Table of Links Abstract, Acknowledgements, and Statements and Declarations Abstract, Acknowledgements, and Statements and Declarations Introduction


Background and Related Work
2.1 Agent-based Financial Market simulation
2.2 Flash Crash Episodes


Model Structure and 3.1 Model Set-up
3.2 Common Trader Behaviours
3.3 Fundamental Trader (FT)
3.4 Momentum Trader (MT)
3.5 Noise Trader (NT)
3.6 Market Maker (MM)
3.7 Simulation Dynamics


Model Calibration and Validation and 4.1 Calibration Target: Data and Stylised Facts for Realistic Simulation
4.2 Calibration Workflow and Results
4.3 Model Validation


2010 Flash Crash Scenarios and 5.1 Simulating Historical Flash Crash
5.2 Flash Crash Under Different Conditions


Mini Flash Crash Scenarios and 6.1 Introduction of Spiking Trader (ST)
6.2 Mini Flash Crash Analysis
6.3 Conditions for Mini Flash Crash Scenarios


Conclusion and Future Work
7.1 Summary of Achievements
7.2 Future Works Introduction Introduction Introduction Background and Related Work
2.1 Agent-based Financial Market simulation
2.2 Flash Crash Episodes Background and Related Work 2.1 Agent-based Financial Market simulation 2.1 Agent-based Financial Market simulation 2.2 Flash Crash Episodes 2.2 Flash Crash Episodes Model Structure and 3.1 Model Set-up
3.2 Common Trader Behaviours
3.3 Fundamental Trader (FT)
3.4 Momentum Trader (MT)
3.5 Noise Trader (NT)
3.6 Market Maker (MM)
3.7 Simulation Dynamics Model Structure and 3.1 Model Set-up Model Structure and 3.1 Model Set-up 3.2 Common Trader Behaviours 3.2 Common Trader Behaviours 3.3 Fundamental Trader (FT) 3.3 Fundamental Trader (FT) 3.4 Momentum Trader (MT) 3.4 Momentum Trader (MT) 3.5 Noise Trader (NT) 3.5 Noise Trader (NT) 3.6 Market Maker (MM) 3.6 Market Maker (MM) 3.7 Simulation Dynamics 3.7 Simulation Dynamics Model Calibration and Validation and 4.1 Calibration Target: Data and Stylised Facts for Realistic Simulation
4.2 Calibration Workflow and Results
4.3 Model Validation Model Calibration and Validation and 4.1 Calibration Target: Data and Stylised Facts for Realistic Simulation Model Calibration and Validation and 4.1 Calibration Target: Data and Stylised Facts for Realistic Simulation 4.2 Calibration Workflow and Results 4.2 Calibration Workflow and Results 4.3 Model Validation 4.3 Model Validation 2010 Flash Crash Scenarios and 5.1 Simulating Historical Flash Crash
5.2 Flash Crash Under Different Conditions 2010 Flash Crash Scenarios and 5.1 Simulating Historical Flash Crash 2010 Flash Crash Scenarios and 5.1 Simulating Historical Flash Crash 5.2 Flash Crash Under Different Conditions 5.2 Flash Crash Under Different Conditions Mini Flash Crash Scenarios and 6.1 Introduction of Spiking Trader (ST)
6.2 Mini Flash Crash Analysis
6.3 Conditions for Mini Flash Crash Scenarios Mini Flash Crash Scenarios and 6.1 Introduction of Spiking Trader (ST) Mini Flash Crash Scenarios and 6.1 Introduction of Spiking Trader (ST) 6.2 Mini Flash Crash Analysis 6.2 Mini Flash Crash Analysis 6.3 Conditions for Mini Flash Crash Scenarios 6.3 Conditions for Mini Flash Crash Scenarios Conclusion and Future Work
7.1 Summary of Achievements
7.2 Future Works Conclusion and Future Work 7.1 Summary of Achievements 7.1 Summary of Achievements 7.2 Future Works 7.2 Future Works References and Appendices References and Appendices ABSTRACT This paper describes simulations and analysis of flash crash scenarios in an agent-based modelling framework. We design, implement, and assess a novel high-frequency agent-based financial market simulator that generates realistic millisecond-level financial price time series for the E-Mini S&P 500 futures market. Specifically, a microstructure model of a single security traded on a central limit order book is provided, where different types of traders follow different behavioural rules. The model is calibrated using the machine learning surrogate modelling approach. Statistical test and moment coverage ratio results show that the model has excellent capability of reproducing realistic stylised facts in financial markets. By introducing an institutional trader that mimics the real-world Sell Algorithm[1] on May 6th, 2010, the proposed high-frequency agent-based financial market simulator is used to simulate the Flash Crash that took place that day. We scrutinise the market dynamics during the simulated flash crash and show that the simulated dynamics are consistent with what happened in historical flash crash scenarios. With the help of Monte Carlo simulations, we discover functional relationships between the amplitude of the simulated 2010 Flash Crash and three conditions: