# Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Model

- Stylized trading agents
- Non-regulated portfolio trading agents
- Regulated portfolio trading agents

#### 3.1. Markets

#### 3.2. Agents

#### 3.3. Agents: Stylized Trading Agents

- F: Fundamentalist component (Estimation based on the fundamental prices)
- C: Chartist component (Trends)
- N: Noise

- Fundamental factor:$${F}_{t}^{i,s}=\frac{1}{{\tau}_{r}^{i}}ln\left(\right)open="("\; close=")">\frac{{p}_{t}^{s}}{{p}_{t}^{*s}}$$
- Chartist factor:$${C}_{t}^{i,s}=\frac{1}{{\tau}^{i}}\sum _{j=1}^{{\tau}^{i}}ln\left(\right)open="("\; close=")">\frac{{p}_{t-j}^{s}}{{p}_{t-j-1}^{s}}$$
- Noise factor:$${N}_{t}^{i,s}\sim N(0,{\sigma}_{N}^{i}),$$

#### 3.4. Agents: Non-Regulated Portfolio Trading Agents

- Cancel orders which have not been contracted yet.
- Calculate reasonable values of every asset in the same way as stylized trading agents.
- Revise the portfolio with the portfolio optimization algorithm described below.
- On the basis of the revised portfolio, make orders for the difference with those of the current portfolio.

#### 3.5. Agents: Regulated Portfolio Trading Agents

- Calculate CAR based on the current position $\mathbb{x}$ (referred to as $\mathrm{CAR}\left(\mathbb{x}\right)$).
- Calculate R.$$\begin{array}{c}\hfill R=\frac{0.08}{\mathrm{CAR}\left(\mathbb{x}\right)}\end{array}$$
- Calculate the current total share price $\mathrm{Val}\left(\mathbb{x}\right)$ using $\mathbb{x}$ and a reasonable value calculated in the same way as stylized trading agents.
- Calculate the new budget limit B.$$\begin{array}{c}\hfill B=\frac{1}{\frac{R-1}{2}+1}\mathrm{Val}\left(\mathbb{x}\right)\end{array}$$
- Under the budget limit B, re-optimize the portfolio and update $\mathbb{x}$ by Markowitz’s mean-variance approach presented in Section 3.4.
- Check the equation:$$\begin{array}{c}\hfill \mathrm{CAR}\left(\mathbb{x}\right)\ge 0.08.\end{array}$$
- If the portfolio still violates Equation (12), go to step 1 again. If not, $\mathbb{x}$ is the final position, which does not violate the CAR regulation.

#### 3.6. Parameters

- Amount of cash per market that each agent holds
- ${w}_{F}^{i}$: Weight for fundamentalist
- ${w}_{C}^{i}$: Weight for chartist
- ${w}_{N}^{i}$: Weight for noise

- Amount of cash per market that each agent holds $\to 6000$
- ${w}_{F}^{i}$: Weight for fundamentalist → exponential distribution with mean 10.0
- ${w}_{C}^{i}$: Weight for chartist → exponential distribution with mean 1.0
- ${w}_{N}^{i}$: Weight for noise → exponential distribution with mean 10.0

## 4. Experiments

- Pre-running length: 30,000 steps
- Simulation length: 60,000 steps
- Number of trials: 100 times per parameter set

#### 4.1. Experiments for Assessing Effects of Portfolio Trading Agents

- Stylized trading agents: 1000 agents (fixed)
- Non-regulated portfolio trading agents: $0,10,20,\cdots ,100$ agents
- Number of markets (number of assets): $1,2,\cdots ,10$ markets (assets)

#### 4.2. Experiments for Assessing Effects of the CAR Regulation

- Stylized trading agents: 1000 agents (fixed)
- Non-regulated portfolio trading agents: $0,10,20,\cdots ,100$ agents
- Regulated portfolio trading agents: $100,90,80,\cdots ,0$ agents
- Number of markets (number of assets): $1,2,\cdots ,10$ markets (assets)

## 5. Results & Discussion

#### 5.1. Stylized Fact Checks

#### 5.2. Effects of Portfolio Trading Agents

#### 5.3. Effects of CAR Regulation

#### 5.4. Summary of Results and its Discussion

- shocks occur more often.
- big price rises occur less frequently.
- push down market prices in total.
- markets fluctuate more.

