5-8 November 2023
2023 IEEE Symposium on Computational Intelligencefor Financial Engineering and Economics (IEEE CIFEr)
https://attend.ieee.org/ssci-2023/

Comparing effects of price limit and circuit breakerin stock exchanges by an agent-based model
Takanobu Mizuta SPARX Asset Management Co. Ltd.
mizutata[at]gmail.com https://mizutatakanobu.com

Isao Yagi

Kogakuin University

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/2023CIFEr.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/2023CIFEr.pdf

3Price Limit v.s. Circuit Breaker
The prevention of rapidly and steeply falling market prices is very very
important to avoid financial crisis. So, some stock exchanges implement,,,

Price Limit
refuses orders that are priced significantly awayfrom the current market price
Stock exchanges in Japan, South Korea, China, and other Asian
countries tend to implement

Circuit Breakerhalts placing orders for a while when the market
prices are largely changedin the USA and Europe tend to implement

It is a big question which regulation best prevents
rapid and large variations in pricehttps://mizutatakanobu.com/2023CIFEr.pdf

4Difficulty of Empirical Study

Empirical studies cannot be conducted to isolate the direct
effect of implementing a trading regulation due to the many
diverse factors affecting price formation in actual markets.

Artificial Market Model

canagent-based model for a financial market

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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 gatheragents orders anddetermines Market Price

Determination market priceComplete Computer Simulation needing NO Empirical Data
✓ can isolate the direct effect of implementing a trading regulation✓ can be conducted to investigate situations that have neveroccurred in actual financial markets✓ can effectively handling micro-macro feedback loops
6[Mizuta 2016]
investigated the price limit and showed that the some conditions(of parameters) prevent large price variations
In [Mizuta 2016] model, the time passes only when an order is placed.

But the model cannot treat “time passing,”: when a circuit breaker is active,
time simply passes without orders being placed,the model needs to be improved before the price limit and circuit
breaker can be compared under an equal condition
So, in this study[Mizuta 2016]

Compares the price limit andcircuit breaker under an equalcondition+

Stop loss behavior
Each agent estimates a fair price and then re-estimates it
when market prices fall significantly below that price. Theagents need a long time for the re-estimation, so theyplace stop-loss orders during the re-estimation,

which enables the model to let time passwithout placing orders7(1) Introduction(2) Our Model(3) Simulation Results(4) Conclusion

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8

Continuous Double Auction

Waiting Orders

Shares
Sell
1030
50
130

When sell order come heretransaction immediately occurs

Price
103
102
101
100
99
98
97
96

Shares
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AgentsThis term is needed To
replicate stylized facts

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

Expected Returnof each agent

Technical𝑡−1
𝑃1𝑃𝑓𝑡𝑟𝑒,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 𝑡
𝑃 𝑒,𝑗 = 𝑃𝑡 exp( 𝑟 𝑡 𝑒,𝑗 )of each agent

10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
Strategy11

Erroneous orders
Erroneous orders period
30000-60000

Dropping
depthtime
Within the period, with a constant probability 15% eachorder of the agents is changed to sell with very low price

Increasing such erroneous sell orders is what makes market prices fall
12

Stop-loss orders
Stop-loss order probability
35％

Each agent estimates a fair price and then re-estimates
it when market prices fall significantly below that price.
The agents need a long time for the re-estimation, so
they place stop-loss orders during the re-estimation,

which enables the model to let time passwithout placing orders

Stop-loss orders
period10000-100000
Time

Each agent starts to place stop-loss orders when a market pricedropped to about 7000-9000. Within the stop-loss period with aprobability 35%(initial) to 0%, gradually reduced, each order of anagent is changed to sell
Erroneous orders cause prices to fall and Stop-loss orders make prices
to continue falling after end of erroneous orders

13

Price limit & Circuit breaker
Price limit

𝑃𝑡−𝑡𝑟

Upper
buy orders

Circuit breaker
𝑃𝑡−𝑡𝑟 + 𝑃𝑟𝑃𝑟𝑃𝑟
Under
sell orders

𝑃𝑡−𝑡𝑟 + 𝑃𝑟
𝑃𝑡−𝑡𝑟

tr: Limit time range

𝑃𝑡−𝑡𝑟 − 𝑃𝑟𝑃𝑟𝑃𝑟

𝑃𝑡−𝑡𝑟 − 𝑃𝑟𝑡𝑟
Pr: Price limit range
Halt placing orders and cancel for a while

Price limit or Circuit braker stars when 𝑃𝑡 reaches 𝑃𝑡−𝑡𝑟 − 𝑃𝑟 (lower limit).
Price limit: any order prices under the lower limit changed to the lower limit
Circuit breaker: placing or cancelling orders are stopped during tr
Price limit 2: cancel sell orders under the lower limit (unrealistic but to understand)For various tr and Pr, we compare effects of Price limit with Circuit breaker14

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

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15

An example of the time evolution of market prices with tr=10000, Pr=100
10500

Market price

10000

9500
9000
8500

8000

Erroneous orders period

0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1000001100001200001300001400007500

no regulationTime
price limit

circuit breakerNo regulations: market prices fell sharply and continued after erroneous orders stopped
With regulations: not significantly fall, an overshoot did not occur
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Averages of falling depth for various tr, Pr

