8-13 July 2023
14th IIAI International Congress on Advanced Applied Informatics
Special Session on Applied Informatics in Finance and Economics (AIFE)
https://aife.mhirano.jp/Frequent Batch Auctions investigatedby Agent-Based Model
Takanobu Mizuta SPARX Asset Management Co. Ltd.
mizutata[at]gmail.com https://mizutatakanobu.com

Kiyoshi Izumi

The University of Tokyo

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/2023AIFE.pdf

1(1) Introduction(2) Our Model(3) Simulation Results(4) Conclusion

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2(1) Introduction(2) Our Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttps://mizutatakanobu.com/2023AIFE.pdf

3Increasing Speed of Order Matching Systems on Financial Exchanges is Good or Bad?
Speed up is GOOD
Increasing Speed: causes increasing liquidity by increasing orders of Market
Maker Strategies (MM) who earn profits by providing liquidity.

Otsuka(2014)
On FBA, profit risks of MM increase, then thestrategies can NOT continue to trade, in the result
execution costs increase.

Conflict

Market Maker Strategies (MM)：earn profits from an order spread by placing
both sell and buy waiting orders as long as
prices oscillate between the sell and buyorders. MM is the most popular strategy forhigh-frequency (high-speed) traders.

Speed up is BAD
Increasing Speed: causes socially wasteful arms race for speed and thesecosts are passed to other investors as execution costs.

Budish et al.(2015)
Proposed Frequent Batch Auction (FBA)
which reduces the value of speed advantages

Frequent Batch Auction (FBA)：On FBA, buy and sell orders are grouped together andthen executed at specific time intervals (e.g., every
several minutes) rather than continuously executed one
by one, a continuance double auction (CDA).
These intervals lead to a reduction in the value ofspeed advantages.

4An empirical study can not handle changing from CDA to FBA
Empirical studies cannot be conducted to investigate situations thathave never occurred in actual financial marketsAn “artificial market model”, agent-based models for financial markets,
can handle that have never occurred, FBA
And it can isolate the pure contribution of the changes to the price formation

However, no previous study has investigated whether MM can continue to provide liquidity
even on FBA using artificial market simulations.
Therefore in this study,
We implemented a price mechanism that is continuously changeable between
CDA (δt=1) and FBA (δt >1) by introducing a new parameter, a batch auction
interval δt, based on the prior model of [Mizuta 2016].
We then analyzed the profits/losses and risks of MM and investigated whether it
can continue to provide liquidity even on FBA.
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 effectively handling micro-macro feedback loops
6(1) Introduction(2) Our Model(3) Simulation Results(4) Conclusion

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7

Our Model
Normal Agents (NAs)exist 1000 agents
To replicate the nature of priceformation in actual financial
markets, I introduced the NA tomodel a general investor.

StockExchange

A Market Maker Agent (MM)We then analyzed the profits/losses and risks of MM andinvestigated whether it can continue to provide liquidity
even on FBA by using an artificial market model.

In this study, the artificial market model was built by adding theMarket Maker Agent (MM) to the prior model of [Mizuta 2016](The details of both agents will be showed later)
8

Continuous Double Auction (CDA)

Waiting Orders

SharesSell
103050130

When sell order come heretransaction immediately occurs

Price10310210110099989796Shares
Buy150

When buy order come heretransaction immediately occurs

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.
9Frequent Batch Auction (FBA)

Introduce: Batch Auction Interval (δt)

To be comparable Continuance Double Auction (CDA,δt=1) with Frequent Batch Auction (FBA,δt>1)

CDA
δt=1

New Order ->time t=0

Sell

99t=1Sell Price Buy1101
1100
99
198
1Sell Price
1101
110019998

Buy
Buy
11Immediately
Executed

FBA
δt=4Sell Price Buy
1101
110099198
1Sell Price
1101110019998

Buy
11Not
Executed

100t=2

Sell Price
1101
11009998

Buy
Buy
11Immediately
Executed

Sell Price
11011100
19998

Buy

111NotExecuted

101t=3Sell Price
11011009998

Sell
Buy
11Sell Price
10110099
198

Immediately
Executed

Sell Price
1101
1100
19998

Buy
1111Not
Executed

98
t=4
Buy

1

Immediately
Executed

Sell Price11011100
199
198

Buy1111

Executed at
specific time

Different results: Executed Volume, Remained Orders and Pt
Pt: (Tentative)Market Price: Executed price if orders were executed at the time10Normal Agents (NAs)This term is needed To
replicate stylized facts