#### 5.5. Future Work

## 6. Conclusions

- Adopting portfolio optimization as each agent’s strategy stabilizes markets.
- The existence of a CAR regulation destabilizes markets.
- CAR regulation can cause significant price shocks.
- CAR regulation may suppress price increases.
- CAR regulation pushes down market prices.
- CAR regulation fluctuates market price.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Avellaneda, Marco, and Sasha Stoikov. 2008. High-frequency trading in a limit order book. Quantitative Finance 8: 217–24. [Google Scholar] [CrossRef]
- Basel Committee on Banking Supervision. 2006. International Convergence of Capital Measurement and Capital Standards. Available online: https://www.bis.org/publ/bcbs107.pdf (accessed on 12 February 2018).
- Basel Committee on Banking Supervision. 2017. Basel III: Finalizing Post-Crisis Reforms. Available online: https://www.bis.org/bcbs/publ/d424.pdf (accessed on 28 May 2018).
- Basle Committee on Banking Supervision. 1996a. Amendment to the Capital Accord to Incorporate Market Risks. Available online: https://www.bis.org/publ/bcbs24.pdf (accessed on 9 February 2018).
- Basle Committee on Banking Supervision. 1996b. Supervisory Framework for the Use of “Backtesting” in Conjunction with the Internal Models Approach to Market Risk Capital Requirements. Available online: https://www.bis.org/publ/bcbs22.pdf (accessed on 9 February 2018).
- Battiston, Stefano, J. Doyne Farmer, Andreas Flache, Diego Garlaschelli, Andrew G. Haldane, Hans Heesterbeek, Cars Hommes, Carlo Jaeger, Robert May, and Marten Scheffer. 2016. Complexity theory and financial regulation: Economic policy needs interdisciplinary network analysis and behavioral modeling. Science 351: 818–19. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Benink, Harald, Jón Daníelsson, and Ásgeir Jónsson. 2008. On the Role of Regulatory Banking Capital. Financial Markets, Institutions & Instruments 17: 85–96. [Google Scholar] [CrossRef]
- Chiarella, Carl, and Giulia Iori. 2002. A simulation analysis of the microstructure of double auction markets. Quantitative Finance 2: 346–53. [Google Scholar] [CrossRef]
- Cont, Rama. 2001. Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance 1: 223–36. [Google Scholar] [CrossRef]
- Dacorogna, Michel, Ramazan Gençay, Ulrich Muller, Richard Olsen, and Olivier Pictet. 2001. An Introduction to High-Frequency Finance. Cambridge, MA, USA: Academic Press. [Google Scholar] [CrossRef]
- FFR+. 2008. III. Measurement and Verification of VaR. Available online: http://www.ffr-plus.jp/material/pdf/0006/risk_meter_quantification_03.pdf (accessed on 18 November 2017). (In Japanese).
- Farmer, J. Doyne, and Duncan Foley. 2009. The economy needs agent-based modelling. Nature 460: 685–86. [Google Scholar] [CrossRef] [PubMed]
- Hermsen, Oliver. 2010. Does Basel II destabilize financial markets? An agent-based financial market perspective. The European Physical Journal B 73: 29–40. [Google Scholar] [CrossRef]
- Hochreiter, Sepp, and Jürgen Schmidhuber. 1997. Long Short-Term Memory. Neural Computation 9: 1735–80. [Google Scholar] [CrossRef] [PubMed]
- Japan Exchange Group. 2017. Equities Trading Services|Japan Exchange Group. Available online: https://www.jpx.co.jp/english/systems/equities-trading/ (accessed on 21 June 2019).
