[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 talk about] Regulations' Effectiveness for Market Turbulenceby Large Erroneous Orders using Multi Agent Simulation1

[This is] Today’s Talk, [table of contents].
[At first, I will describe] Motivation and our artificial market model (Multi-AgentSimulation)[In] Experiment 1, [we will investigate about] Characteristics of Erroneous-OrderTurbulence [and will show that]Market prices declined not only during but also for a while after the period oferroneous orders.
[And,] The amount of erroneous orders decided ranges of price falls.
[In] Experiment 2, [we will investigate about] Effects of Price Variation Limits to
the Turbulence [and will show that][The] Condition to Prevent the Large Turbulence [is], the limit time span should
be shorter than the time of erroneous orders existing.
[Lastly, I will mention] Summary & Implication to market regulations.

2[First, I will describe] Motivation and our artificial market model.

3Motivation.
[In financial markets], large erroneous orders [sometimes] induce large pricefluctuations.
[Such] fluctuations [often cause] financial market turmoil.
For example, Flash Crush, in US, 2010.
[Therefore, there is] a big debate over which price regulations prevent [thisinducing].
[In] this study, [we build] Artificial Market Model (Multi-Agent Simulation) [toinvestigate][Characteristics of Erroneous-Order Turbulence][And, Effects of] Price Regulations
This presentation only shows the case of “Price Variation Limit”
Although the proceeding shows other cases of price regulations.

4Why Artificial Market Model?
Empirical Studies are very difficult to discuss such price regulations [because],
So many factors cause price formation in actual markets that an empirical study
cannot isolate the pure contribution of these regulations to price formation[and because],
It is impossible to conduct experiments for new regulations in real financialmarkets[On the other hand], Artificial Market Model (Multi-Agent Simulation) can do[them].

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[This study's model is Similar to previous my presentation, previous technicalsession.
I think, some people did not attend it. So, I will give similar talk here, again.][We built an artificial market model] on basis of Chiarella et. al. 2009.
●[Pricing mechanism is] Continuous Double Auction. [It is not simple, but, weneed] to implement realistic price variation limit●Agent Model is Simple. [This is] to avoid arbitrary result, “Keep it short andsimple” [principle].
[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, anagent expects a positive return, and vice verse].
・[Third term is] noise.
[Plus, We implemented] Learning Process. [This is] different from Chiarella’s
study and previous my presentation

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[About] Learning Process,Previous Our Study Mizuta et. al., 2013a Last year’s CIFEr (SSCI in Singapore)[showed that]
Even thought without Learning Process→ the model could replicate static characters of price variations.
→ however the model could NOT replicate Dynamic charactersof price variations, such as large fluctuations.

[therefore,] This Study also need Learning Process Because of treating large
price fluctuations

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Details of Learning Process[Agents are] comparing Historical Return [and] each Strategy[’ term,Fundamental strategy term, and Technical strategy term].
[When the strategy’s expected return and Historical Return are] Same Sign,[This means] good performer Strategy.
[The strategy’s] Weight is Up.
[When the strategy’s expected return and Historical Return are] Opposite Sign,[This means] bad performer Strategy.
[The strategy’s] Weight is Down.
[We also added] random learning.
In this way, agents learn better parameters and switch to the investment strategy
that estimates correctly.

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[Next, I show simulation results of] Experiment 1 [about] Characteristics ofErroneous-Order Turbulence9Model of Erroneous Orders[There are] two parameters for the model: pg, density of erroneous orders, tg,
time of erroneous orders existing.
With a probability pg, His order is changed to Market Order Sell.
[Such market sell orders are] immediately done, and induce market price down.
This situation is maintained during tg.

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[This figure shows] a time evolution of market prices with erroneous orders.
[We shade the time rage in which] erroneous orders exist.
Market prices declined not only during but also for a while after the period oferroneous orders.

