BESC 2020
The 7th International Conference on Behavioural and Social Computing
http://besc-conf.org/2020/

How Many Orders does a Spoofer Need?
- Investigation by Agent-Based Model Takanobu Mizuta

SPARX Asset Management Co., Ltd.
Mail: mizutata[at]gmail.com
HP: https://mizutatakanobu.com

Note that the opinions contained herein are solely those of the authors and do notnecessarily reflect those of SPARX Asset Management Co., Ltd.

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

1(1) Introduction(2) Model(3) Simulation Result(4) Summary

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

2

(1) Introduction(2) Model(3) Simulation Result(4) Summary

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

3

Spoofing orders
Most financial markets prohibit unfair trades as they reduce
efficiency and diminish the integrity of the market
Spoofing orders
Spoofers place orders they do not intend to trade in order tomanipulate market prices and profit illegally
Most financial markets prohibit such spoofing orders as unfair trades

However, how many orders a spoofer needs
to place in order to manipulate prices andprofit has yet to be clarified
4

Difficulty of Empirical Study✓ Most financial markets prohibit unfair trades as they reduce efficiency
and diminish the integrity of the market✓ Since many factors affect price formation, an empirical study cannot
isolate the direct effect of spoofing orders on price formation.

Artificial Market Simulation using Agent-Based Model can do
In this study
I modified a prior market model by Mizuta(2013) to show how animbalance of buy and sell orders affects the expected returns of normal
agents (NAs) . I implemented a spoofer agent (SA) in the model.

I investigated how many orders the SA needed to place tomanipulate market prices and profit illegally.

5

An artificial market model = an agent-based model for a financial market

Virtual and Artificial financial Market built on Computers
ModelsIncludeAgents (Artificial Investors)＋
Price Mechanism (Artificial Exchange)
Order

Price
Mechanism(Exchange)

Agent(Investor)

Each Agent determines anorder by some rules,
Price Mechanism gather
agents orders anddetermines Market Price

Determination market priceComplete Computer Simulation needing NO Empirical Data
✓ can discuss on the mechanism between the micro-macro feedback✓ can be conducted to investigate situations that have neveroccurred in actual financial markets✓ can be conducted to isolate the direct effect of Spoofing orders6

(1) Introduction(2) Model(3) Simulation Result(4) Summary

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

7

Stock Exchange (Price Mechanism)

continuous double auction

Shares
Sell
1030

Shares
BuyPrice103
Waiting Orders
102
101
50
100
When buy order come here
130
99
transaction immediately occurs
98
150
When sell order come heretransaction immediately occurs
97
96
70
Multiple buyers and sellers compete to buy and sell stocks in the market, andtransactions can occur at any time whenever an offer to buy and an offer tosell match.
8

Normal Agents (NAs)j: agent number (1,000 agents)
ordering in number ordert: tick time

Expected Return of each NA

Historical Return+ Order Imbalance(Original)
𝐷𝑏 − 𝐷𝑠𝑡𝑡−𝜏𝑗𝑡𝑟ℎ,𝑗 = log 𝑃 /𝑃+ log(1 + 𝑤4,𝑗 𝛿𝑑)
𝐷𝑏 + 𝐷𝑠
Technical(details are showed later)

Pf1 tt  w1, j log t + w2, j rh, j + w3, j j r =P
i wi, j te, jnoise

Fundamental

Parameters for agentswi , j and  j

PfFundamental Price

Random ofUniform Distribution

Pt

Market Price at t

wi , jji=1,3: 0～1
i=2: 0～100～10000

 tj

10000 = constantExpected Price of each NA

Random ofNormalDistribution
Average=0
σ=3%

P = P exp(r )te, jtte, j9Fundamental and Technical Strategies
Fundamental Strategy
Fundamental Price ＞ Market Price -> Expect + return
Fundamental Price < Market Price -> Expect - return
Technical Strategy (Historical Return)
Historical Return ＞ 0 -> Expect + return
Historical Return < 0 -> Expect - return
TechnicalStrategy

FundamentalPriceMarketPrice

Fundamental
Strategy10Order Imbalance
I modified the model, Mizuta 2013, to show how an imbalanceof buy and sell orders affects the expected returns of normal
agents (NAs)

Term of Technical Strategy
𝐷𝑏 − 𝐷𝑠𝑡𝑡−𝜏𝑗𝑡𝑟ℎ,𝑗 = log 𝑃 /𝑃+ log(1 + 𝑤4,𝑗 𝛿𝑑)
𝐷𝑏 + 𝐷𝑠
Historical Return

Order Imbalance (original)

𝑤4,𝑗 : 0~1, 𝛿𝑑 = 0.3%

𝐷𝑏 , 𝐷𝑠 : the number of buy or sell orders within ±0.3 from the mid-priceexpects a positive return, when more waiting buy orders than sell orders
expects a negative return, when more waiting sell orders than buy orders
Many technical traders use the order imbalance as a technical indicator
An empirical study, Chordia 2004, showed that traders will profit whenusing this indicatorhttps://doi.org/10.1016/S0304-405X(03)00175-2

11Spoofer Agent (SA)Buyone shareSell
one share

100000 ticks
Spoofing buyorders (Dp shares)

Buy
one share

100000 ticks
Spoofing sellorders

100000 ticks
Spoofing buyorders

Dp = No. of Spoofing Orders

1. SA buys one share
2. shows Dp shares of spoofing buy orders
3. sells the share
4. shows Dp shares of spoofing sell orders

within 100000 tick timeto raise market prices
within 100000 tick time
to drive down market prices

repeats these actions in all simulation periods

12(1) Introduction(2) Model(3) Simulation Result(4) Summary

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

13

Dp per average depth for various No. of Spoofing orders
100
10
10.1
0.01

100
200
500
1000
2000
5000
10000
20000
50000
1000002000005000001000000/Averaged depth

No. of spoofing orders

1000

No. of spoofing orders

No. of spoofing orders/Averaged depth

Average depth = (𝐷𝑏 +𝐷𝑠 )/2
𝐷𝑏 , 𝐷𝑠 : the number of buy or sell waiting orders within ±0.3 from the mid-price
The averaged depths for any No. of Spoofing orders are almost constant, 5000.
The depth is almost the same as No. of Spoofing orders at 5000,
where is an important boundary for changing market price features.

