Joint Discussion Paper Series in Economics...ventory control and simulated the 2010 Flash Crash (May 6, 2010) scenario, where a sudden market drop was triggered by a volume-inline

Joint Discussion Paper Series in Economics

by the Universities of

Aachen · Gießen · Göttingen Kassel · Marburg · Siegen

ISSN 1867-3678

No. 15-2015

Alexandru Mandes

Impact of inventory-based electronic liquidity providers within a high-frequency event- and agent-based modeling

framework

This paper can be downloaded from http://www.uni-marburg.de/fb02/makro/forschung/magkspapers/index_html%28magks%29

Coordination: Bernd Hayo • Philipps-University Marburg

School of Business and Economics • Universitätsstraße 24, D-35032 Marburg Tel: +49-6421-2823091, Fax: +49-6421-2823088, e-mail: [email protected]

Impact of inventory-based electronic liquidity

providers within a high-frequency event- and

agent-based modeling framework

Alexandru Mandes∗

University of GiessenLicher Str. 64, 35394 Giessen, Germany

[email protected]

June 4, 2015

Abstract. This contribution addresses the impact of high-frequency elec-tronic liquidity provision strategies on financial markets’ intraday dynam-ics, by evaluating the interaction between multiple trading strategies withina computer laboratory, i.e. an artificial stock market. Initially, a realisticbase-line model is set up around a continuous double auction market, withtrading being pursued only by four types of low-frequency market partici-pants. Sequentially, the high-frequency agents are added to the model andthe corresponding changes related to various measures of market quality andmarket systemic risk are analyzed, under both regular and market stress con-ditions, such as when the order flow balance is suddenly disrupted by a largevolume-in-line sell program. A detailed intraday analysis of a flash crashemergence is also conducted. Finally, possible regulatory policies such asminimum holding or quote resting time and financial-transaction taxes areassessed.

Key Words: agent-based modeling, continuous double auction, high-frequencytrading, electronic liquidity provision, market quality, systemic risk, flashcrash, regulatory policies

JEL classification: C63, G17, G28

∗The author would like to thank Deutscher Akademischer Austauschdienst (DAAD) forthe awarded PhD scholarship. Also, the author is grateful to WEHIA 2015 participantsfor their comments and suggestions.

Introduction

The recent technological advances and the development of electronic financialmarkets have led to an unprecedented level of market automation, whose con-sequences are still a heated subject of media debate. According to a TABBgroup estimate presented in November 2009, the market volume share ac-counted for by high-frequency trading (HFT) in the USA has reached 61%.1

A more recent report published by the ESMA, covering a sample of 100stocks from nine EU countries for May 2013, shows that the HFT activityaccounted for between 24% or 43% of the total traded value, depending onthe estimation method, i.e. based on the primary business of firms (directapproach) or on the lifetime of orders (indirect approach). For the numberof trades the corresponding numbers for HFT activity were 30% and 49%,and for the number of orders 58% and 76% respectively.2

In 2012 the UK Government Office for Science has commissioned a fore-sight project to address the complex issue of computer generated tradingin financial markets and to provide policy strategic options (Foresight: TheFuture of Computer Trading in Financial Markets (2012)). The scientificevidence shows that, on one side, the general market quality has been im-proved, but on the other side there might be a greater risk of periodic illiq-uidity. Still, many specific questions have remained unanswered due to thesignificant challenges in the empirical evaluation of HFT, determined ei-ther by a lack of proper data identification (Friederich and Payne (2011))or by endogeneity issues – HFT growth coincides with the 2008–2009 mar-ket turmoil (Brogaard (2010)). For example, one open problem refers to thehigh-frequency traders’ (HFTs) liquidity providing behavior during regularmarket conditions versus situations of market stress. Friederich and Payne(2011) question the robustness of a system relying on the liquidity providedby HFTs without any obligations of staying in the market, as well as theeconomic value of predatory strategies which profit at the expense of tradi-tional investors. Nevertheless, even if passive HFTs would not flee duringthe periods of high order toxicity, it might be that their trading strategiescould temporarily amplify some liquidity issues, even if they are not theirdirect cause. Regarding the causal relation between HFT and volatility,Brogaard (2010) and Linton (2011) show that it is not clear whether largervolatility is the effect of HFT or just a favorable condition which stimu-lates HFT activity. Given that groups of stable systems could interact inhighly unstable ways (“fallacy of composition”), Danielsson and Zer (2012)suggest that the systemic risk of computer-based strategies is currently notwell understood. One factor which might contribute to an increase of thesystemic risk is a large homongeneity of strategies, e.g., when large clusters

1“High Frequency Trading – What Is It & Should I Be Worried?”, Larry Tabb, WorldFederation of Exchanges, 2009

2“High-frequency trading activity in EU equity markets”, European Securities andMarkets Authority, Economic Report Number 1, 2014

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of market participants are following exactly the same strategies. Farmer andSkouras (2011) and Sornette and Von Der Becke (2011) underline the chaoticproperties of the financial system, determined by the complex interactionsbetween the market participants, which can sometimes exhibit very differentbehaviors as a result of very small initial state changes. Also, it is not clearto what extent do HFTs contribute to these non-linear dynamics and rein-forcing feedback loops. Regarding the price discovery mechanism, Brogaard(2010) and Brogaard et al. (2012) conclude that by trading in the directionof the incoming information, HFTs positively contribute to price efficiency.However, since HFTs put more emphasis on short term rather than funda-mental information, the arrival of information – concentrated or diffused –is also important. Finally, with respect to policy making, further analysisfor a better understanding of the potential impact of the various regulatoryoptions is recommended in order to prevent any unexpected and detrimentalmarket reactions.

Given the challenges faced by the empirical approach, a viable alternativefor testing the various hypothesis regarding the impact of HFT, as well asthe potential effect of policy regulations, is to run simulations within an ar-tificial stock market by means of agent based modeling. A list of prominentmilestones of designing intraday financial market models should start withChiarella and Iori (2004), Chiarella et al. (2009) who have developed a con-tinuous double auction model with stylized agents corresponding to humanstrategies. The authors have shown that, by including chartist strategies, thesimulated price time series exhibit realistic stylized facts such as the fat tailsof returns, volatility clustering and the fat-tailed distribution of limit orderplacement relative to the midpoint. Gsell (2008) has extended the previousmodel and made a first step towards modeling computer-based trading byadding two different implementations of an algorithmic trader. More recently,Vuorenmaa and Wang (2013) has included market-makers with a tight in-ventory control and simulated the 2010 Flash Crash (May 6, 2010) scenario,where a sudden market drop was triggered by a volume-inline execution algo-rithm. Their results show that the probability of a flash crash increases withthe number of high-frequency (HF) agents, tightness of inventory sizes andsmaller tick size, while quality metrics such as spread-at-touch and volatilitydepend diametrically on the previous parameters.

However, the previous intraday market designs suffer from a series of se-vere limitations. For once, the time dimension is not properly operationalized– being reduced to an atemporal sequence of simulation steps – and thereforethese models do not function as expected when agents are supposed to act atdifferent time frames, as detailed in Section 2. Secondly, low-frequency (LF)agents place their trading orders randomly and do no react to the changingmicrostructure conditions. In reality, the order book is not just a tradinginstrument, but also an important source of endogenous information, whichinfluences to a large extent the way HFTs behave. The importance of build-

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ing a realistic and robust model, which could then be successfully used as alaboratory for policy simulation, has been underlined by Prof. Alan Kirmanduring the WEHIA 2015 round table: “If we wish to build a model whichwill be useful for studying the effect of policy measures we should base iton realistic assumptions derived from observed empirical behavior. However,we should also make sure that simulations of that model do not depend on avery limited set of parameter values for these assumptions. We want a modelwhich is robust in the sense that small modifications in the assumptions donot change radically the nature of the results.”

The current contribution proposes a higher fidelity intraday market modelwith a proper implementation of time which allows for simulating tradingstrategies at different temporal frequencies. Additionally, a microstructure-based order submission mechanism as in Mandes (2014) is included, whichallows LF agents to react to the current liquidity and volatility conditions.Based on the proposed model, a series of simulations is run in order to answerseveral research questions regarding the impact of HFT on market qualityand systemic risk, as well as the effects and side-effects of two policy mea-sures. Section 1 presents a list of market quality indicators which helps inassessing the various market scenarios. Section 2 introduces the underlyingframework of the agent-based models, as well as the various LF and HF mar-ket participants. In Section 3, the set of simulated scenarios are described,covering different market configurations, agent parameterizations and possi-ble market states. The main outcomes are interpreted in Subsection 3.2 andthe flash crash event is analyzed distinctly in Subsection 3.3. Two potentialregulatory policies, i.e. imposing a financial-transaction tax and minimumholding/ quote resting times, are evaluated in Section 4 and afterwards thefinal conclusions are drawn.

