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 5 2010 Flash Crash Scenarios As a real-world application, the proposed model is used to investigate market dynamics during flash crash events and the conditions for the occurrence of flash crash scenarios. This section will present the reproduction and investigation of a famous historical flash crash event - the flash crash on May 6th, 2010. In the next section, we will investigate conditions for the occurrence of mini flash crash events. 5.1 Simulating Historical Flash Crash We simulate the 2010 Flash Crash within the framework of our high-frequency financial market simulator. The flash crash happened in the afternoon trading session on May 6th, 2010, starting at around 14:30. As mentioned before, the model parameters are calibrated to the data in the morning trading session (8:00-12:30) to avoid overfitting[10]. According to the CFTC-SEC staff report, an automated execution algorithm, which aimed at selling a large number of contracts, was identified as one important trigger for the flash crash. Consistent with this report, an institutional trader is introduced in the simulator to mimic the automatic Sell Algorithm. The institutional trader will initiate a Sell Algorithm that intends to sell a large quantity of contracts at 14:30 in our simulator. The parameters associated with the institutional traders are tuned to reproduce realistic flash crash behaviours as in historical data. We present the trading configuration of the institutional trader in the subsequent session, followed by a detailed analysis of the market dynamics during the simulated flash crash event. 5.1.1 Introduction of Institutional Trader (INS) 5.1.1 Introduction of Institutional Trader (INS) 5.1.2 Market Behaviours during Flash Crash 5.1.2 Market Behaviours during Flash Crash To generate a realistic flash crash event, we fine-tune the parameters of the newly introduced institutional trader. According to SEC and CFTC (2010), the flash crash event is potentially caused by the "hot-potato" effect among highfrequency market makers and the mismatch of the trading frequency between different types of traders. Consequently, we also tune the market maker inventory limit and the trading frequency of fundamental traders. The effect of these parameters on the flash crash event will be presented in subsequent sessions. All other model parameters are fixed and are given exactly the same values that are calibrated to the morning trading session data on May 6th, 2010. This configuration helps to reduce the degree of freedom and avoid the potential problem of overfitting. The resulting simulation of the price time series mimics the real-world flash crash event. Figure 4 presents such a single simulation of the price trajectory that undergoes a flash crash scenario. The corresponding parameter configuration is shown in Appendix C. Figure 5 presents a comparison between simulated trading volume and historical trading volume during the whole day. Carefully examining such a single simulation provides useful insights into how the trading behaviour of different types of traders interact to bring about a flash crash scenario. By visual inspection, the simulation accurately replicated the defining characteristics of a flash crash. Figure 6 presents the total inventory level for each type of trader around the simulated flash crash event, and the market sell order volume of the institutional trader. To assist with detailed inventory analysis during the flash crash event, Figure 7 presents the inventory level for each type of traders against simulated price during the time interval from 14:30 to 14:50. Figure 8 displays the market depth for both sides of the simulated limit order book, and the comparison between simulated bid-ask spread and historical bid-ask spread. Detailed examination shows that the simulated flash crash accurately matches the market dynamics during the historical 2010 Flash Crash. The dynamics around the simulated flash crash event are as follows. • The overall market sentiment in the simulation is negative, as we can see that the fundamental value is broadly decreasing before 14:00. At 14:00, according to Figure 6 the fundamental traders accumulate a negative inventory due to continuously decreasing fundamental value, while market makers accumulate a positive inventory. Before the flash crash event, the market depth for both sides of the limit order book is relatively stable, while the simulated bid-ask spread is at a relatively low level. • At 14:30 in the simulated market, the market price has already dropped by 2.63% compared to the opening price level. Regardless of the downward market trend, the institutional trader initiates a sell program to sell a large number of inventories, which is 120,000 in our simulation. The institutional trader decides to execute the sell program via an automated execution algorithm, which is set to feed market selling orders into the market to target an execution rate of 9%. That is, for each minute the institutional traders aim to sell 9% of the market trading volume calculated over the previous minute. Neither price nor time is considered by the Sell Algorithm. Refer to Algorithm 7 for specific trading logic of the institutional trader. • In our simulation, market makers correspond to the high-frequency traders in the real market. The above selling pressure is initially absorbed by market makers in our simulated market, which is consistent with the dynamics in the historical market (SEC and CFTC 2010). This is shown by the inventory change for each type of traders in Figure 7. From 14:30:00 to 14:40:50, the total inventory for market makers is rapidly increasing, while the total inventory for low-frequency fundamental traders barely changed. During this approximately 11-minute time period, the price undergoes a further 2.61% drop. At 14:40:50, the market depth in the limit order book has slightly decreased