- Krizhevsky, Alex, Ilya Sutskever, and Geoffrey Hinton. 2012. ImageNet Classification with Deep Convolutional Neural Networks Advances in Neural Information Processing Systems 25.t pp. 1097–105. Available online: http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networ (accessed on 6 November 2019).
- Lux, Thomas, and Michele Marchesi. 1999. Scaling and criticality in a stochastic multi-agent model of a financial market. Nature 397: 498–500. [Google Scholar] [CrossRef]
- Markowitz, Harry. 1952. Portfolio Selection. The Journal of Finance 7: 77–91. Available online: http://www.jstor.org/stable/pdf/2975974.pdf (accessed on 13 November 2017).
- Miyazaki, Bungo, Kiyoshi Izumi, Fujio Toriumi, and Ryo Takahashi. 2014. Change Detection of Orders in Stock Markets Using a Gaussian Mixture Model. Intelligent Systems in Accounting, Finance and Management 21: 169–91. [Google Scholar] [CrossRef]
- Mizuta, Takanobu, Shintaro Kosugi, Takuya Kusumoto, Wataru Matsumoto, Kiyoshi Izumi, Isao Yagi, and Shinobu Yoshimura. 2016. Effects of Price Regulations and Dark Pools on Financial Market Stability: An Investigation by Multiagent Simulations. Intelligent Systems in Accounting, Finance and Management 23: 97–120. [Google Scholar] [CrossRef]
- Mizuta, Takanobu. 2019. An Agent-based Model for Designing a Financial Market that Works Well. Available online: http://arxiv.org/abs/1906.06000 (accessed on 21 June 2019).
- Moss, Scott, and Bruce Edmonds. 2005. Towards Good Social Science. Journal of Artificial Societies and Social Simulation 8: 13. Available online: http://jasss.soc.surrey.ac.uk/8/4/13.html (accessed on 5 February 2020).
- Nagumo, Shota, Takashi Shimada, Naoki Yoshioka, and Nobuyasu Ito. 2017. The effect of tick size on trading volume share in two competing stock markets. Journal of the Physical Society of Japan 86. [Google Scholar] [CrossRef]
- Nanex. 2010. Nanex—Market Crop Circle of The Day. Available online: http://www.nanex.net/FlashCrash/CCircleDay.html (accessed on 23 June 2019).
- Tashiro, Daigo, and Kiyoshi Izumi. 2017. Estimating stock orders using deep learning and high frequency data. Paper presented at the 31nd Annual Conference of the Japanese Society for Artificial, Nagoya, Aichi, Japan, 23–26 May 2017; p. 2D2–2. (In Japanese). [Google Scholar]
- Tashiro, Daigo, Hiroyasu Matsushima, Kiyoshi Izumi, and Hiroki Sakaji. 2019. Encoding of High-frequency Order Information and Prediction of Short-term Stock Price by Deep Learning. Quantitative Finance, 1–8. [Google Scholar] [CrossRef]
- Torii, Takuma, Kiyoshi Izumi, and Kenta Yamada. 2015. Shock transfer by arbitrage trading: Analysis using multi-asset artificial market. Evolutionary and Institutional Economics Review 12: 395–412. [Google Scholar] [CrossRef]
- Torii, Takuma, Tomio Kamada, Kiyoshi Izumi, and Kenta Yamada. 2017. Platform Design for Large-scale Artificial Market Simulation and Preliminary Evaluation on the K Computer. Artificial Life and Robotics 22: 301–7. [Google Scholar] [CrossRef]
- Torii, Takuma, Kiyoshi Izumi, Tomio Kamada, Hiroto Yonenoh, Daisuke Fujishima, Izuru Matsuura, Masanori Hirano, and Tosiyuki Takahashi. 2019. PlhamJ. Available online: https://github.com/plham/plhamJ (accessed on 19 April 2019).