1 Market quality measures

In Brogaard (2010) and Foresight: The Future of Computer Trading in Fi-nancial Markets (2012) market quality is assessed along three different di-mensions: (i) liquidity and transaction costs, (ii) price efficiency and pricediscovery, and (iii) volatility and financial market stability.

Liquidity and transaction costs

According to Harris (2002), liquidity is the most important characteristic ofwell-functioning markets, reflecting the ability of executing large orders ina short period of time and with low trading costs. Besides the explicit costcomponents related to commissions and other fees, which are constant andfixed by brokers or stock exchanges, the implicit costs are highly dependent

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on the variable market conditions and often have a greater impact on theoverall trading performance (up to 80% of overall transaction costs).3 Forexample, if the spread is wide, the execution of a market order is expensive,i.e. the cost of immediacy is high. Furthermore, if the order size is large,one has to take into account also the available total quantity, as well as thedispersion of resting limit orders, which are to be sequentially matched untilthe entire market order is filled (“walking up the book”).

Harris (2002) summarizes the different attributes of liquidity as: imme-diacy, market width, market depth and market resiliency. The immediacy,also known as tightness or spread-at-touch, represents the cost of liquidityfor small orders. It is reflected by the bid-ask difference or, more common, bythe relative spread computed as the ratio of the bid-ask spread to mid-price.The market width or breadth captures the market impact of executing largerorders and can be measured as the cost of filling a given order size. Alterna-tively, the market width could be sampled by recording the potential marketimpact of all orders submitted by fundamental traders, which correspondsto an unconditional market impact function. If only actual executions aretaken into consideration, the average effective spread can be computed asthe share-weighted average of the double amount of the signed difference be-tween the order arrival price and the actual execution price. Additionally,the displayed market depth represents the order size that can be executedat a given cost. For example we will measure the average market depth, atone-minute frequency, as total volumes available at the best quotes, as wellas within a 1% and 2% range around the mid-price level. Finally, marketresilience refers to the speed with which the order book is replenished andformer market equilibrium is restored after a series of orders executed byuninformed traders have moved the prices away. However, even if highlyimportant for informed traders, this last property will not be tackled in thecurrent paper.4

Price efficiency and price discovery

Prices are considered to be efficient when they correctly reflect the asset’sunderlying fundamental values. According to Hendershott (2011), varianceratios are standard ways to measure price efficiency. For example, the vari-ance of weekly returns can be compared with (five times) the variance ofdaily returns. If the variance ratio is one, markets are considered to be effi-cient, while lower variance ratios imply that prices tend to overreact, whereas

3“Market quality: The new benchmark for trading venues”,The Trade, Issue 35, Jan–Mar 2013, http://www.xetra.

com/blob/1208528/2fe40dfdebf6ba7c9cff52a879894d17/data/

Xetra-Market-Quality-Article-in-The-Trade.pdf4Foresight: The Future of Computer Trading in Financial Markets (2012) reviews also

other liquidity measures, such as the Amihud measure of illiquidity, which measures theamount of price change per unit of trading volume.

4

http://www.xetra.com/blob/1208528/2fe40dfdebf6ba7c9cff52a879894d17/data/Xetra-Market-Quality-Article-in-The-Trade.pdf



higher variance ratios imply that prices tend to follow short-term trends. Inorder to assess the impact of high-frequency traders we will compute the fol-lowing variance ratios: 10 to 1 minute variance and 1 minute to 10 secondsvariance.

Volatility and financial market stability

Harris (2002) describes volatility as the tendency for prices to change unex-pectedly, either in response to new fundamental information (fundamentalvolatility) or to impatient traders’ demand for liquidity (transient volatility).In the current implementation, the underlying fundamental value basicallyremains unchanged during the entire trading session. However, the flashcrash scenario described in Section 3 can also be interpreted as the casewhen a single market participant, in possession of some new informationabout the fundamental values, trades accordingly, even if in a highly aggres-sive manner. On the other side, the transitory volatility is well designed inour model by a rich heterogenous ecology of order flow generating agentsand by the realistic implementation of the microstructure-based order sub-mission mechanism. Volatility is not constant through time, and episodesof low volatility alternate with high volatility periods (volatility clustering).From the perspective of financial market stability, the episodes of extremevolatility are of interest. For example, rare events when large price changeshappen in a short period of time, just to recover as fast to their previouslevels, can be interpreted as market failures.

In this paper, the high-frequency volatility is estimated in various ways.One first measure is the volatility range, computed as the percentage ratioof the highest over the lowest price, within some period of time. Anotherestimate is the daily standard deviation of one-minute returns, given by therealized variance equal to the sum of squared price changes at the selectedfrequency. Subsampling at a frequency lower than every tick reduces theeffect of microstructure noise, e.g., the bid-ask bounce. Finally, for analyzingthe patterns of the one-minute price series, we compute the Higuchi fractaldimension (Higuchi (1988)).

2 The market model

The most common price discovery mechanism implemented by regulated ex-changes all over the world is the continuous double auction. Basically, mar-ket participants send either limit or market orders, which are sequentiallymatched against the outstanding limit orders previously stored in a doublequeued order book. Technically, the incoming order flow is processed by amatching engine which generates trades based on a price and time priority.

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For example, buy market orders and crossing limit orders, i.e. with a limitprice higher than the lowest price of the outstanding sell orders, are executedat once under the available size constraint, while non-crossing limit ordersare placed in the buy side of the order book, waiting to be matched by afuture opposite counterparty order.

An important key-word used in the above description of the continuousdouble auction mechanism is “sequentially”, which means that the orderof incoming trading orders is essential. Most intraday agent-based models(ABMs) deal with this asynchrony issue by activating the agents one at atime. For example, Chiarella and Iori (2002), Chiarella et al. (2009) pro-pose a random polling model where individual agents are randomly pickedat each simulation step, and with a fixed probability may enter the market.In Gsell (2008) two distinct frequency-classes of agents (stylized and algorith-mic traders) are reflected by different probabilities of market participationas expressed by a latency multiplier. Similar, Vuorenmaa and Wang (2013)model both low- and high-frequency agents and introduce a dynamic randompolling mechanism, where the latency factor (activity frequency) of a HFTagent is a function of its inventory, i.e. the higher its asset holdings, the moreactive the HF trader is.

However, the previous activation mechanisms distort the historical pricetime series, which is essential for the investment decision of LF traders. Anexample of mixing various time-frequencies is given in Figure 1. The uppertimeline illustrates the activity of a LF trader, who follows a τ frequency,as represented by the main ticks on the horizontal (time) axis. The secondfrom the top timeline shows the potential activity of a HF agent, which isable to trade at a higher granularity than τ . For example, while the LFtrader “rests” between τ = 5 and τ = 6, the HF trader executes two trades.The third timeline reflects the outcome of random polling which assures thesame activation sequence given by the combined previous LF and HF agents.In this case, the time span between two consecutive LF events is widened(but could also be contracted) depending on the number of in-between HFevents. For example, the dynamic random polling in Vuorenmaa and Wang(2013) leads to intense activity clustering when HF traders are responsiblefor almost the entire market activity. If the time frame of LF traders isnot decoupled from the fluctuation in number of market events, i.e. timeis not independently represented from order flow frequency, LF traders willend up miss-behaving by applying their LF strategies at a HF time frame.Furthermore, no market statistics which are to be computed as related totime can be computed.

The bottom timeline in Figure 1 represents the correct output where theLF time-stamps are not shifted in time anymore and which can be achievedby implementing an event-driven model as described in Muchnik et al. (2006)and Daniel (2006). Under this event-driven framework, agents decide in an

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1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10* * * ** * *

1 2 3 4 5 6 7 8 9 10* * * ** * *

1 2 3 4 5 6 7 8 9 10* * * * * *

Figure 1: Mixing low and high time-frequencies

autonomous manner when to become active, depending on their ’inner’ clock(time frame) or external market events, allowing for a more realistic imple-mentation of time. Each model component has its own, independent timelinewhich intersects now and then with the timelines of the other processes. Thecentral polling component is thus replaced with dispersed and autonomousagents’ trading requests, which are queued and executed sequentially basedon their arriving time priority.

The model proposed in the current paper builds on the previously men-tioned event-based model and adds a proper implementation of various pricetime series, conditioned on the required time frame, as a necessary base for de-veloping trading strategies which operate at different frequencies. Basically,besides agents’ wake-up requests, time series update events are added to amaster queue, from where all events are dispatched to their correspondinghandlers in a timely order. Therefore, a low-frequency time series (differentfrom a high-frequency tick-by-tick time series) can be updated at fixed timeintervals, e.g., every minute, independent of the number of trades occurringwithin each time interval. Explicitly, each agent type has its own tradingfrequency and its activation follows a Poissonian process, where the inter-wake-up durations are random draws from an exponential distribution withthe rate parameter λ = 1/βtf, where βtf is equal to the individual charac-teristic frequency. Additionally, three price time series at tick-by-tick, oneminute and daily frequencies are recorded. The daily price series is initial-ized for the time-period preceding the simulation start by means of a randomwalk process with a daily price drift µeod and a daily price volatility σ2

eod.5

The initial fundamental value is set and is kept constant during the tradingsession – the fundamental time series is allowed to change only at the end ofthe trading day. It might be worth mentioning here that all actions relatedto the market matching engine are also modeled as independent events, e.g.,new orders, order removal/expiration, trade and quote change notifications.