11[This figure shows] a time evolutions of strategies weights.
During erroneous-Order Existing switching Fundamental strategy to TechnicalStrategy.
Because of increased technical strategy weight, market prices continued todecline, even after the erroneous orders were gone,12

[Next, we Measure] maximum Range of Price Declines and Reaching times tothe minimum price for various tg, pg under sg = tg times pg = const.
Maximum Range of Price Decline [is defined like this, from minimum market priceto initial market price].
Reaching times to the minimum price [is defined like this, from starting erroneousorders to reaching time at minimum market price].

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[This figure shows] maximum ranges of price declines for various tg, pg under sg= tg times pg = const.
[Horizontal axe is] times of erroneous orders existing tg.
[The amount of erroneous orders, s_g on each line is constant.]
Ranges of price declines were almost the same when sg was constant, andwhen, sg, was increasing more, the rages were increasing more.
[Therefore], The amount of erroneous orders, Sg, decided ranges of price falls,[and] sg is a key parameter.

14[This figure shows] reaching times to the minimum under sg = tg times pg =const.
☆ Reaching times to the minimum price increase sufficiency less thanincrementation of tg.
☆ When sg was larger, reaching times were longer

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[Next, I show simulation results of] Experiment 2 [about] Effects of Price
Variation Limits to the Turbulence16[We modeled] the price variation limit [like this].
[There are] two constant parameters.
Tpl is a limit time span, and ⊿Ppl is limit price range.
[We referred] market price [Before tpl],[and any agents] can Not order OutSide Pt-tpl ± ⊿Ppl

[I mean, Any] buy order prices above here, [they are] changed to this price.
[and any] sell order prices under here [they are] changed to this price.

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[This figure shows a time evolution of market prices] with the price variation limit.
[In these parameters], The price variation limit succeeded to prevent the large
turbulences.

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What is parameters’ Condition to Prevent Large Turbulence?
Large Erroneous Orders [have] 2 parameters: tg, pg
Price Variation Limits [have] 2 parameters:ΔPpl, tpl
We want to know
How should we set ΔPpl, tpl to prevent inducing
Large price fluctuation?
We measured Maximum Range of Price Declines
for various parameters, tg, pg, ΔPpl, tpl

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Parameter Searching for 4 parameters is too heavy,[Therefore, we] Reduce Searching Space Dimension 4 → 2[As mentioned in] Experiment 1,
Characteristics of large erroneous orders are similar when Amount of erroneousorders (Sg=tg×pg)= constant.
[Therefore, we] fix Sg.

[As mentioned in] Previous Our Study Mizuta et. al., 2013a,bPrice Variation Limits have the same effectiveness when Limit Price Range(⊿Ppl) / Limit Time Span (tpl) = constant.
[Therefore, we] ⊿Ppl / tpl
Under these conditions,
We measured Maximum Range of Price Declines for various parameters, tg, pg,ΔPpl, tpl

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[This table lists] maximum ranges of price declines for various parameters.
Green Area [satisfy], tpl smaller than tg. [In these regions], Small Price Decline.
Condition to Prevent the Large Turbulence[is the] limit time span should be shorter than [the] time of erroneous ordersexisting.

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[Lastly, I will mention] Summary & Implication to market regulations.

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[We built a simple] artificial market model to investigate effects of price variation
limits in large price fluctuation caused by large erroneous orders.
[In] Experiment 1, [we investigated about] Characteristics of Erroneous-Order
Turbulence [and showed that]Market prices declined not only during but also for a while after the period oferroneous orders.
[And], The amount of erroneous orders decided ranges of price falls.
[In] Experiment 2, [we investigated about] Effects of Price Variation Limits to theTurbulence [and showed that][The] Condition to Prevent the Large Turbulence is, the limit time span should beshorter than the time of erroneous orders existing.

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[Lastly, I will mention] Implication [of this study result] to market regulations
In these days HFT (High Frequency Trading) are growing, very short time andvery dense amount erroneous-orders may happen.
[As I mentioned], price variation limit [should have] smaller limit time span [than]time of erroneous orders existing.