**Figure 1.**Model outline. The model consists of a number of markets in which three types of agent trade assets.

**Figure 2.**Continuous double auction mechanism for setting the market price. (

**a**) Before inputting a new order. (

**b**) Inputting 80 buy orders at 400.53 (highlighted in yellow). (

**c**) Contracting 50 orders at 400.5 and 30 orders at 400.528 (highlighted in yellow). (

**d**) After contracting.

**Figure 3.**Autocorrelation function (ACF) for logarithm returns. Error bars mean standard deviation for each lag among 500 markets in 100 simulations. The green area shows the 95% confident interval corresponding to each lag.

**Figure 4.**Autocorrelation function (ACF) for 50-step standard deviations of logarithm returns. Error bars mean standard deviation for each lag among 500 markets in 100 simulations. The green area shows the 95% confident interval corresponding to each lag.

**Figure 5.**Frequency distribution of normalized log returns. The blue plot shows the results from simulations. Error bars mean standard deviation for each lag among 500 markets in 100 simulations. The orange plot shows the Gaussian (Normal) distribution.

**Figure 6.**${N}_{DV}$ of experiments assessing the effect of portfolio trading agents. The horizontal axis is the number of non-regulated portfolio trading agents, and the vertical axis in the number of steps in which the market price is below $exp(-0.1)$ times the fundamental price. (Details are explained with Equation (14)). Each series of plots shows results for the corresponding number of markets in the simulation. Error bars show standard deviations.

**Figure 7.**${N}_{DV}$ graph assessing the effect of capital adequacy ratio (CAR) regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the number of steps in which the market price is below $exp(-0.1)$ times the fundamental price. (Details are explained with Equation (14)). Each series of plots shows a simulation series for a certain number of markets. Error bars show standard deviations.

**Figure 8.**${N}_{DV}$ graph assessing the effect of CAR regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the number of steps in which the market price is below $exp(-\mathbf{0}.\mathbf{5})$ times the fundamental price. (Details are explained with Equation (15)). Each series of plots shows a simulation series for a certain number of markets. Error bars show standard deviations. Please note that the vertical axis is logarithmic.

**Figure 9.**Kurtosis of price changes in the experiments for assessing the effect of CAR regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is kurtosis. Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Figure 10.**Mean $DV$ in experiments for assessing the effect of CAR regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the mean of $D{V}_{t}$, which is defined in Equation (14). Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Figure 11.**Steps in which the market prices went up. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the mean number of Steps in which the market prices went up. Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Figure 12.**Steps in which the market prices went down. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the mean number of Steps in which the market prices went down. Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Table 1.**Kurtosis of 5 min interval (Cont 2001).

Data | Kurtosis |
---|---|

S&P 500 | 15.95 |

Dollar/DM | 74 |

Dollar/Swiss | 60 |

Data | Kurtosis |
---|---|

Nikkei 225 | $5.18$ |

TOPIX | $5.65$ |

Compositions in Nikkei225 | $5.84\pm 3.16$ |

Compositions in TOPIX | $9.09\pm 9.84$ |

Less Regulated | More Regulated | |
---|---|---|

Price shocks | Less | More |

Fat tail of lower side (A) | Low | High |

Kurtosis | High | Low |

Fat tail (B) | High | Low |

A+B => Fat tail of upper side | High | Low |

Mean of price | High | Low |

Price up/down | Less frequent | More frequent |

Level of fluctuation | Low | High |

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## Share and Cite

**MDPI and ACS Style**

Hirano, M.; Izumi, K.; Shimada, T.; Matsushima, H.; Sakaji, H.
Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations. *J. Risk Financial Manag.* **2020**, *13*, 75.
https://doi.org/10.3390/jrfm13040075

**AMA Style**

Hirano M, Izumi K, Shimada T, Matsushima H, Sakaji H.
Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations. *Journal of Risk and Financial Management*. 2020; 13(4):75.
https://doi.org/10.3390/jrfm13040075

**Chicago/Turabian Style**

Hirano, Masanori, Kiyoshi Izumi, Takashi Shimada, Hiroyasu Matsushima, and Hiroki Sakaji.
2020. "Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations" *Journal of Risk and Financial Management* 13, no. 4: 75.
https://doi.org/10.3390/jrfm13040075