5By this, we set up an initial trend for the end-of-day low frequency chartists, asdetailed in Subsection 2.1.

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This allows for an effective representation of latency differences which couldlead to different market quotes from the moment of creating and sending theorder until the order actually “hits” the market.

2.1 Low frequency agents

The agents’ design starts from the classification in (Kirilenko et al.; 2011)where six categories were identified to participate in the E-mini S&P 500stock index futures market between 3-6 May, 2010: intermediaries, HFTs,fundamental buyers and sellers, small traders and opportunistic traders. Thefirst two categories correspond to whats is known as high-frequency trading(will be described in Subsection 2.2), while the latter four can be consideredlow-frequency trading.

• Low-frequency strategies

We define a pool of low-frequency strategies S which can be employedby the LF traders, as follows: fundamental, trend following, mean reversionand noise trading. Fundamentalists’ expectations are equal to their ownevaluations of the fundamental value and can be defined as in (2.1), whereεfund ∼ U(0.99, 1.01) is a noise term, contributing to the heterogeneity of themodel:

Et[pfund] = ft ε

fund (2.1)

The two chartist strategies can be applied both at daily (end-of-day),as well as at intraday frequencies. The future price expectation of trendfollowers at time t, Et[p

trend], is based on extrapolating the weighted averageof the average past return over some previous time-span τ and the currentreturn rt (see equation (2.2)).6 End-of-day time spans are random deviatesfrom a uniform distribution τeod ∼ U(1, 9), as well as intraday time spansτid ∼ U(10, 60). On the opposite, reversal strategies expect the price toreturn to a long-term moving average (see equation (2.3)). In the case ofthe daily time frame, the pt time series refers to end-of-day (closing) prices,while for intraday time frames it depends on the selected frequency, e.g., 5minutes, 1 minute or tick-by-tick.

Et[ptrend(eod/id)] = pt ∗

(1 +

(0.95

1

τ

τ∑i=1

rt−i + 0.05 rt

)τ

)(2.2)

6The current return is based on the most recent intraday trading price relative to theprevious daily closing price or relative to the previous time stamp for intraday time series,respectively.

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Et[prev(eod/id)] =

1

τ

τ∑i=1

pt−i (2.3)

Finally, the expectations of the noisy trading components are build aroundthe current mid-price mt as in equation (2.4), with the noise term εnoise ∼U(0.96, 1.04).

Et[pnoise] = mt ε

noise (2.4)

The implementation of a low frequency trader can mix up several strate-gies, as in Chiarella and Iori (2002), Chiarella et al. (2009), given individualweights allocated to each individual strategy, i.e. fundamentalist wfund, end-of-day/ intraday trend following wtrend(eod)/ wtrend(id), end-of-day/ intradaymean reversion wrev(eod)/ wrev(id) and noise strategy wnoise.

Et[p] =

∑s∈S

wsEt[ps]∑

s∈Sws

(2.5)

• Agent activation

The trade frequency of each trader type, which proxies the activity oftraders, is considered to be proportional to the market participation (% oftrades) computed in Kirilenko et al. (2011) – even if some orders are notexecuted at all, while others are counterpart to multiple trades. We computethe time frame βtf of an agent cluster, i.e. the mean time duration betweensuccessive activity wake-ups, as the total length of a trading session expressedin microseconds divided by the number of trades for which the trader typeis accounted for.

• Order size

The actual order sizes are randomly generated from an upper-truncatedexponential distribution. The mean and upper bound of these exponentialdistributions are specific for each trader type and are set to match the sum-mary statistics of trader categories in Kirilenko et al. (2011). Thus, given thedesired order size mean, an appropriate pair of rate λ = 1/βsize and right-side cutoff parameter bsize – corresponding to the maximum order size – of

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the exponential distribution modeling order sizes can be chosen.7 Moreover,all random draws are rounded to the closest integer, except for values smallerthan one which are only upper rounded (ceiling function) in order to avoidnull order sizes.

• Order submission

The order placement mechanism is built around an optimization problemwhich minimizes the risk adjusted execution cost, taking into considerationa set of relevant micro-structure factors – such as order book liquidity, orderflow proxied by the order book imbalance and transient volatility –, as wellas intrinsic agents characteristics – such as the sense of urgency. The entireprocedure is described in detail in Mandes (2014) and is reproduced withoutany changes in the current implementation.

• Order cancellation

Since the low-frequency traders are not modeled as individuals, but asclusters, we rely on a probabilistic order cancellation process as in Cui andBrabazon (2012). At each activation, the agent cluster makes a randomchoice between removing its oldest outstanding limit order with probabilityλc and trading, i.e. submitting a new order, with the complementary proba-bility 1− λc.

Fundamental buyers and sellers

The actual low-frequency trader types match the previous trading strategieswith the trader categories in Kirilenko et al. (2011). Thus, we consider funda-mental buyers and sellers to form price expectations by employing a mixtureof end-of-day strategies such as fundamental, trend following and mean re-version. However, the decision of buying, respectively selling, is constant andhard-coded for each of the two types, similar to Cui and Brabazon (2012) –the main feature of these two traders is that they accumulate directional po-sitions to be held for longer periods of time. In the current implementation,their future price expectations do not influence their trading decision, butonly their order size distribution by tilting its mean βsize = (Et[p]/pt) βsize.

7The mean of the truncated exponential distribution fX(x|β, b) =1β exp(−x/β)1−exp(−b/β) , for

0 < x ≤ b where β > 0, is E[X] = β 1−(k+1) exp(−k)1−exp(−k) , where k = b/β (see Olive (2008,

Chapter 4)). Therefore, by knowing E[X] and b, one can solve the previous equation forβ. However, if k is large enough (e.g., k ≥ 7) then β ≈ E[X].

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Opportunistic/ day traders

Opportunistic traders are considered to be day traders, which follow a mix ofvarious strategies applied both at daily as well as intraday time frames. Toaccount for heterogeneity within the cluster, at each trader activation, theweights associated with the individual strategy components are randomlyshuffled according to an uniform distribution U [0, 1). The trading decisionto buy or sell a specific asset quantity is generated by comparing the expectedprice Et[p] with the current midpoint or market price pt.

Small traders/ noise traders

Finally, small traders, which trade very few contracts per day, are modeledas zero-intelligence/ liquidity traders, i.e random buying or selling. In otherwords, in order to fit to the standardization described at the beginning of thecurrent subsection, small traders’ “strategies” are based only on the noisytrading component.

2.2 High frequency agents

Market professionals consider high-frequency traders (HFT) to be not a strat-egy by itself, but a technology which allows for the automation and for theapplication of a wide spectrum of trading strategies at a “drastically com-pressed time scale”,8 where human traders are not able to react. However,a set of common denominators for the entire range of HFT-based strategieshas been identified both by academic researchers (see Aldridge (2009), Bro-gaard (2010)), as well as by market regulators across the world.9 The listof common attributes could be summarized as follows: (1) computer-basednon-discretionary/ automated strategies, (2) proprietary trading (as opposedto agency activity), (3) use of low latency technologies (e.g., co-location ser-vices, proximity hosting, direct market access, individual data feeds offeredby exchanges), (4) real-time tick-by-tick data processing, (5) high amountof intraday messages (orders, quotes or cancellations) and trades, (6) smallmargins per trade, (7) high capital turnover, (8) flat over-night positions (no

8NYSE Euronext comments on the Committee of European Securities Regulators’(CESR) call for evidence on micro-structural issues of the European equity markets.

9BaFin (German HFT Bill – Hochfrequenzhandelsgesetz), European Comission (MiFid2 – Directive 2014/65/EU of the European Parliament and of the Council of 15 May 2014on markets in financial instruments and amending Directive 2002/92/EC and Directive2011/61/EU), European Securities and Markets Authority (consultation paper “Guidelineson systems and controls in a highly automated trading environment for trading platforms,investment firms and competent authorities” – Reference ESMA/2011/224), Securitiesand Exchange Commission (“Concept release on equity market structure” – Release No.34-61458, File No. S7-02-10, page 45).

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positions or fully hedged). A comparison to lower-frequency strategies showsthat HFT-based strategies address very short time frames for generating en-try and exit signals (associated with small expected returns), hold positionsfor very short periods of time (in terms of seconds or milliseconds), tradevery often and need a smaller risk capital, which they are able to relocateseveral times on a short-time basis, leading to their overall profitability (highvolume).