the percentage of volume of the Sell Algorithm, the market maker inventory limit, and the trading frequency of fundamental traders. Similar analyses are carried out for mini flash crash events. An innovative "Spiking Trader" is introduced to the model, aiming at precipitating mini flash crash events. We analyse the market dynamics during the course of a typical simulated mini flash crash event and study the conditions affecting its characteristics. The proposed model can be used for testing resiliency and robustness of trading algorithms and providing advice for policymakers. Acknowledgements The support of the UK EPSRC (Grant Nos. EP/L016796/1, EP/N031768/1, EP/P010040/1, EP/S030069/1 and EP/V028251/1), Xilinx, and Intel is gratefully acknowledged. Kang Gao holds a China Scholarship Council-Imperial Scholarship. Statements and Declarations Competing Interests The authors declare that they have no further conflict of interest. Competing Interests 1 Introduction With the advent of electronic financial markets for the exchange of securities, the electronic centralized limit order book has become the standard market mechanism for transaction matching and price discovery. This form of order book offers market participants a more liquid market system with a small bid-ask price spread, increased market depth and decreased transaction times. Algorithmic trading is commonly defined as the use of computer algorithms to automatically make trading decisions, submit orders, and carry out post-submission order management. In the past decade algorithmic trading has grown rapidly across the world and has become the dominant way securities are traded in financial markets, currently generating more than half of the volume of U.S. equity markets. Constantly improving computer technology and its application by both traders and exchanges, together with the evolution of market micro-structure, automation of price quotation and trade execution have together enabled faster trading. Nowadays the speed of order submission has become a principal characteristic for distinguishing trading agents. Market participants known as high-frequency traders are capable of trading hundreds of times in a second, using fast algorithms and specialized network connections with exchanges. high-frequency traders are often orders of magnitude faster in order submission than other traders, and even other trading algorithms. The rise of algorithmic trading and high-frequency trading has had broad impacts on financial markets, especially on the price discovery process and market price stability. One conspicuous impact is the increasingly frequent "flash crash" in major financial markets. The flash crashes comprise large and rapid changes in the price of an asset that does not coincide with changes in economic fundamental value for the asset. The flash crash events have occurred in markets that are among the largest and most liquid exchanges in the world. One representative flash crash event is the famous 2010 Flash Crash, which happened in the U.S. stock market on May 6th, 2010. During this flash crash event, one market participant’s algorithm caused a sharp price drop in the E-mini S&P futures market. The flash crash soon spread to other futures markets and equity markets. The market price fell almost 6% in just several minutes, while the bulk of losses was recovered nearly as quickly. The 2010 Flash Crash led to turmoil market conditions and caused huge market value loss. As for the cause of the 2010 Flash Crash, Kirilenko et al. (2017) show that the key events in the 2010 Flash Crash have clear relationships with regard to algorithmic trading. The 2010 Flash Crash seems to be singular because of the fact that no following events have rivalled its depth, breadth, and speed of price movement. Nevertheless, flash crashes on a smaller scale happen frequently. These events are termed mini flash crashes (Johnson et al. 2012). According to Johnson et al. (2012), there were more than 18,000 mini flash crashes that are identified in the U.S. equity market between 2006 and 2011. As scaled-down versions of the 2010 Flash Crash, mini flash crashes are abrupt and severe price changes occur in an extremely short time period (Golub et al. 2012). Mini flash crashes are attracting great research interest because their frequent occurrence could destabilize the financial market and undermine investor confidence (Golub et al. 2012). The flash crash episodes[2], including large flash crash and mini flash crash events, are of significant concern to researchers, practitioners, and policymakers. Financial