ineﬃciency and liquidity as the indicators to measure theinfluence on the market. The market ineﬃciency Mie is calculated based on the

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S. Nishioka et al.

diﬀerence between the fundamental price Pf (t) and the lit market price Plit (t)[11]:
t +T −1
1 s ∑ |Plit (t) − Pf (t)|
Mie =
,
(6)
T t=t
Pf (t)swhere ts is the time step when the analysis period starts after the preparation
period of simulation. T is the duration of the analysis period. In this study,
ts = 500, T = 10, 000. If the divergence of Plit (t) from Pf (t) is larger, the market
is more ineﬃcient.
The liquidity Lm of market m={lit, dark pool w/HFT, dark pool wo/HFT}
is defined based on the transaction rate:
ntrans,m,(7)
Lm =norder,mwhere ntrans,m is a number of all transactions and norder,m is a number of allorders in market m during t = (ts , ts + T − 1).
3.2

Parameter setting

In this study, values of the parameters are set as tables 1-4. These values were
determined with reference to [11]. Under these parameter values, our model
could replicate both long-term statistical characteristics (the fat-tail of return
distribution and volatility clustering) and short-term market micro structures(transaction rates and cancel rates) of real financial markets.
Table 1. Parameters of markets
Start of analysis periodts =500
Duration of analysis periods T = 10,000
Tick sizeδP =1Fundamental pricePf = 10,000

Table 2. Parameters of stylized trader
Number of stylized tradersn=
100
Maximum weight of fundamental term w1,max =1.0
Maximum weight of chartist term
w2,max =0.1
Maximum weight of noise term
w3,max =1.0
Minimum time interval of chart analysis
τmin =
100
Maximum time interval of chart analysis τmax =200
Standard deviation of noise termσϵ = 0.001
Standard deviation of expected price
Pσ = [0, 0.1]

Impact on Financial Markets of Dark Pools, Large Investor, and HFT

9Table 3. Parameters of large investor
Number of large investor
nlarge =1
Maximum weight of fundamental term w1,max =1.0
Maximum weight of chartist term
w2,max =0.1
Maximum weight of noise term
w3,max =1.0
Time interval of chart analysisτj =150Standard deviation of noise termσϵ = 0.001
Standard deviation of expected price
Pσ = [0, 0.1]
Probability of slicing startp=
0.05
Order size of each orderµ=5
Number of slicingk=
5
Table 4. Parameters of market maker
Number of market makernM M =
1
Spread rateθ=
0.001
Coeﬃcient of position control wM M = 0.000002
Initial positions(0) =
0
Duration of holding orders
tC =
1

3.3

Market eﬃciency results

First, we examined the influence on the market eﬃciency of the dark pool without
HFT. Figure 5 shows the relationship between the market ineﬃciency Mie , theprobability of dark pool orders by the stylized traders dS , and the probabilityof dark pool orders by the large investor dL . The more the stylized traders use
the dark pool (the larger dS ), the less eﬃcient the market is (the larger Mie ).
On the contrary, the more the large investor uses the dark pool (the larger dL ),the more eﬃcient the market is (the smaller Mie ), as Figure 6 shows. Next, we
also examined the change of market eﬃciency with HFT. The market eﬃciency
with HFT is larger than that without HFT.
We considered the mechanism of those two results is as follows:
1. When too many stylized traders use the dark pool (ds is too large), the number and volume of orders in the lit market become too small. Then the pricechanges caused by one order become large and the lit market becomes unstable. That is, the market price Plit (t) tends to derive from the fundamental
price Pf (t) and the market ineﬃciency Mie becomes larger.
2. When the large investor uses the lit market, its large order at a certain
price disturbs the free price movement and sticks the market price Plit (t)away from the fundamental price Pf (t). Thus, the large investor uses thedark pool (dL is larger), the market price can return to the fundamental
price level more easily and the market becomes more eﬃcient (Mie becomes
smaller).
3. When HFT exists in a lit market, there are both selling and buying orders around the mid price constantly. Those orders block the market price’s
deviation from the fundamental price.

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S. Nishioka et al.

Fig. 5. Market ineﬃciency and the probability of dark pool orders by the stylized
traders dS

3.4

Market liquidity results

In this study, HFT trader is the market maker (MM). MM provides many orders
to the markets and makes it easier to match orders. Thus, the liquidity (transaction rate) of the dark pool with HFT Ldark pool w/HF T tends to be larger thanthe liquidity of the dark pool without HFT Ldark pool wo/HF T . We examined thechange of the diﬀerence between those liquidity ∆L when the percentage of using
the dark pools by the stylized traders dS changed.
∆L = Ldark pool w/HF T − Ldark pool wo/HF T(8)

Figure 7 shows the relationship between ∆L and dS . The more stylized
traders use the dark pools, the smaller the diﬀerence becomes. That is, thestylized trader’s use of the dark pools reduced MM’s contribution to the market
liquidity.
We also examined the percentages of MM’s use of the dark pool in changing the percentages of the stylized traders’ use of the dark pools dS . The resultsshows that the more the stylized traders use the dark pools, the less MM uses thedark pool. The decrease of MM’s use of the dark pool reduces the liquidity advantage of the HFT-accepted dark pool in comparison with the HFT-prohibited
dark pool.
The mechanism of those results is considered as follows. MM usually uses
the lit market. It however uses the HFT accepted dark pool when it has alarge positive or negative amount of assets and there are orders on the opposite

Impact on Financial Markets of Dark Pools, Large Investor, and HFT

11

Fig. 6. Market ineﬃciency and the probability of dark pool orders by the large investordLside in the dark pool. The simulation data shows that the rate at which thefirst condition (the large amount of assets) was satisfied was almost constantat every utilization rate of the stylized traders dS . On the contrary, the rate at
which the second condition (the existence of opposite orders in the dark pool) is
satisfied decreases as dS increases. When the stylized traders uses the dark pools
frequently (dS is larger), the orderbooks of the dark pools become similar to theorderbook of the lit market. Thus, the unbalance of orders and the absence of
opposite orders tend to appear both in the lit market and the dark pools. Thatis, the second condition is not satisfied more frequently.

4

Conclusions

In this research, we expanded an artificial market model on the bases of themodel of [11, 8] including the lit market, the dark pools, the large investor, andthe market maker (HFT). Using the model, we investigated their influences on
the market eﬃciency and liquidity.
We found that too much usage of the dark pool by the stylized traders (normal traders) would lead to the ineﬃciency of the market (the large deviationfrom the fundamental price). This result is similar to the preceding study’s results[11]. On the contrary, the large investor’s usage of the dark pool made themarket more eﬃcient. The market maker (HFT) improved the market liquidity(the transaction rate of orders). However, the increasing usage of the dark pool

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S. Nishioka et al.

Fig. 7. Diﬀerence of liquidity and the probability of dark pool orders by the stylized
traders dS

by the stylized traders reduced the improvement rate of the market liquidity by
HFT.
These results suggested that dark pools may improve the market eﬃciency
if their usage rate were under some threshold. Especially, It is desirable that themain users of the dark pool are large investors. A certain kind of HFT such as
the market making strategy may provide the market liquidity if their usage rate
were under some threshold.

Acknowledgments
This research was supported by KAKENHI (no. 15H02745) and MEXT via
Exploratory Challenges on Post-K computer (Study on multilayered multiscale
space-time simulations for social and economic phenomena).

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