Both categories from the classification of Kirilenko et al. (2011) whichwere not treated previously, i.e. intermediaries and HFTs, stand for shorthorizon investors which participate in a large number of transactions with-out accumulating a significant net position. For example, intermediaries sumup to less than 2% of all traders, but account for around 10% of all tradesand volume, while their total net holding is not more than 2000 contracts.The case of HFTs is even more extreme in the sense that, while representingonly 0.1% of all traders, they account for almost one third of the total dailytrading volume. Moreover, their net position tends to quickly revert to amean of about zero (an estimated half-life of the inventory holding periodof 137 seconds) and rarely exceeds more than 3000 contracts. Moreover, theaverage order sizes of intermediaries are almost half of those of HFTs, and in-termediaries tend to reduce their inventories to their target levels at a slowerrate than HFTs do it (inventory half-life is 173 seconds), by primarily usingmarketable orders. Overall, for both HFTs and intermediaries, almost 80%of their orders are entirely passively executed, even if these stand for only50% of their traded volume, which still corresponds to lower aggressivenessratios than those of LFTs.

Besides the previous quantitative statistics which might be given by in-trinsic features such as latency, trading frequency, order sizes, target inven-tories, there is also more substantial behavioral discrepancy between the twotypes, which also leads to a difference in their profitability. According to Kir-ilenko et al. (2011), HFTs seem to correctly anticipate price changes, openpositions aggressively in the direction of the current price (contemporaneousand of the past four seconds), and try to close their positions by submittingresting limit orders in the direction of the anticipated price move. How-ever, if their risk and inventory management objective requires it, HFTs canalso offset their positions by submitting marketable orders.10 On the otherside, intermediaries trade in the opposite direction of the immediate pricesand their first two lags, but in the direction of the past three to eight seconds.

As in the previous section we try to model and implement strategiesmatching the empirically observed behaviors. According to EUREX, themain HFT-based strategies are liquidity provision, (statistical) arbitrage,

10After about 10 to 20 seconds, HFTs appear to reverse the direction of their trading.

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short term momentum trading and liquidity detection.11 Except for thestatistical arbitrage, which deals with pairs of assets rather than a singleasset, the other identified strategies can be classified in two main groups: (i)passive (uninformed) strategies which try to cash in the bid-ask spread whenthe order flow is balanced, and (ii) active (informed) strategies which try topredict the short-term market direction due to new information or just dueto participants’ order flow. Strategy-wise, we consider these two classes tocorrespond to the intermediaries and HFT types described in Kirilenko et al.(2011), i.e. we propose an electronic liquidity provision (ELP) strategy forintermediaries and a predatory strategy for HFTs. In the current contribu-tion, we will deal only with the first type and leave the latter for furtherresearch.

Electronic liquidity provision (ELP) – liquidity traders

ELP is a high-frequency quasi market making strategy, which seeks to cap-ture both the bid-ask spread and the rebates paid by the trading venues asincentives for posting liquidity, with no obligation of participating in the mar-ket at all times. ELP agents are poorly informed about fundamental valuesand therefore try to minimize the risk of liquidity provision by quickly offset-ting even small inventory imbalances or by trying to identify toxic order flowwhich would ultimately lead them to opening positions against the futuremarket move.12 These tight inventory management objectives make themuse marketable orders more often than what would be expected in the caseof traditional market makers. However, even if their round-trip gains andinventory sizes are smaller than the ones of better informed (human) marketmakers, their overall profitability comes from a larger number of round-tripsdue to quoting more often at the best bid and ask, which is equivalent tocashing in a higher cumulative spread.

Our implementation of the ELP agents reproduces to a large extent themodel proposed in Vuorenmaa and Wang (2013), which is further based onthe model introduced by Avellaneda and Stoikov (2008) – a representativemodel for inventory-based market making. In more detail, the optimal bidand ask quotes are identified following a two-step procedure. First, a reser-vation price (a personal indifference valuation for the asset) is computed asa deviation from the mid-price mt, given the current inventory imbalance It

11“High-frequency trading – a discussion of relevant issues”, London, 8 May2013, http://www.eurexchange.com/blob/exchange-en/455384/490346/6/data/

presentation_hft_media_workshop_lon_en.pdf12In a literature review, Aldridge (2013) identifies two main types of automated market

making models: inventory- and information-based models. The first class is concernedonly with the effective management of inventory, without any opinion on the drift or anyautocorrelation structure, while the latter tries to identify the true value from the marketitself, rather than relying on external fundamental information.

13

http://www.eurexchange.com/blob/exchange-en/455384/490346/6/data/presentation_hft_media_workshop_lon_en.pdf

http://www.eurexchange.com/blob/exchange-en/455384/490346/6/data/presentation_hft_media_workshop_lon_en.pdf

and the current instant volatility σ2t (see equation(2.6)).

rt(It) = mt − γelp It σ2t (2.6)

where γelp stands for the risk aversion coefficient.

In the second step, the optimal spread size around the reservation pricert is determined. For this, we rely on the simplified version proposed byVuorenmaa and Wang (2013), where the market maker’s spread is arbitraryequal to st + 2 exp(|ξ|), where st is the (current) bid-ask spread and ξ is anormal distributed noise with a standard deviation σξ = 0.01, contributingto some heterogeneity. Most of the heterogeneity in quotes is induced bythe different inventory holdings and by the effective activation and requotingtime. Furthermore, we consider the bid and ask quote sizes to be constantand equal to βELP

size – if one of the quotes is partially or completely filled, itwill be replaced with a new full-sized quote at the next agent activation. TheELP agents’ wake-up clock is fixed at constant time intervals βELP

tf . In orderto desynchronize their activation processes, only the first wake-up event isdrawn from an exponential distribution with λ = 1/βELP

tf . However, not everywake-up coincides with quotes being updating, since requoting is set up asa probabilistic event constrained by the current inventory imbalance relativeto the maximum allowed inventory threshold IELPmax – the higher the inventoryimbalance, the more probable a requoting event is, and when the inventoryimbalance exceeds the maximum threshold requoting becomes certain (seeequation(2.7)).

Probt(It) = max(1, (It/IELPmax )2) (2.7)

3 Simulations setup and results

3.1 Model parameters and calibration

Simulations are run over one individual trading day which lasts for 6 hoursand 45 minutes (from 08:30 to 15:15 CT), summing up to 243e05 microsec-onds.13 Before recording the actual trading session, each simulation is warmed-up for one hour. The underlying fundamental value f = 1200.00 is consid-ered constant throughout the entire simulation – since during the trading daythere are no exogenous fundamental shocks, the entire intraday dynamics isonly due to endogenous micro-structure factors. The daily time series of the

13This period corresponds to the open hours of the components of S&P 500 index, whichis the underlying asset of the CME S&P 500 E-mini futures.

14

previous ten closing prices is initialized using a random walk process withan initial closing price peod−10 = f , a daily drift µeod = −0.005 f and a dailyvolatility σeod = 0.005 f , corresponding to an overall negative daily trend.

As already mentioned, the LF agents are represented by a cluster-typeimplementation, i.e. one single instance per type, since their trading deci-sions are not influenced by the current individual portfolios. The parame-ters of the clusters refer to the following dimensions: time frame βtf, strat-egy weights (i.e. fundamentalist wfund, end-of-day/ intraday trend followingwtrend(eod)/wtrend(id), end-of-day/ intraday mean reversion wrev(eod)/wrev(id),and noise strategy wnoise respectively), order size distribution mean βsizeand upper cutoff bsize. The time frame, the order size distribution meanand upper cutoff are computed as described in Subsection 2.1, in order toreproduce the traders category descriptive statistics from (Kirilenko et al.;2011). These setup parameters are marked as bold in Table 1. The otherparameters represent ad-hoc choices, so that the emergent market propertiesreproduce a set of target statistics, reflecting a wide range of market andtrader categories characteristics such as: price, volume, trading frequency,quotes and order flow, agents’ aggressiveness, market share and net invento-ries. A second set of parameters deals with the order submission mechanismand their values are set as in Mandes (2014): order book imbalance baseµ = 2, book depth levels N = 3, size penalty exponent η = 0.8, volatilitybands σis = 7σ, σdyn = 7.5σ, and the weights of the adjusted risk cost func-tion α0 = 0.1, α1 = 0.5, α2 = 0.25, β = 2.5. The cancellation probability forthe oldest order sent by a LF cluster is λc = 0.4771 as in Cui and Brabazon(2012), where it was determined from empirical data.

BUY SELL OPP. SMALLβtf (ms) 268 268 81 1226βsize 14.09 14.20 8.80 1.23bsize 200 200 100 9wfund 0.9 0 – 0wtrend(eod) 0.2 0.9 – 0wtrend(id) 0 0 – 0wrev(eod) 0 0.2 – 0wrev(id) 0 0 – 0wnoise 0 0 – 1

Table 1: Calibration of the LFT types

The implementation of the ELP agents is realized in more detail thanin the LFT case. Instead of building clusters of trading agents, each ELPis individually instantiated, with its own timeline and portfolio. The strat-egy time frame is assumed to be constant βELP

tf = 1 second – dependent onthe agents’ technological capacities, i.e. fixed activation time, and its valuecorresponds to the average trading frequency documented in Kirilenko et al.(2011). Furthermore, the risk aversion coefficient is common for all ELPagents γELP = 1.0, as well as their default quote sizes βELP

size = 7. The two

15

missing parameters related to ELP, i.e. the number of agents NELP and theirmaximum inventory thresholds IELPmax , are described together with the simula-tion scenarios in Subsection 3.2.