This result implies that Price Variation Limit having very short tpl is needed.
[For Example], Tokyo Stock Exchange: two Price Variation Limits○ “special quote”: tpl = 3 min○ “daily price limits”: tpl = 1 bussiness day (5 hours)[There limit time span may be] Too longer than time scale of HFT, [and they]
Need shorter tpl Price Variation Limit.

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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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We built an artificial market model on basis of Chiarella et. al. [2009].
Chiarella’s model did not include Learning Process, however,We built Learning Process of agents.
And we are comparing between the case with Learning Process and without it.
Our Agent Model is Simple. This is to avoid arbitrary result, “Keep it short andsimple” principle.
We think Artificial Market Models should explain Stylized Facts as Simply as
possible,
Our pricing mechanism is Continuous Double Auction
It is not simple, but, we need to implement realistic price variation limit
Learning process
Here, Learning process means agents are switching strategy, fundamental
strategy or technical strategy.
We will show that, an Overshoot occurred in the case With the learning process,however, overshoot did not occur in the case WithOut the process28

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 apositive return , and vice verse.

Second term is a technical strategy:
When historical return is positive, an agent expects a positive return, and viceverse.
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 lists Traditional stylized facts in each case.
In all cases, both kurtosis and autocorrelation for square returns for all i arepositive.
This means that all cases replicate Traditional stylized facts: fat-tail and volatilityclustering.

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We examined two Cases, Case 1, Fundamental Value is constant,
Case 2, Fundamental value is rapid incremented like this. This is bubble inducing
trigger.
For Each cases, we examined With learning process And WithOut learning
process.
Therefore, we examined four cases in all.

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This Figure shows time evolution of market prices in case 1, Fundamental Valueis constant.
In both cases, With learning process and without learning process. the results arevery similar,
The prices were small fluctuating around Fundamental Value, here, Ten
Thousand35

This Figure shows time evolution of prices in case 2.
Fundamental value was changed at this time, increased to New Fundamental
Value, Fifteen Thousand.
This is the bubble inducing trigger.
Without Learning Process, Black line, Overshooting was not occurred.
On the other hand, with Learning Process, Red line,

the price went far beyond the new fundamental value.
Only with learning process, Overshoot occurred.

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This Table lists Traditional stylized facts in each case.
In all cases, both kurtosis and autocorrelation for square returns for all i arepositive.
This means that all cases replicate Traditional stylized facts: fat-tail and volatilityclustering.

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We propose Hazard Rate as New Stylized fact to verify model replicating
overshootHazard Rate Hi is conditional probability that sequence of positive return ends ati, given that it lasts until i.
For Example i=3, H3 means like this.
1st, positive return, 2nd, positive, 3rd positive,
In this condition, H3 is probability of 4th return become negative.
Empirical Studies showed that, Any cases, Hi for most of i are smaller than 50%
And when including overshoot period, Hi decline rapidly with i,This show that the overshoot returns tend to continue to be positive
And this tendency stronger continuing positive returns longer

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This Table lists New Stylized Facts: Hazard Rate in each case.
In case 2 with learning, hazard rate declined rapidly.
This case can replicate a significant Overshoot like actual markets.
On the other hand, the case without learning, hazard rate dose not declined
rapidly.
The case can not replicate Overshoot.
Case 1, without learning, Hazard rates are upper 50% for all i.
This is Not consistent with empirical study.
On the other hand, Case 1, with learning, Hazard rates for most of i are smaller
than 50%, even when price fluctuations are stable.
This consistent with empirical study.
Therefore, only cases with Learning Process were verified by Hazard Rate,and only Case 2 can replicate overshoot.

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Result Summary Experiment 1 relationship between Learning process andreplicating OvershootThe cases With learning process, both case 1 and case 2, were Consistent with
Empirical study verified by Hazard Rate.
And case 2 can replicate overshoot, bubble and crush
The cases Without Learning Process were Not consistent with Empirical study
Not verified by Hazard Rate.

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