markets in which price changes are orderly and reflect proper changes in valuation factors are desirable. However, flash crash episodes could potentially disorganise such a desirable market and cause adverse consequences for financial stability if they were to impede investment by undermining investor confidence in the price at which securities could be transacted (Karvik et al. 2018). To prevent flash crash episodes from becoming more frequent and longer-lasting, it is important to understand how such episodes arise. In this paper we explore the dynamics during both large flash crashes and mini flash crashes. The main methodology employed here is financial market simulation in agent-based models. The agent-based financial market simulation provides realistic synthetic financial market data and a testbed for exploring dynamics during flash crash episodes and conditions that influence the characteristics of flash crash episodes. Financial market simulation based on agent-based models is a promising tool for understanding the dynamics of financial markets. With huge potential academic and industrial value, agent-based financial market simulation has gained extensive research attention in recent years. Financial market simulation by agent-based models is an exciting new field for exploring behaviours of financial markets. An agent-based financial market simulation consists of a number of distinct agents that follow predetermined rules in a manner analogous to how real-world trader behaves in reality. Unlike traditional economic theories, there is no equilibrium assumption in agent-based financial markets. In addition, traders are no longer assumed to have rational behaviours as in traditional economic theories. The removal of these assumptions makes agent-based financial market simulation more realistic than traditional equilibrium-based economic and financial theories. These advantages of agent-based financial market simulation make it possible to explore complex phenomena such as flash crash episodes in modern financial markets, which is unachievable with traditional equilibrium-based theories. Various agent-based simulators have been developed in the literature. However, there are still gaps in creating ideal agent-based financial market simulators that are capable of generating synthetic high-frequency market data that are realistic. Specifically, most existing agent-based financial markets are of lower frequency such as daily or weekly. To explore market dynamics that involve high-frequency trading, a higher simulation frequency is needed. In addition, instead of using full exchange protocols, many simulators make assumptions about the price formation process and use mathematical formulas to approximate the matching engine. This significantly undermines the realism of the simulator. Last but not the least, the proper calibration and validation of agent-based financial market simulation are still an open problem. To sum up, there are two challenges that this paper aims to address: challenges • C1: To design and implement a high-frequency agent-based financial market simulator with full exchange protocols, and with proper calibration and validation process to reproduce a realistic artificial financial market. • C2: Under the proposed agent-based financial market simulator, investigate the market dynamics during flash crashes (including both large flash crashes and mini flash crashes) and explore the conditions that influence the characteristics of flash crashes. Motivated by the above challenges, we developed a novel high-frequency financial market simulator to narrow the existing gaps. The simulator is then employed to explore the dynamics during flash crashes and the conditions that affect flash crashes. Broadly speaking, our contributions in this paper are three-fold: contributions • A high-frequency agent-based financial market simulator is implemented, with each simulation step corresponding to 100 milliseconds. Full exchange protocols (limit order books) are implemented to simulate the order matching process. In this way, we provide a microstructure model of a single security traded on a central limit order book in which market participants follow fixed behavioural rules. The model is calibrated using the machine learning surrogate modelling approach. As for model validation, statistical test and moment coverage ratio results show that the simulation is capable of reproducing realistic stylised facts in financial markets. • Under the framework of the proposed high-frequency agent-based financial market simulator, the 2010 Flash Crash