3.2 Simulation scenarios

In this section, several scenarios trying to capture various market configu-rations and global outcome possibilities are defined. In order to assess theimpact of HFTs, a base-line scenario with LFTs only is set up (markedwith “LFT” in Table 2 and following tables). One comparative HF scenariomarked with “LFT w. hom. ELPs” extends the previous scenario by addingNELP = 100 electronic liquidity provision agents with a tight and homoge-neous maximum inventory threshold IELPmax = 10. The homogeneity assumptionis useful for the grid-analysis of the relation between various pairs of factorsand associated outcomes, and could be explained by agents applying a set ofcommon popular algorithms and by using the same short-time window high-frequency data as input.14 The homogeneous ELPs scenario is further dividedinto two sub-scenarios, one without and one with financial transaction taxes,as explained in Section 4. As an alternative to the homogeneous setup, wealso run a heterogenous scenario marked “LFT w. het. ELPs”, where thequoted sizes are uniformly distributed βELP

size ∼ U(1, 12) and IELPmax = k βELPsize

are multiples of the quoted sizes, where k ∼ U(1, 10) – the ELPs’ strategiesremain common, but they have different parameterizations.

The previous market configurations are run under two different marketstates, representing regular and extreme (“stressed”) market conditions. Thelatter correspond to the “Flash Crash of 2:45” scenario, as described in Kir-ilenko et al. (2011). Their investigation results show that the flash crashwas triggered by a large sell program of 75,000 contracts, which has usedan execution algorithm based on a volume-in-line strategy (also known aspercentage of volume), targeting an execution rate of 9% of the previousminute trading volume. Therefore, in the flash crash scenario an additionalagent (marked as “POV”), reproducing the sell program described earlier, isadded to the implementation. The agent is activated at 13:30 CT and exe-cutes market sell orders of a size equal to 9% of the previous minute volumewithout its own execution share, at a fixed βPOV

tf = 1 minute frequency, untilthe program is finished or until the end of the trading session, i.e. 15:15 CT.

Each of the scenarios is run 100 times with different random seeds andboth the mean and the standard deviation of the individual key statisticsare reported. Tables 3 and 4 present a list of descriptive statistics reflectingvarious facets of market quality, corresponding to the previously introduced

14Actually, this is one of the concerns expressed by Danielsson and Zer (2012) – a toolarge homogeneity of strategies could contribute to an increasing systemic risk.

16

Transaction taxMarket state

regular stressed

Age

nts

LFT only no

LFT w. hom. ELPsnoyes

LFT w. het. ELPs no

Table 2: Simulation scenarios configurations

experiment setups. Moreover, Tables 5 and 6 capture the agents’ tradingstatistics under the various scenarios. The results show that under bothmarket conditions, the total trading volume increases substantially (six toeight times) when ELPs agents are introduced. When no extreme eventoccurs (such as a flash crash), ELPs account for about 45% of the total num-ber of trades and total trading volume – the extreme event outcome willbe treated separately in Subsection 3.3. The overall liquidity is also highlyimproved in the simulations including ELPs. All spread measures are fourtimes smaller when the ELPs are homogenous and three times smaller withheterogenous ELPs, as compared to the base-line scenario. The virtual mar-ket impact of executing a market order with a size of 100 is also three to fourtimes lower. The market depth at quotes and within a 25 bps range aroundthe mid-price are about two times larger, while the market depths within50 and 100 bps are similar, and the total market depth within 200 bps isactually slightly smaller. This means that the total order book liquidity islower and concentrated more towards the best quotes (thinner tails) in thescenarios with ELPs. On one side, this is due to the ELPs strategy of placingquotes close to the best bid and asks, but also because of LFTs preferringto send four times more market orders, and corespondent fewer limit orders,due to the lower immediacy costs. The same aspect can also be identified inthe increasing trade and volume aggressiveness ratio of LFTs, i.e. the shareof orders and proportion of orders consuming order book liquidity (in otherwords, executed against passive/ outstanding limit orders). It is to be notedthat, in our implementation, the LFTs’ order submission behavior is reactiveto the market microstructure factors. As a consequence, LFTs might alsocompete with ELPs for a better execution chance by placing more aggressivelimit orders. The improved liquidity can also be observed in the case of thePOV sell program, which is able to execute a larger share of its initial orderand with smaller execution costs. By looking at the percentage of marketdepth accounted by ELPs, one can see that ELPs contribute with 80% of thetotal volume at the best quotes and their contribution decreases for furtheraway price levels. The book gaps measures have a high standard deviationand we cannot conclude for any significant differences. However, the logiccould argue that the sum of the first gaps is smaller for heterogenous ELPsdue to their strategy differences.

Both range volatility and the realized standard deviation at 1-minutefrequency show a substantial decrease – the standard deviation of 1-minute

17

returns is almost half than in the base-line model and the daily range volatil-ity gets close to zero. Consequently, also the daily return is close to zerowhile it is negative in the LFT-only case.15 The differences are even morepronounced when the market stress scenario is evaluated. In the base-linecase the market drop is one percent larger and the range volatility is higher,while these statistics remain unchanged when the ELPs are present and noextreme event occurs. Basically, for the HF set ups, no major differences be-tween the regular and stress market states can be identified by looking at thegeneral market statistics. A deeper analysis of the flash crash events, lookingat the inter-agents feed-back loops, is conducted in the next section. Finally,regarding price efficiency, both considered variance ratios do no capture anysignificant difference, but in the end there is no new exogenous informationincoming into the model during the trading day.

The differences between the base-line and the high-frequency setups canalso be assessed by visually inspecting the plots 3, 4 and 5, where a mixedscenario is recorded – in the first two and a half hours of the trading dayboth LFTs and ELPs are active, while after 11:00 CT ELPs are switched offand the market is made by LFTs only – actually, for about an hour, someremaining ELP limit orders are still in the market, but are not refreshed aftertheir execution. These plots reflect the intraday dynamics of various marketand agent measures for a single run. Regimes switches at the moment whenELPs are disabled can be observed in the intraday time series for most ofthe individual plots, and the changes are also in line with the average resultspreviously described in this section.

3.3 The anatomy of a flash crash

A flash crash is a market event of extreme volatility, where the price experi-ence a sudden drop, followed by a rapid rebound. The most notorious flashcrash is the one which has occurred on May 6, 2010 on the E-mini S&P 500stock index futures market.16 However, since 2007 more than 15,000 differ-ent events similar to a flash crash have been identified in several individual

15The negative day return in the LFT-only set up is due to the previous descendingdaily trend and due to the selected mix of strategies applied by the opportunistic traders,which puts a larger weight on chartist components – there are four chartist versus onefundamentalist component.

16On that day, according to Kirilenko et al. (2011), a large sell program started sometimeafter 13:30 CT. During a 13 minute period, between 13:32:00 and 13:45:27 CT, the E-minicontract declined with 5.1%. Over the course of the next second, a cascade of executedorders caused the price of the E-mini to drop another 1.3% and the following transactionwould have triggered a drop in price of another 6.5 index points. This has triggered theCME Globex Stop Logic Functionality, which pauses all transactions for 5 seconds even ifthe market remains open for orders to be submitted, modified or canceled. At 13:45:33,the E-mini exited the Reserve State, the market resumed trading and after fluctuating fora few seconds, the price began a rapid ascent until it reached the levels before the drop.

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stocks.17

In our artificial environment, similar sudden price drops can be replicatedfor HF set ups including ELPs and a POV sell program. The probability ofa flash crash depends however on the chosen set of model parameters. Forexample, in order to test the influence of the number of ELP agents NELP

and of the maximum inventory threshold IELPmax , under the homogeneity as-sumption, we run a grid simulation over the Cartesian product for two setsof values, one for each factor, and plot the results in the upper heatmap ofFigure 2.18 It seems that the critical number of agents, which can coordinatein a way leading to the emergence of a flash crash, is between 10 and 50.Moreover, the tighter the inventory control, the higher is the probability ofa flash crash. Even if seldom, extreme events occur also for larger popu-lations of ELPs when their maximum inventory thresholds are small. Theparameters-wise heterogenous ELPs scenario is also tested and its resultswith respect to different levels of activity time frame and agents number arerepresented in the bottom plot of Figure 2. Compared to the homogenousset up, the flash crash probabilities for the time frame (1000 milliseconds)and same average inventory threshold (approx. 30) become zero, even withinthe critical agents number range.

