Do Dark Pools Stabilize Markets and Reduce Market Impacts? -- Investigations using Multi-Agent Simulations --

[Thank you very much. I’m] Takanobu MIZUTA from SPARX Asset
Management.
[I’m also belonging to] The University of Tokyo.
[Today, I’m going to give a presentation under the title of This.]
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[This is] Today’s Talk, [table of contents is like this].
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[First, I will describe] Motivation and our artificial market model, Base Model
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・Dark Pool is a kind of Stock Market (matching venue)
・Dark Pool never provide any order books and quotes to traders
・[Dark Pools are] Becoming widely used, especially by institutional investors
Becoming More widely used Dark Pool leads,
[Some people says], Because very large market impacting orders are
decreased, Market is more Stable.
[This opinion means Dark Pool is] good [for financial market].
[On the other hand], a conflicting opinion,
[Other some people says], Because Dark Pool has Never Price Discovery
Function,
Price-discovery function of Whole Financial Market is decreasing.
[This opinion means Dark Pool is] Bad [for financial market].
[These 2 opinions are big battle.]
In EU, many discussion about Regulations of Dark Pool. MiFID II will restrict Dark
trading to 8% of total EU liquidity.
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Why Artificial Market Model?
[Many] Previous discussions [are such as] Dark Pool is Perfect Justice or Perfect
Evil?
[However, we] should discuss how much usage rate of Dark Pool is best.
Empirical Studies are very difficult to discuss it [because],
So many factors cause price formation in actual markets that an empirical study
cannot isolate the pure contribution of Dark Pool.
[and because],
It is impossible to conduct experiments for Becoming More widely used Dark Pool in
real financial markets
[On the other hand], Artificial Market Model (Multi-Agent Simulation) can do
[them].
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We built an artificial market model on basis of Chiarella et. al. 2009.
[Pricing mechanism] is Continuous Double Auction. [We need to implement
market selection model].
Agent Model is Simple. [This is to avoid arbitrary result].
[We think Artificial Market Models should explain Stylized Facts as Simply as
possible].
[There are] heterogeneous 1000 agents. [All agents calculate] Expected
Return [using this equation],
[And, the] strategy weights [are] different for each agent
・[First term is a] Fundamental [Strategy: When the market price is smaller
than the fundamental price, an agent expects a positive return , and vice
verse].
・[Second term is a] technical [strategy]: [When historical return is positive,
an agent expects a positive return, and vice verse].
・[Third term is] noise.
[We also] replicate micro structures, [this is our] Original.
Trade number, cancel rate, 1 day return 1 day Volatility, and so on.
Replicate Micro Structures is needed because investors select a market using
Smart Order Routing automatically and high speed
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[Next, I talk about] Reducing Volatility by Dark Pool [using the model
combined Base model plus Dark Pool mode]l.
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[At First, I will describe] Model of Dark Pool.
[Left side is an Example of Order Book of Normal Market, providing all order
book to Traders],
[we call “Lit Market” as a opposite term “Dark Pool”].
[In Lit Market], Traders determine Sell or Buy, Price, No. of Shares.
[Right side is an Example of Order Book of Dark Pool providing no
information to Traders],
No traders see this number.
[In dark Pool], Traders determine Only Sell or buy, No. of Share.
Trade Price is determined Mid price between best ask and best bit in the Lit Market.
[In this example], When sell is ordered, Trade Price (100+99)/2=99.5
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Why is Market Volatility reduced by Dark Pool?
[I show a example using these order books].
When market 3 shares sell is ordered,
[In the] Case of Lit Market Only → Price is down to 98
[In the] Case of usage Dark Pool → Trade Price is 99.5
Dark Pool will absorb big market impact orders.
→ Market Volatility will be reduced.
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[Next, I describe] Model of Market Selection.
Normal Agents orders to Dark Pool with probability dn.
[And, to Lit Market at a rate of 1-dn].
dn corresponds traders’ usage rate of Dark Pool
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[This Figure shows] Relationship between Usage Rate of Dark Pool and
Volatility
[Horizontal Axis is] Usage Rate of Dark Pool, dn
Increasing Usage Rate of Dark Pool, Decreasing Volatility, [Red Line].
However, Kurtosis [is also] Increasing [in right side from about 50%]
→ [This means fat tail become more fat], Fatter Tail.
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[Next, I talk about] Market Impact by Algorithm Agents [using the model
combined Base model plus Algorithm Agents].
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Model of Algorithm Agent
[Algorithm agents make only buy orders in a regular cycle].
[We investigate two cases].
Case (a) [They make only] Market Buy Order
Case (b) [They make only] Limit Buy Order at Best Bit. Case (b) is for comparison
to (a) .
Algorithm Agents Exists at a Number of na
They increase Market Price. [This incrementation is corresponding to] Market
Impact
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Definition of Market Impact
We define Market Impact = (Average Trade Price – Fundamental Price) /
Fundamental Price
In the case without Algorithm Agents (Only Normal Agents)
Average Trade Price = Fundamental Price
Therefore Market Impact is zero.
This definition means that Price Difference between Algorithm Agents are Existing
or NOT
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[This figure shows relationship between] Market Impacts and Existing Ratio
of Algorithm Agents
Increasing Algorithm Agents, Increasing Market Impact.
Eave though in Case (b), [limit orders do not change market prices directly],