1000 agents
j: agent number ordering in number ordert: tick time

Expected Returnof each NA

Technical𝑡−1
𝑃1𝑃𝑓𝑡
𝑟𝑒,𝑗=𝑤1,𝑗 log 𝑡−1 + 𝑤2,𝑗 log 𝑡−𝜏𝑗 + 𝑤3,𝑗 𝜀𝑗𝑡
σ𝑖 𝑤𝑖,𝑗𝑃𝑃

noisewi , j and  jFundamental

Pf Fundamental Price tj

Random ofUniform Distribution

P t Market Price at t

Parameters for agentswi , jji=1,3: 0～1
i=2: 0～100
0～10000

Random ofNormalDistribution
Average=0
σ=3%10000 = constantThis term is needed toprevent the prices goout far away

To keep agents varied
To keep simulation runs stably

Expected Price 𝑡𝑃 𝑒,𝑗 = 𝑃𝑡 exp( 𝑟 𝑡 𝑒,𝑗 )of each NA11

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

Fundamental
Price
MarketPrice

Fundamental
Strategy
12Market Maker Agent (MM)Order both Sell and Buy at once

Sell order

𝑃𝑓𝑎𝑖𝑟 + 𝑃𝑠𝑝𝑟𝑒𝑎𝑑

Sell

Order every time within a batch auction

Price Buy
𝑃𝑓𝑎𝑖𝑟 + 𝑃𝑠𝑝𝑟𝑒𝑎𝑑
10011
1 10010
10009
10008
10007
𝑃𝑓𝑎𝑖𝑟
10006
10005
Fair value
10004
10003
10002 1
𝑃𝑓𝑎𝑖𝑟 − 𝑃𝑠𝑝𝑟𝑒𝑎𝑑
10001
Buy order
10000

Sell

Price Buy
1 10011
1 10010
10009
10008
𝑃𝑓𝑎𝑖𝑟
10007
10006
10005
10004
𝑃𝑓𝑎𝑖𝑟 − 𝑃𝑠𝑝𝑟𝑒𝑎𝑑
10003 110002 110001
10000✓ Order both Sell and Buy at once
𝑃𝑓𝑎𝑖𝑟 Fair value: calculation ways are different
Buy: 𝑃𝑓𝑎𝑖𝑟 − 𝑃𝑠𝑝𝑟𝑒𝑎𝑑from MM types (details are showed later)
Sell: 𝑃𝑓𝑎𝑖𝑟 + 𝑃𝑠𝑝𝑟𝑒𝑎𝑑
𝑃𝑠𝑝𝑟𝑒𝑎𝑑 Spread: Constant✓ Order every time on both FBA and CDA→ Cancel all its orders immediately after a batch auction
On CDA, every time cancel after NA places an order
A whole number of orders Do not depend on δt-> Amount of liquidity supply is constant13

Four kinds of MM✓ Simple MM𝑃𝑓𝑎𝑖𝑟 = 𝑃𝑡

Holding position risk is very high: impracticableControl orderprices not to makeposition too much

✓ Position MM𝑃𝑓𝑎𝑖𝑟 = (1 − 𝑘𝑆 3 )𝑃𝑡

S: Holding Position of MM, k: constantHolding position risk is reduced in intra-day, but remain over night risk: impracticable✓ Position MM3, Position MM4 ［Our Original］

It trade making position Zero Within Last 2,000 time steps in One day(20,000 time steps)
To eliminate over night risk, inventory risk:-> when MM has over night position it’s very risky if there is a big news within over night
Position MM3
Do not order increasing position

To make position
Zero to avoid overnight risk

In the case of negative position,
within last 2,000 time steps

Sell

Price Buy
1 10011
Do not 10010
order↑ 10009 ← Pfair
10008
10007 1Position MM4
Change order price that of opposite side (buy/sell)In the case of negative position,
within last 2,000 time steps

Sell

More aggressively
make position Zero toavoid over night risk

Price Buy
10011 1 ←change order price
10010
here
10009 ← Pfair
10008
10007

14

(1) Introduction(2) Our Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttps://mizutatakanobu.com/2023AIFE.pdf

15

Holding Position of several kinds of MM
Simple MM
Average of ||S||δt

1(CDA)
2
5
1020
50
100
200
500
1000

Whole
Period12,357
17,422
4,409
1,744
548
384
369
174
72
290

Pspread/Pf = 0.03%

Position MM

Position MM3

Position MM4

EndEnd
End
End
Whole
Whole
Whole
PeriodPeriodPeriodPeriodPeriodPeriodPeriodon a dayon a dayon a dayon a day
12,371
17,441
4,414
1,744
548
385
370
174
71
290

3.18
3.10
3.87
4.44
4.84
5.27
5.57
5.91
5.75
5.943.08
3.25
3.95
4.34
4.71
5.14
5.51
6.11
6.06
6.11

2.90
2.79
3.48
4.01
4.52
5.02
5.56
5.92
5.70
5.61

0.00
0.00
0.00
0.02
0.78
2.63
4.26
5.69
5.81
5.80

2.89
2.79
3.48
3.96
4.35
4.63
4.80
4.38
2.32
1.76

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.03
0.06

δt is Larger (FBA), only Position MM4 can make its position ZeroSo, only MM4 is reality
16