In order to analyze what happens during a flash crash, we select the mar-ket configuration “LFT w. hom. ELPs” described in the previous subsection,i.e. number of ELP agents NELP = 100 and maximum inventory thresholdIELPmax = 10. This corresponds to a flash crash probability of 6% which makesit a rare event. The overall market quality measures in Table 4 and theagents’ activity statistics in Table 6 show that the total trading volume in-creases fivefold – on May 6, 2010 a twofold increase in activity has beenreported. Individually, the ELPs carry the main responsibility with a factorof ten increase in activity. The fundamental buyers, the day traders andthe POV sell program also contribute by doubling to tripling their tradedvolumes. However, the general market quality is worse than in the non-flashcrash scenario, under all aspects – the order book liquidity is thinner, thevolatility skyrockets and the variance ratios show an increasing price overre-action. Another important remark is that the aggressiveness ratios of ELPsjumps from 6% to 50%, which reflects a very hectic inventory managementactivity. On the other side, the LF market participants find the opportunityof executing their trades in a more favorable passive manner. A striking dif-ference can be observed with respect to the ELPs total profitability – theirsteady profits made during normal market conditions or during market stress,but without a flash crash, conditions become very volatile when a flash crashoccurs and can turn even into huge losses. The large standard deviation fullyreflects this uncertainty.

17http://www.nanex.net/FlashCrash/OngoingResearch.html18The other ELP-related parameters are fixed as follows: activation time frame βELPtf = 1

second, risk aversion coefficient γELP = 1.0 and default quote sizes βELPsize = 7.

19

http://www.nanex.net/FlashCrash/OngoingResearch.html

Next, we propose a “radiography” of the intraday dynamics along a largeset of indicators computed at a one-minute frequency. Two runs with thesame calibration as previously described, but with different random seedsand opposite outcomes with respect to the flash crash occurrence, are chosenand depicted in two sets of figures: 6, 7, 8 and 9, 10, 11 respectively. Fromthe “ELP long holdings” time series (the third plot from the top) one canobserve that, when the POV sell program starts, the long positions of ELPsrise to levels two times higher than at any previous moment during the day.In the no flash outcome, these positions are offset quickly just by quotingmore aggressive sell limit orders – the “Spread” time series shows how thebid-ask spread tightens. The main consequence is that ELP trading is con-ducted with LFTs – there is little ELP to ELP volume as indicated by the“ELP-ELP volume share” time series. Afterwards and until the end of thetrading session, ELPs mostly carry a total net short position caused by LFopportunistic traders’ activity, which is compensated and complementary tothe continued POV sell activity. Actually, after start of the sell program weobserve an increased market quality reflected by the lowest daily values ofinstant volatility, higher depth at quotes and steady bid-ask spreads.

On the other side, in the flash crash case, the initial shock to the ELPs’long positions induced by the beginning of the POV sell program is offset ag-gressively against other ELPs which open other long positions instead (“hot-potato” or “pass-the-parcel” effect) – observable in the “ELP-ELP volumeshare” time series of Figure 9. This activity is associated with a one-minutevolume spike which triggers larger POV sell market orders, and a volumefeed-back loop is created. In repeatedly trying to close their refreshed andincreasingly larger long positions, ELPs get more and more aggressive, andconsume the order book liquidity on their way (see all market depth timeseries). The LFTs seem not to be capable of significantly refilling the bid sideof the order book in such a short period of time, and the ELPs are left to bethe main liquidity providers at quotes and within the 25 and 50 bps rangesaround the mid-price (see the correspondent “ELP depth share” time series).Eventually, the order book liquidity deteriorates and no market participantcan provide the necessary liquidity required by the “hyperinflated” POV sellprogram.

4 Testing regulatory policies

After a crisis or after extreme events like the May 6, 2010 Flash Crash, reg-ulators are faced with a large amount of public pressure to take action andcorrect what went wrong. This is not always an easy task, because an unam-biguous historical precedent from which to draw conclusions might not exist,

20

or just because financial markets constitute such complex systems whose re-action might be very tricky to be assessed. Moreover, regulators have to takeinto consideration the risk that the consequences of their actions could exac-erbate or generate a new bigger problem than the one which is supposed to betackled. A variety of possible policies targeted to improving the overall mar-ket performance and to reducing the risks of market failure, in the contextof large market automation, have been proposed in Foresight: The Future ofComputer Trading in Financial Markets (2012). These include notification ofalgorithms, circuit breakers, minimum tick size requirements, market makerobligations, minimum resting times, minimum order-to-execution ratios, pe-riodic auctions, maker-taker pricing, order priority rules and internalisationof agency order flow. In Europe there are also heated debates around the op-portunity of imposing financial-transaction taxes, and countries like Franceand Italy have already implemented such taxes for specific asset types.

Agent-based modeling frameworks are attractive because they allow forthe virtual experimentation of innovative policy options and for simulating alarge range of scenarios. If the model assumptions are realistic enough, themodel parameters are calibrated to the specific problem at hand, and themodels are able to reproduce realistic market behaviors in a robust manner,reliable policy making could also be developed within such artificial labo-ratories. The current contribution tries to assess the impact of imposingminimum resting times and financial-transaction taxes. Harris (2002) sug-gests that transaction taxes penalize HF strategies more than longer-terminvestors, since the former imply a larger number of trades. In our imple-mentation, the resting time can be simulated by controlling the activity timeframe of the ELPs, while the introduction of a transaction tax is consideredto increase the minimum quoted spread size of the ELPs, in order to coverthe extra trading cost and remain profitable.19

In order to experiment the previously mentioned policy options, we setup a model with the most unfavorable parametrization corresponding to a100% flash crash probability under market stress condition, i.e. NELP = 30homogenous ELPs with IELPmax = 10 maximum inventory threshold. Two rangesof values for the two policy factors are proposed and 100 runs for each of thepossible combinations are recorded. The results are presented in the formof a heatmap in Figure 2 and show that the flash crash probability reactsmore to varying the minimum spread than to the agents’ trading frequency.The main explanation is that by quoting larger spreads, ELPs diminish theirshare of volume at best quotes with about 30%, and thus the “hot-potato”effect can be avoided.

Nonetheless, imposing a financial transaction tax, which completely elim-

19Just for completion, all other simulations in the paper consider a no minimum quotedspread, which is equivalent to a minimum quoted spread size of zero.

21

inates the risk of a flash crash, has also an impact on the agents’ tradingactivity and on the overall market quality. HFTs’ market share drops from46% to around 20% and the majority of most market quality measures takevalues between the LFT-only and HFT with no transaction tax market con-figurations, but more closer to the LFT-only base-line set up.

5 Conclusions and outlook

We have designed and implemented an event-driven agent based model of acontinuous double auction financial market. This design allows for a realisticrepresentation of time and for the independent activity of all its components,with no central control. As a consequence, the agents included in our modelcan be calibrated according to various time-related trading statistics whichare found in the literature or computed from empirical data. Furthermore,the model output can be compared directly with real time series. The fourtypes of low-frequency agents identified in the literature – fundamental buy-ers and seller, opportunistic day traders, small noisy traders – have beenimplemented, matching their empirical trading statistics. The order sub-mission mechanism is a key component of order book trading and we haveincluded one of the most realistic existing models, which is built around anoptimisation problem minimizing the risk-adjusted execution cost and tak-ing into account a relevant set of microstructure factors. This makes the LFagents reactive to their trading environment, which is ultimately influencedalso by HF market participants. Finally, one type of HFTs corresponding tothe electronic liquidity provision strategies has also been included into themodel.

Next, a sequence of different scenarios has been simulated in order totry to answer some of the open questions regarding the impact of HFTs oncurrent financial markets. We find that in general ELPs have a positivecontribution to the market quality, as assessed by a large range of marketquality indicators, grouped along three main lines: (i) liquidity and transac-tion costs, (ii) price efficiency and price discovery, (iii) volatility and financialmarket stability. These results are also in line with the empirical findings.Furthermore, at least for ELP strategies, there is no causality between ELPactivity and increased volatility. We can also confirm that a large homogene-ity with respect to HFT strategies can contribute to the systemic risk – whenheterogeneity within parameters is simulated, even for a common strategy,the market becomes more robust under stress conditions.

Moreover, we have also reproduced the chaotic properties of financialsystems and showed how rare events such as flash crashes can emerge byconducting a detailed inspection. Thus, we can conclude that even if ELPs

22

are not the primary cause of a flash crash, they can amplify the total tradingvolume while trying to aggressively offset their inventory imbalances. WhenELPs discard their positions to other ELPs, a “hot-potato” effect emergeswhich is associated with an increased traded volume. If a POV sell program,targeting a fixed trading rate linked to the previous market volumes, doesnot implement also some limits in order to account for extraordinary andunexpected scenarios, we have the sufficient ingredients for keeping alive avolume feed-back loop. One useful side-note for execution algo developers isthat volume alone should not be mistaken for liquidity. Finally, two possi-ble policy options regarding minimum resting times and financial-transactiontaxes have been evaluated within the developed artificial environment. Wehave shown that imposing transaction taxes helps by lowering the probabilityof flash crashes, but they also negatively impact the ELPs activity and theoverall market quality.