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1.0%

0.8

0.8%

0.6

0.6%

0.4

0.4%

0.2

0.2%

0.0

0.0%

Volatility

1.0

NA
0
100
200
500
1000
2000
5000
10000
20000
50000
1000002000005000001000000

Imbalance

Order Imbalance and Volatility

No. of spoofing orders
Imbalance

Volatility

More Spoofing Orders leads to increased imbalance and volatility
Increasing the spoofing orders amplifies price fluctuation especially inNo. of Spoofing Orders > Average Depth (Waiting orders by NAs)

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1.2%

2.0%

1.0%

1.5%

0.8%

1.0%

0.6%

0.5%

0.4%

0.0%

0.2%

-0.5%

0.0%

Market inefficiency

2.5%

NA0
100
200
500
1000
2000
5000
10000
20000
50000
1000002000005000001000000

ReturnReturns from the SA’s buy/sell trades and market inefficiency

No. of spoofing orders
Return per buy and sell trades
Market inefficiency

Higher No. of Spoofing Orders leads to increased return and Mie
especially in No. of Spoofing Orders > Avg. Depth

More spoofing orders than waiting orders in the order bookenables the spoofer to profit illegally, amplifies price fluctuation,and reduces the market’s efficiency

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(Illustration)

Waiting Orders
by NA

spoofing orders
by SA
Waiting Orders
by NA

Shares
Sell
1030
300
50
130

Price
103
102
101
100
99
98
97
96

Shares
Buy

15070

Order Imbalance is very negative -> Investors feel bad sentiment -> Sell

More spoofing orders than waiting orders in the order bookenables the spoofer to profit illegally, amplifies price fluctuation,and reduces the market’s efficiency

17

(1) Introduction(2) Model(3) Simulation Result(4) Summary

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

18

Summary✓ In this study I modified a prior market of Mizuta 2013 to show thatthe imbalance of buy and sell orders affects the expected returns ofnormal agents (NAs), and I implemented the spoofer agent (SA) inthe model. I then investigated how many orders the SA needs toplace to manipulate market prices and profit illegally.
✓ The results indicate that showing more spoofing orders than waitingorders in the order book enables the spoofer to earn illegally,
amplifies price fluctuation, and reduces the market’s efficiency.

You can download this presentation material fromhttps://mizutatakanobu.com/2020BESC.pdf

19

Appendix

20

Verification: Stylized Facts
The purpose of simulation is understanding the reasons and mechanism,
not replicating ALL Stylized Facts
The simplicity of the model is very important because unnecessary replication of macro phenomena
leads to models that are overfitted and too complex. Such models prevent understanding anddiscovery of mechanisms affecting price formation because of the increase in related factors.
Many empirical studies, e.g., Sewell 2006 have shown that both stylized facts (fat-tail and volatilityclustering) exist statistically in almost all financial markets.
Conversely, they also have shown that only the fat-tail and volatility-clustering are stable for any asset
and in any period because financial markets are generally unstable.

Fat-tail

1 to 100

kurtosis of price returns is positive

Volatility-clustering

0 to 0.2

square returns have a positive auto-correlation

The magnitudes ofthese values areunstable and vary
greatly depending on
the asset and/orperiod.

For the above reasons, an artificial market model should replicate these values as significantly positive
and within a reasonable range as I mentioned. It is not essential for the model to replicate specificvalues of stylized facts because the values of these facts are unstable in actual financial markets.
21Stylized Facts

The model of Chiarella (2002) is very simple but replicates long-term statistical characteristics observed in actual
financial markets: a fat tail and volatility clustering.
In contrast, Mizuta (2013) replicates high-frequency micro structures, such as execution rates, cancel rates, andone-tick volatility, that cannot be replicated with the model of Chiarella (2002).
The simplicity of the model is very important for this study, because unnecessary replication of macro phenomena
leads to models that are overfitted and too complex. Such models prevent understanding and discovery ofmechanisms affecting price formation because of the increase in related factors.

22Normal Agent(NA)The model of Mizuta (2013) is based on Chiarella (2002).
The model is satisfied with stylized facts (statistical characteristics
observed in actual financial markets).

Expected Return of each NA

TechnicalPf1 tt  w1, j log t + w2, j rh, j + w3, j j r =P
i wi, j te, jFundamental

noise

All NAs use this same equation to obtain an expected return,however, because w is different each agents, expected returns aredifferent each agents. This leads heterogeneous (many order prices
are diversified) although the model is simple.

The simplicity of the model is very important.
Models include too many related factors prevent
understanding and discovery of mechanisms affecting
price formation.

23

Order Price and Buy or Sell
Price

Order Price of each NA

P t o, jSell(one unit)

Random(GaussDistribution)

Expected Price of each NA

P e, j = P exp( r e, j )tttBuy(one unit)

To replicate many waiting limit orders,order price is scattered around expected price
NA places one buy order when order price > expected price
NA places one sell order when order price < expected price24