is realistically simulated by introducing an institutional trader that mimics the real-world Sell Algorithm on May 6th, 2010. We investigate the market dynamics during the simulated flash crash and show that the simulated dynamics are consistent with what happened in historical flash crash scenarios. We then explore the conditions that could have influenced the characteristics of the 2010 Flash Crash. According to our Monte Carlo simulation, three conditions significantly affect the amplitude of the 2010 Flash Crash: the percentage of volume (POV) of the Sell Algorithm, market maker inventory limit, and the trading frequency of fundamental traders. In particular, we found that the relationship between the amplitude of the simulated 2010 Flash Crash and the POV of the Sell Algorithm is not monotonous, and so is the relationship between the amplitude and the market maker inventory limit. For the trading frequency of fundamental traders, the higher the frequency, the smaller the amplitude of the simulated 2010 Flash Crash. • Similar analysis is carried out for mini flash crash events. An innovative type of trader called "Spiking Trader" is introduced to the agent-based financial market simulator, creating more price shock and precipitating more mini flash crash events. Market dynamics for a typical simulated mini flash crash event are analysed. We also explore the conditions that could influence the characteristics of mini flash crash events. Experimental results show that the market maker inventory limit significantly affects both the frequency and amplitude of mini flash crash events. However, the trading frequency of fundamental traders shows no obvious influence on mini flash crash events in our experiments. The novelty of our approach lies in several features. Firstly, the proposed agent-based financial market simulator has a higher frequency than most other simulators in the literature. Our simulation step is at milliseconds level, which allows for the investigation of high-frequency dynamics in the simulated financial market, while most simulation models in literature adopt larger simulation steps of 1 second or 1 minute. Secondly, we explore the influence of different market configurations on the amplitude of the 2010 Flash Crash. To the best of our knowledge, there are few similar experiments in the existing literature. Thirdly, an innovative type of trader named "Spiking Trader" is proposed to precipitate more mini flash crash events. Fourthly, the experiments that explore the conditions that influence the frequency and amplitude of mini flash crash events are also a novelty of this work. novelty The remainder of the article is organized as follows. Section 2 presents general background on the agent-based financial market simulation and an overview of previous research about flash crash events. Section 3 shows the structure and details for the proposed agent-based model, while Section 4 presents the model calibration p process and model validation results. Section 5 and Section 6 provide simulation and analysis for the 2010 Flash Crash scenario and mini flash crash scenarios, respectively, in the framework of the proposed agent-based financial market simulation. Section 7 concludes and gives directions for future work. Authors:
(1) Kang Gao, Department of Computing, Imperial College London, London SW7 2AZ, UK and Simudyne Limited, London EC3V 9DS, UK (kang.gao18@imperial.ac.uk);
(2) Perukrishnen Vytelingum, Simudyne Limited, London EC3V 9DS, UK;
(3) Stephen Weston, Department of Computing, Imperial College London, London SW7 2AZ, UK;
(4) Wayne Luk, Department of Computing, Imperial College London, London SW7 2AZ, UK;
(5) Ce Guo, Department of Computing, Imperial College London, London SW7 2AZ, UK. Authors: Authors: (1) Kang Gao, Department of Computing, Imperial College London, London SW7 2AZ, UK and Simudyne Limited, London EC3V 9DS, UK (kang.gao18@imperial.ac.uk); (2) Perukrishnen Vytelingum, Simudyne Limited, London EC3V 9DS, UK; (3) Stephen Weston, Department of Computing, Imperial College London, London SW7 2AZ, UK; (4) Wayne Luk, Department of Computing, Imperial College London, London SW7 2AZ, UK; (5) Ce Guo, Department of Computing, Imperial College London, London SW7 2AZ, UK. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv [2] We use "flash crashes", "flash crash episodes" and "flash crash scenarios" interchangeably in this article.

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A High-Frequency Model for Analyzing the 2010 Flash Crash and Mini Crash Events

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