Future research suggestions include the assessment of other policy mea-sures such as minimum order-to-execution ratios, notification of algorithmsaccompanied by volume throttling, minimum tick size requirements andmaker-taker pricing. Additionally, the heterogeneity of ELPs could be ex-tended to other strategy parameters such as the sensitivity coefficient γelp

or even to implementing different ELP strategies such as those from theinformation-based class. An example of a market making strategy relyingon Bayesian learning to combine new information with prior beliefs aboutthe true market value is provided by Das (2005, 2008). Also the currentlyimplemented ELP and POV strategies could be upgraded to more intelligentalgorithms, including also a risk management component. For example, theELPs could monitor an flow toxicity metric such as the Volume-SynchronizedProbability of Informed Trading introduced by Easley et al. (2012) and switchoff when order flow becomes toxic. On the other side, the POV executionalgorithm could also include a price cap and stop selling when the price dropsbelow a given limit. Finally, a further extension should implement also thesecond class of HFT described in Kirilenko et al. (2011), i.e. predatory ororder anticipating strategies.

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Olive, D. J. (2008). Applied robust statistics, Preprint M-02-006.,http://www.math.siu.edu .

Sornette, D. and Von Der Becke, S. (2011). Crashes and high frequencytrading, UK Government Office for Science, Foresight Driver Review -The Future of Computer Trading in Financial Markets .

Vuorenmaa, T. A. and Wang, L. (2013). An agent-based model of the flashcrash of may 6, 2010, with policy implications, Available at SSRN 2336772.

25

Reg

ula

rm

ark

etco

nd

itio

ns

LF

Ton

lyL

FT

w.

hom

.E

LP

sL

FT

w.

het

.E

LP

sn

on

tran

sact

ion

tax

tran

sact

ion

tax

Tra

din

gvolu

me

134,6

70

(8,9

82)

1,0

39,1

63

(136,3

08)

356,5

77

(48,9

98)

866,9

09

(75,3

66)

Aver

age

trad

esi

ze4.3

9(0

.037)

4.4

7(0

.058)

4.5

8(0

.037)

4.1

9(0

.15)

1-m

intr

ad

ing

freq

uen

cy75.8

0(4

.92)

573.8

3(6

7.5

6)

192.1

4(2

5.1

1)

511.0

0(5

0.8

5)

Per

centa

ge

retu

rn(%

)-1

.54

(0.5

2)

-0.0

13

(0.2

6)

0.5

9(0

.8)

-0.3

9(0

.15)

Mark

etord

ers

share

(%)

4.6

9(0

.35)

23.0

7(1

.91)

11.9

1(1

.77)

20.9

7(1

.55)

Mark

etim

pact

exp

on

ent

0.7

6(0

.12)

0.8

7(0

.17)

0.7

7(0

.075)

0.8

4(0

.11)

Sp

read

-at-

tou

ch2.6

7(0

.19)

0.6

4(0

.069)

1.8

3(0

.03)

0.8

1(0

.071)

Sp

read

-at-

tou

ch(b

ps)

23.6

8(1

.90)

5.6

6(0

.60)

16.0

4(0

.43)

7.1

4(0

.63)

Rel

ati

ve

effec

tive

spre

ad

(bp

s)22.2

4(2

.08)

6.0

0(0

.39)

16.4

8(0

.36)

7.4

1(0

.41)

Imp

act

for

100

un

its

(bp

s)14.7

7(2

.15)

3.7

1(0

.55)

8.5

3(0

.22)

4.3

6(0

.41)

Mark

etd

epth

(at

qu

ote

s)9.9

3(0

.44)

24.4

1(8

.38)

13.8

6(0

.8)

20.4

2(1

.79)

Mark

etd

epth

(≤25

bp

s)1,0

59

(113)

2,2

42

(144)

1,4

85

(119)

2,1

58

(158)

Mark

etd

epth

(≤50

bp

s)3,0

54

(214)

4,0

93

(289)

2,8

79

(281)

4,0

79

(325)

Mark

etd

epth

(≤100

bp

s)6,7

81

(519)

7,0

68

(561)

5,6

48

(512)

7,1

95

(611)

Mark

etd

epth

(≤200

bp

s)12,0

57

(1,2

92)

10,6

70

(972)

9,6

99

(913)

11,2

02

(1,1

08)

EL

Pd

epth

share

(at

qu

ote

s)85.8

9(2

.04)

52.5

1(4

.1)

79.2

2(2

.70)

EL

Pd

epth

share

(≤25

bp

s)29.5

6(4

.17)

49.4

8(4

.55)

29.3

6(2

.79)

EL

Pd

epth

share

(≤50

bp

s)17.3

4(1

.40)

26.7

4(3

.02)

16.1

6(1

.67)

EL

Pd

epth

share

(≤100

bp

s)10.1

1(0

.81)

12.8

5(1

.09)

9.2

1(1

.01)

EL

Pd

epth

share

(≤200

bp

s)6.7

4(0

.64)

7.5

4(0

.66)

5.9

8(0

.76)

Book

gap

s(≤

25

bp

s)49.3

4(5

.63)

59.1

7(1

9.8

7)

35.4

(5.2

5)

35.3

5(1

1.9

2)

Book

gap

s(≤

50

bp

s)166.1

2(1

0.8

6)

212.2

6(1

3.3

4)

126.4

3(1

7.9

9)

201.9

8(1

6.2

8)

Book

gap

s(≤

100

bp

s)471.5

3(2

3.6

3)

469.4

4(3

1.5

6)

556.3

7(3

9.5

1)

477.4

5(3

0.8

9)

Book

gap

s(≤

200

bp

s)1,1

69.9

0(6

2.8

1)

955.3

1(6

9.8

5)

1,1

69.4

6(9

5.5

5)

979.0

1(7

6.2

2)

10-m

invar.

/1-m

invar.

0.1

5(0

.043)

0.1

2(0

.029)

0.4

2(0

.14)

0.1

2(0

.022)

1-m

invar.

/10-s

ecvar.

0.2

3(0

.028)

0.1

8(0

.017)

0.2

2(0

.025)

0.1

7(0

.012)

Ran

ge

vola

tility

(%)

1.9

7(0

.52)

0.3

7(0

.16)

1.5

4(0

.49)

0.4

7(0

.11)

Rea

lize

d1-m

inst

d.

dev

.(%

)0.0

23

(0.0

02)

0.0

10

(0.0

01)

0.0

21

(0.0

02)

0.0

12

(0.0

01)

Fla

shcr

ash

pro

bab

ilit

y0.0

(0.0

)0.0

(0.0

)0.0

(0.0

)0.0

(0.0

)H

igu

chi

fract

al

dim

ensi

on

1.8

6(0

.033)

1.9

4(0

.028)

1.6

4(0

.054)

1.9

4(0

.020)

Tab

le3:

Mar

ket

key

met

rics

under

nor

mal

condit

ions

Th

em

arke

tw

idth

refl

ects

the

cost

per

un

itof

liqu

idit

yan

dw

eco

mp

ute

itin

term

sof

mark

etim

pact

totr

ad

ea

size

of

100,

i.e.

the

cost

totr

ad

eco

mp

are

dto

the

mid

-poi

nt.

Th

eeff

ecti

vesp

read

istw

ice

the

mid

poin

tb

ench

mark

edtr

an

sact

ion

cost

an

dth

ere

lati

veeff

ecti

vesp

read

rep

rese

nts

the

rati

oof

the

effec

tive

spre

adto

the

curr

ent

mid

poi

nt.

Ab

asis

poi

nt

(ab

bre

via

ted

as

’bp

s’)

isa

un

itth

at

iseq

ual

to1/100th

of

1%

.M

ark

etd

epth

isco

mp

ute

din

nu

mb

erof

shar

es.

Th

eva

lues

inp

aren

thes

isre

pre

sent

the

stan

dard

dev

iati

ons

of

the

des

crip

tive

stati

stic

sco

mp

ute

dov

er30

run

s.