102050
100
200
500
1000

Limit time range (tr)1000 2000 5000 10000 20000
298
157
73
45
33577
302
134
79
521227 721
313
167
110
2000 1296 612315
2092194 2111 1140
615
408
2054 2054 2053 1419
906
2054 2054 2054 2054 1433

Circuit breaker
Price limit range(Pr)

Price limit range(Pr)

Price Limit

10
2050
100
200
500
1000

Limit time range (tr)1000 2000 5000 10000 20000
152103
57
34
22297
207
107
58
43
702
487
266
163
105
1222 869
520
315
208
1954 1522 821614
407
2054 2054 2038 1061
503
2054 2054 2054 2054 1006

[Mizuta 2016] showed the condition that price limit prevent large fallsPr / tr < falling speed of market prices
Yellow shading indicates this is not satisfied (cannot prevent falls)
So, we should see only the non-shading areatr≧10000 : almost the same effectiveness to prevent the fallingtr<10000 : the circuit breaker was more effective
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Price limit range(Pr)the differences between price limit - circuit breaker

1020
50100200500
1000Limit time range (tr)1000 2000 5000 10000 20000
146
54
16
121128095
27219525 2344745778 427
9201240 589 319
110015359
403
0000427It is clarified the circuit breaker was more effective when tr<10000

18

An example of the time evolution of market prices with tr=2000, Pr=20
10100

Market price

10000

9900
9800
9700
9600

price limit version twoprice limit

140000130000120000110000Time100000

90000

80000

70000

60000

50000

40000

30000

20000

10000

0

9500

circuit breaker

Price limit version two were almost the same as circuit breaker19Price limit range(Pr)the differences between price limit 2 - circuit breaker

10
20
50
100
200
500
1000

1000
-856
212
418
69
00Limit time range (tr)2000 5000 10000 20000-17-13-5-13-4
2-3
83
16-14-6247
38-17-10413
231-23-100
15318
392
000417

Price limit 2 were almost the same as circuit breaker

20Mechanism of price limit is less effective when tr<10000

Sellorders

𝑃𝑡−𝑡𝑟 − 𝑃𝑟
Buyorders

The threshold, tr=10000, is exactly the same as the cancel period, tc
𝑃𝑡−𝑡𝑟 − 𝑃𝑟 is changed before the accumulated sell orders are cancelled,which leads to the accumulation of more sell orders of various prices

This accumulation then acts like a wall against buy orders,which prevents rising prices

21

The order books at t=600000 (tr=2000, Pr=20)

Only in the case with the price limit,
many sell orders were accumulated
and they prevented the prices from rising22

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

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

23

Summary✓ In this study, we expanded on Mizuta et al.'s artificial market model[Mizuta 2016] by adding stop loss behavior of the agents and a circuit
breaker and then used it to investigate whether the price limit or thecircuit breaker is more effective to prevent falling market prices.
✓ Our findings showed that the price limit and the circuit breaker arebasically equally effective when the limit price range (Pr) and limit time
range (tr) parameters are the same.
✓ However, the price limit is less effective when tr is smaller than the cancel
time range (tc). In the case with the price limit, many sell orders areaccumulated around the lower limit price. When tr<tc, the lower limit
price is changed before the accumulated sell orders are cancelled, whichleads to the accumulation of more sell orders of various prices. Thisaccumulation then acts like a wall against buy orders, which prevents theprices from rising.
https://mizutatakanobu.com/2023CIFEr.pdf

24Future Works✓ These results pertain only to a limited situation. Specifically, the fact that the circuit
breaker is better than the price limit should be adapted only in the case where thereason for falling prices is erroneous orders and where individual stocks are regulated. Incases where other reasons make the market prices fall (for example, large variations in
the fundamental price) or in cases where individual stocks are not regulated (for example,stock indexes are regulated), the results might be different.
✓ In fact, in real financial markets, market prices frequently fall for reasons other thanerroneous orders, and there are many cases where a stock index is regulated by circuit
breakers while individual stocks are not regulated.
✓ [Wang 2022] indicated that if a stock index is regulated and the index closes to the limit
price of circuit breaker, some traders are in a hurry to sell and their sell orders make theindex fall, which means that sometimes a circuit breaker induces a sharp fall rather thanpreventing it.
✓ In the current work, we did not examine such behavior of traders, so these mentioned
above will be the focus of our future work.
https://mizutatakanobu.com/2023CIFEr.pdf

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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⚫ [Wang 2022] X. Wang, M. H. Kim, and S. Suardi, “Herding and China’s market-wide circuitbreaker,” Journal of Banking and Finance, vol. 141, p.106533, 2022,
https://doi.org/10.1016/j.jbankfin.2022.106533

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26

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 Market
Regulations And/Or Rules, SSRN Working Paper Series
https://ssrn.com/abstract=2710495

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27

Appendix

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

28Order Price and Buy or Sell
Price

Order Price of each NA

P t o, jSell(one unit)
Random(GaussDistribution)

Expected Price of each NAttte, je, jP= P exp(r)Buy(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 price29

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.
30

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.

31