Execution Rate of MM for Order Spread (Pspread) and δt
In the case of Position MM4Pspread/Pf
Execution Rate of MM
0.03% 0.10% 0.30% 1.00%
1(CDA) 8.06% 1.53% 0.00% 0.00%
2 6.30% 0.88% 0.00% 0.00%
5 3.93% 0.37% 0.00% 0.00%
10 2.47% 0.14% 0.00% 0.00%
20 1.49% 0.02% 0.00% 0.00%
δt
50 0.77% 0.00% 0.00% 0.00%
100 0.48% 0.00% 0.00% 0.00%
200 0.32% 0.00% 0.00% 0.00%
500 0.21% 0.00% 0.00% 0.00%
1000 0.22% 0.00% 0.00% 0.00%

δt is Larger (FBA), Execution Rate of MM is Smaller
Decrease Liquidity Supply17Final Profit

In the case of Position MM4, Pspread/Pf = 0.03%

Final Profit of MM/Pfδt1(CDA)
2510
20
50
100
200
500
1000

51.98
-29.42-14.90
-4.08
1.51
3.68
2.53
0.93
-0.06
-0.10

Average of ||S||Execution
Execution
End
Whole
Rate of MM
Rate of NA
PeriodPeriodon a day
2.89
0.00
8.1%
39.1%
2.79
0.00
6.3%
39.1%
3.48
0.00
3.9%
37.6%
3.96
0.00
2.5%
36.3%
4.35
0.00
1.5%
34.9%
4.63
0.00
0.8%
33.4%
4.80
0.00
0.5%
32.5%
4.38
0.00
0.3%
31.8%
2.32
0.03
0.2%31.0%
1.76
0.06
0.2%
30.5%

δt is Larger (FBA), MM take few profits or lose money

Market Maker Strategies can NOT continue to trade18

(1) Introduction(2) Our Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttps://mizutatakanobu.com/2023AIFE.pdf

19

Conclusion
We implemented a price mechanism that is changeable between a comparable
continuance double auction (CDA, δt=1) and a frequent batch auction (FBA,δt>1) by continuously introducing a new parameter, a batch auction interval δt,
based on a prior model of [Mizuta 2016].
Our simulation results showed that when δt is larger, the execution rates of
MM are smaller, and this causes the liquidity supplied by MM to be reduced.
Further, when δt is larger (FBA), MM cannot avoid both an overnight risk and a
price variation risk intraday. We also found that when δt >1(FBA), it is very
difficult for MM to be rewarded for risks and to continue providing liquidity. MMis rewarded for risks and continues to provide liquidity only in the case of δt =1(CDA).
These findings imply that while MM provides liquidity on CDA, it cannot
continue to provide liquidity on FBA, which leads to many MMs being retired
and ultimately to liquidity being reduced. This implication is consistent with thefindings of prior research [Otsuka 2014].
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20Reference[Mizuta 2016] Mizuta, T., Kosugi, S., Kusumoto, T., Matsumoto, W., Izumi, K., Yagi, I., andYoshimura, S., “Effects of Price Regulations and Dark Pools on Financial Market Stability: An
Investigation by Multiagent Simulations”, Intelligent Systems in Accounting, Finance andManagement, Vol. 23, No. 1-2, pp. 97-120, 2016, https://doi.org/10.1002/isaf.1374[Otsuka 2014] Otsuka, T., “High frequency trading and the complexity of the U.S. equities market(japanese only),” in JPX Working Paper, no. Special Report. Japan Exchange Group, 2014.
https://www.jpx.co.jp/english/corporate/researchstudy/working-paper/index.html[Budish 2015] Budish E., et al., “The high-frequency trading arms race: Frequent batch auctions
as a market design response,” The Quarterly Journal of Economics, vol. 130, no. 4, pp. 1547–
1621, 2015. https://doi.org/10.1093/qje/qjv027

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21Reference (Reviews of agent-based models for a financial market)
Review of an agent-based model for designing a financial market
Mizuta (2020) An agent-based model for designing a financial market that works well, CIFEr 2020
arXiv https://arxiv.org/abs/1906.06000
Slide: https://mizutatakanobu.com/2021kyushu.pdf
YouTube: https://youtu.be/rmlb72ykmlEMizuta (2022) Artificial Intelligence (AI) for Financial Markets: A Good AI for Designing Better Financial
Markets and a Bad AI for Manipulating Markets https://doi.org/10.1007/978-981-19-0937-5_13
Citing many previous studies
Mizuta (2016) A Brief Review of Recent Artificial Market Simulation Studies for Financial MarketRegulations And/Or Rules, SSRN Working Paper Series
https://ssrn.com/abstract=2710495

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22Appendix

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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

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 100kurtosis of price returns is positive
Volatility-clustering 0 to 0.2
square returns have a positive auto-correlation

The magnitudes ofthese values are
unstable 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.
25

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.

26