They “indirectly” impact market price.
Afterward, We fix na/n = 1%
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[Next, I investigate], Dark Pool Reduces Market Impact ?
U[sing the model combined] Base model [plus] Dark Pool [and plus]
Algorithm Agents
[Fixsing Dark pool] Usage Rate 30%
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[We investigated two cases].
[Case] (a), Algorithm Agents order to Dark Pool at a rate of da, da is variable.
Normal Agents order to Dark Pool at a rate of dn, dn = 30% = constant,
general usage rate of Dark Pool
[Case] (b), [for comparison to case (a)]
Algorithm Agents Limit order to Lit Market at a rate of sa, sa is variable.
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[This figure shows Market Impact for various da and sa].
[Horizontal Axis is da or sa]
Dark Pool Reduces Market Impact ?
Yes, Dark Pool Reduces Market Impact !!
Increasing Algorithm Agents use Dark Pool, Market Impacts are reduced, more than
case (b),
limit order to Lit Market. 100% Dark Pool, Market Impact is ZERO.
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[Lastly, I investigate], Bad Effect at too High Usage Rate of Dark Pool
Higher [Dark pool] Usage Rate
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[Analysis Setting is similar to previous analysis].
[but in reverse to previous analysis],
da and sa are fixed, 30%
Dn is variouble.
[We investigated that ]
Increasing dn (general usage rate of Dark Pool),
Does Effect of reducing Market Impact by Dark Pool Change ?
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[This figure shows market Impact, Horizontal Axis is] general usage rate of
Dark Pool, dn.
[Very high usage area, we can not plot data],
[because] Too Great Market Impact [and] unstable simulation runs
At very High Usage rate of Dark Pool, Dark Pool can not reduce Market
Impact.
Traders must use Dark Pool more than many others to decrease Market
Impact.
Traders will less use Lit Market, and decreasing price-discovery function.
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[Lastly, I will mention] Summary.
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・ We built an artiﬁcial market model to investigate how is Dark Pool effects Market
Price formations.
・ Dark Pool is increasingly used, markets become more stable.
・ Using Dark Pool more reduces the market impacts.
・ However, when Usage Rate become Upper “some Threshold”, Dark Pool can not
reduce Market Impact. Traders must use
Dark Pool more than many others to decrease Market Impact. Traders will less use
Lit Market, and decreasing price-discovery function.
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[These opinions are I mentioned at Motivation.]
[This study showed that], BOTH Opinions is Right under/upper the
Threshold.
Becoming More widely used Dark Pool leads,,,
Because very large market impacting orders are decreased, Market is more
Stable?
Yes, under the Threshold
Because Dark Pool has Never Price Discovery Function, Price-discovery
function of Whole Financial Market is decreasing?
Yes, upper the Threshold
[Therefore],
Dark Pool is GOOD, the Usage Rate Under Threshold,
Dark Pool is BAD, the Usage Rate Upper Threshold
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Future Works
[About This EU Regulation],
Our results suggest the threshold might be about 50%,
which is much lager than about 8%.
However, need more investigations about the threshold.
Investigation the most suitable the threshold.
How the threshold depend on the design of the artiﬁcial agents.
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Could you say that again? (もう一度、おっしゃっていただけますか？)
I don’t quite understand your question. (ご質問の趣旨が良く分からないのです
が)
Could you please rephrase your question? (ご質問を分かりやすく言い換えてい
ただけますか)
So, you are asking me about.... (つまり、お尋ねの内容は...ですね)
I totally agree with you. (私も全くあなたと同意見です)
That’s a very challenging question for me to answer. (それは私にとって非常に
答えがいのある質問です)
That’s a question I’m not sure I can answer right now. (そのご質問にすぐお答
えできるかどうか分かりません)
It would require further research. (さらなる研究結果を待ちたい)
You are right on that point. (その点に関してはあなたが正しい)
Our method will not solve the problem. (我々の方法ではその問題は解決できな
い)
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Next, I will describe agent model.
All agents calculate Expected Return using this equation.
First term is a Fundamental Strategy:
When the market price is smaller than the fundamental price, an agent
expects a positive return , and vice verse.
Second term is a technical strategy:
When historical return is positive, an agent expects a positive return, and
vice verse.
Third term is noise,
After the expected return has been determined, an expected price is
determined like this.
And, agents order base on this Expected Price.

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Next, agents determine order price and, buy or sell.
To Stabilize simulation runs for the continuous double mechanism,
Order Prices must be covered widely in Order Book.
We modeled an Order Price, Po, by Random variables of Uniformly
distributed in the interval from Expected Price, Pe, minus constant, Pd, to
Pe plus Pd.
And then,
When Po lager than Pe, the agent orders to sell one unit.
When Po smaller than Pe, the agent orders to buy one unit.

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This table list traditional Stylized Facts and statistics of Micro Structures for
various Tick Size, in the case that there is One Market.
In all cases, both kurtosis and autocorrelation for square returns for all lag
are positive.
This means that all cases replicate Traditional stylized facts: fat-tail and
volatility-clustering.
Trade rate, Cancel rate, 1 tick and 1 day volatility are very similar to those of
real stock markets.
Therefore the model replicate micro structures.
We found that Tick Time 20,000(twenty thousand) in simulation correspond to
1 day in real world.
Therefore we can convert simulation time and real time.
We emphasis that 1 tick volatility at Tick Size is enough small, 0.05% is very
important number.
Whether Tick Size is bigger or smaller than 1 tick volatility, effects aspect of
moving share of trading volume.
I define as Sigma t Var.

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