and the bid-ask spread has slightly increased. The scale of change for the market depth and bid-ask spread is restricted because of the existence of market makers. • In addition to the above observations, the market transacted volume is continuously increasing during the above 11-minute time interval due to the trading activities of the Sell Algorithm, as shown in Figure 5. Because of its procyclical nature, the Sell Algorithm used by the institutional trader responds to the increased volume by increasing the volume of sell orders that it is feeding into the market, even though the orders that it already submitted to the market were not yet fully absorbed and have caused non-trivial market turbulence. The increasing order volume of the institutional trader is shown in panel (b) of Figure 6. • As market makers are the buyers of the initial batch of orders sent by the institutional trader, they have accumulated massive temporary long positions of the contracts. Nevertheless, the inventory of market makers cannot accumulate infinitely. At 14:40:50, the inventory limits for many market makers are exceeded. At this point, a dramatic and significant market crash starts. Those market makers, who have accumulated excessive positions than their inventory limits, stop providing liquidity and begin to aggressively sell their inventories in order to reduce their temporary long positions. This is consistent with the typical trading practice that a market maker tends to maintain a relatively small aggregate inventory for the purpose of risk management. Consequently, these market makers contribute further selling pressure to the market in addition to the Sell Algorithm. Still lacking sufficient demand from fundamental traders, the aggregate sell volume is consumed by remaining market makers who are still quoting in the market. As a result, more market makers accumulate excessive positions than their inventory limits, which in turn forces them to sell their long positions to the market. The same positions rapidly pass among all market makers. Such so-called "hot-potato" effect quickly sweep almost all market makers in the market, resulting in a dramatic price drop and quoting suspension of almost all market makers. • The combined selling pressure from the Sell Algorithm and market makers drove the price down by more than 4.16% in less than two minutes from 14:40:50 to 14:42:20, with the price reaching its intra-day low of 1053.5. Along with the price plunge, the market suffers from great liquidity loss. The liquidity loss can be reflected by the sharp decrease of market depth during the simulated flash crash event. In the simulated morning trading session, the average market depth for both bid and ask sides are around 5000. In contrast, during the simulated large price plunge that starts at around 14:40, the market depth for both bid and ask sides are less than 1000, even reaches 0 in bid side for more than 1 minute. The significant liquidity loss in our simulation is mostly because of the withdrawal of market makers from the market. The withdrawal of market makers in our simulation is consistent with empirical findings in SEC and CFTC (2010), which states that real market makers did stop trading during the 2010 Flash Crash event. According to Figure 8, the market depth for both sides of the limit order book dropped dramatically during this time period. There is less than 1% of bid-side market depth observed during normal trading hours, with even zero bid-side market depth for around 30 seconds in the middle of 14:41. The bid-ask spread widens dramatically, reaching more than 20 ticks at this short time interval. • As price drops quickly, the demand from fundamental traders gradually increases according to Equation 1. Figure 7 shows that fundamental traders do absorb a portion of selling volume during the sharpest price drop. However, the sudden decline in both price and liquidity indicates that the price was moving so fast that fundamental traders were incapable of providing enough buying support. • After the price hits the intra-day low level, the demand from fundamental traders finally increased to a level that is able to counteract the selling pressure from the institutional trader. Starting at 14:42:20, the price hovers at the lower level for approximately one minute and then starts to bounce back quickly towards the fundamental value. The Sell Algorithm continues to feed sell orders to the market until about 14:47, at which point the inventory of the institutional trader has been emptied. The above is a detailed analysis of the market dynamics of a simulated flash crash event. The simulated dynamics accurately match the dynamics of the historical 2010 Flash Crash event. Both simulated flash crash and historical flash crash have an amplitude of around 7% (starting from 14:30:00), and both prices undergo a similar "flash crash" shape. A large Sell Algorithm is replicated to trigger the simulated flash crash, and is executed for around 17 minutes, which is close to the 20 minutes execution time of the historical Sell Algorithm. The overall liquidity loss during the flash crash is replicated accurately, with decreased market depth and enlarged bid-ask spread as emergent properties of the simulation. We also reproduce realistic patterns in the simulated market trading volume. The detailed progress of the simulated flash crash also matches the empirical analysis of the historical flash crash event. In the subsequent section we will explore the conditions that influence the severity of the flash crash event. 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 [10] Except for market maker inventory limit and fundamental trader trading frequency, which are key to generating realistic flash crashes. [11] The step_seconds in the institutional trader logic is the number of seconds since the beginning of the simulation.

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