26

LF

Ton

lyL

FT

w.

hom

.E

LP

sL

FT

w.

het

.E

LP

sn

on

tran

sact

ion

tax

tran

sact

ion

tax

non

Fla

shC

rash

Fla

shC

rash

Tra

din

gvolu

me

131,1

07

(9,3

27)

1,0

57,9

07

(139,3

12)

5,0

15,9

89

(469,4

87)

358,5

26

(48,1

01)

870,1

14

(74,6

34)

Aver

age

trad

esi

ze4.4

5(0

.048)

4.5

4(0

.056)

4.5

8(0

.096)

4.6

1(0

.035)

4.1

9(0

.15)

1-m

intr

ad

ing

freq

uen

cy72.7

8(5

.02)

574.9

1(6

8.9

1)

2,7

06.1

7(2

67.5

6)

191.8

6(2

4.6

3)

513.0

2(5

0.7

4)

Per

centa

ge

retu

rn(%

)-2

.45

(0.7

4)

0.0

09

(0.2

6)

-100.0

0(0

.000)

-0.8

1(0

.54)

-0.4

3(0

.14)

Mark

etord

ers

share

(%)

4.5

0(0

.35)

23.0

7(1

.98)

4.8

1(0

.89)

11.5

5(1

.62)

20.6

8(1

.52)

Mark

etim

pact

exp

on

ent

0.8

3(0

.22)

0.8

6(0

.18)

–0.7

5(0

.077)

0.8

3(0

.11)

Sp

read

-at-

tou

ch2.7

1(0

.20)

0.7

7(0

.073)

1,6

62.2

6(1

,576.7

1)

1.8

3(0

.028)

0.9

2(0

.068)

Sp

read

-at-

tou

ch(b

ps)

24.1

1(1

.98)

6.7

5(0

.64)

16,5

83

(5,7

36.4

8)

16.0

7(0

.40)

8.1

1(0

.59)

Rel

ati

ve

effec

tive

spre

ad

(bp

s)22.3

5(1

.97)

6.6

6(0

.43)

63.1

2(2

55.9

5)

16.5

2(0

.35)

8.0

9(0

.39)

Imp

act

for

100

un

its

(bp

s)15.1

2(2

.23)

4.0

6(0

.61)

4.1

1(1

.38)

8.5

7(0

.22)

4.6

9(0

.41)

Mark

etd

epth

(at

qu

ote

s)10.5

0(0

.46)

31.8

0(9

.12)

19.5

5(4

.19)

16.5

9(1

.89)

24.1

2(1

.80)

Mark

etd

epth

(≤25

bp

s)982.3

6(1

00.7

5)

2,1

88.1

2(1

44.1

9)

1,5

78.3

1(9

9.0

7)

1,3

67.0

5(9

6.8

1)

2,1

17.7

1(1

55.9

5)

Mark

etd

epth

(≤50

bp

s)2,8

61.5

1(2

01.6

0)

4,0

42.2

4(2

95.4

1)

2,8

03.5

5(1

71.2

9)

2,6

71.8

8(2

44.9

2)

4,0

47.8

3(3

21.2

5)

Mark

etd

epth

(≤100

bp

s)6,4

98.2

6(4

96.1

4)

7,0

21.6

4(5

74.3

8)

4,9

08.2

5(2

98.9

8)

5,4

72.8

8(4

85.7

8)

7,1

74.6

6(6

06.4

4)

Mark

etd

epth

(≤200

bp

s)11,8

83

(1,1

96.5

0)

10,6

27

(1,0

04.2

2)

7,3

28.6

9(5

40.5

0)

9,8

06.2

5(9

04.0

1)

11,1

81

(1,1

04.9

4)

EL

Pd

epth

share

(at

quote

s)87.8

6(2

.06)

66.2

2(1

0.4

7)

58.3

8(3

.81)

81.2

7(2

.28)

EL

Pd

epth

share

(≤25

bp

s)28.9

9(3

.99)

24.7

0(1

.59)

53.6

9(4

.40)

28.8

9(2

.84)

EL

Pd

epth

share

(≤50

bp

s)16.9

0(1

.44)

14.1

3(0

.60)

29.1

2(3

.19)

15.8

0(1

.67)

EL

Pd

epth

share

(≤100

bp

s)9.8

1(0

.83)

8.0

9(0

.45)

13.1

0(1

.13)

8.9

8(1

.01)

EL

Pd

epth

share

(≤200

bp

s)6.5

4(0

.65)

5.4

7(0

.29)

7.4

0(0

.66)

5.8

3(0

.75)

Book

gap

s(≤

25

bp

s)50.3

7(5

.46)

56.7

1(1

8.1

7)

43.7

5(2

7.5

9)

38.5

8(4

.86)

34.9

0(1

1.5

8)

Book

gap

s(≤

50

bp

s)170.9

9(1

0.3

0)

209.3

0(1

2.9

3)

164.7

2(1

6.2

8)

141.6

8(1

9.3

9)

204.6

7(1

5.6

5)

Book

gap

s(≤

100

bp

s)479.4

0(2

2.8

2)

462.8

7(3

1.0

0)

369.3

8(3

0.6

5)

568.1

0(3

7.6

5)

472.2

2(3

0.8

2)

Book

gap

s(≤

200

bp

s)1,1

72.1

8(5

9.8

7)

929.8

5(6

8.3

6)

784.9

8(3

4.1

0)

1,1

79.8

1(9

0.8

9)

960.6

1(7

5.4

5)

PO

Vp

rogra

mco

mp

lete

d(%

)3.5

3(0

.59)

30.3

7(2

.49)

81.0

5(1

6.0

9)

11.4

8(2

.25)

24.5

8(1

.50)

PO

Vim

ple

m.

short

fall

-6.8

2(4

.22)

-0.6

2(0

.55)

-1,0

72.0

2(3

86.2

0)

-7.3

6(2

.97)

-1.4

9(0

.33)

PO

Vim

ple

m.

short

fall

(%)

-0.6

(0.4

)-0

.1(0

.0)

-93.0

(32.0

)-0

.64

(0.2

6)

-0.1

(0.0

)10-m

invar.

/1-m

invar.

0.2

0(0

.061)

0.1

4(0

.037)

0.0

25

(0.3

8)

0.4

9(0

.16)

0.1

3(0

.027)

1-m

invar.

/10-s

ecvar.

0.1

8(0

.059)

0.1

2(0

.016)

0.0

08

(0.0

12)

0.1

9(0

.029)

0.1

1(0

.009)

Ran

ge

vola

tility

(%)

2.7

6(0

.81)

0.4

2(0

.18)

254,0

20,4

59

(208,4

46,6

79)

1.7

2(0

.27)

0.4

7(0

.10)

Rea

lize

d1-m

inst

d.

dev

.(%

)0.0

23

(0.0

04)

0.0

09

(0.0

01)

332,2

81

(362,7

87)

0.0

21

(0.0

02)

0.0

10

(0.0

01)

Fla

shcr

ash

pro

bab

ilit

y(%

)0.0

(0.0

)6.0

(0.0

)0.0

(0.0

)0.0

(0.0

)H

igu

chi

fract

al

dim

ensi

on

1.7

9(0

.044)

1.8

9(0

.035)

1.6

5(0

.29)

1.6

1(0

.049)

1.9

1(0

.023)

Tab

le4:

Key

met

rics

under

the

mar

ket

stre

sssc

enar

io(i

ncl

udin

gP

OV

)

Th

eim

ple

men

tati

onsh

ortf

all

ofth

eP

OV

Sel

lP

rogr

amis

com

pu

ted

as

the

diff

eren

ceb

etw

een

the

volu

me

wei

ghte

dav

erage

exec

uti

on

pri

ce(V

WA

P)

an

dth

ear

riva

lp

rice

.

27

LF

Ton

lyL

FT

w.

hom

.E

LP

sL

FT

w.

het

.E

LP

sn

on

tran

sact

ion

tax

tran

sact

ion

tax

BUY

Tra

din

gvolu

me

56,8

79

(3,9

85.5

1)

205,9

33

(20,1

29)

113,1

64

(23,3

00)

183,8

07

(13,6

37)

Tra

din

gm

ark

etsh

are

(%)

17.9

2(0

.43)

8.8

6(0

.70)

13.6

3(0

.93)

9.3

3(0

.75)

Volu

me

mark

etsh

are

(%)

20.5

6(0

.67)

9.4

8(0

.92)

15.2

7(1

.14)

10.1

3(0

.93)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

74.7

3(5

.87)

96.3

3(1

.22)

94.8

9(1

.34)

94.9

2(0

.34)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

72.2

0(7

.26)

95.5

5(1

.45)

94.6

3(1

.60)

93.4

1(0

.56)

e-o-d

inven

tory

56,8

79

(3,9

85.5

1)

205,9

33

(20,1

29)

113,1

64

(23,3

00)

183,8

07

(13,6

37)

e-o-d

pro

fit

(x1,0

00)

-63,1

07

(21,5

09)

-233,5

77

(26,0

49)

-130,0

16

(30,2

89)

-209,4

24

(16,9

21)

SELL

Tra

din

gvolu

me

70,7

79

(4,0

67.8

7)

412,2

51

(25,3

40)

154,8

99

(10,9

91)

372,2

55

(13,8

29)

Tra

din

gm

ark

etsh

are

(%)

23.1

6(1

.47)

18.3

1(1

.23)

19.5

7(1

.50)

19.5

1(1

.34)

Volu

me

mark

etsh

are

(%)

25.8

0(1

.80)

19.5

4(1

.56)

21.4

2(1

.65)

21.0

3(1

.35)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

25.9

9(7

.45)

84.9

4(1

.92)

39.1

6(6

.30)

80.9

7(1

.70)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

27.7

6(8

.10)

83.2

4(2

.23)

37.9

1(6

.46)

77.7

0(2

.23)

e-o-d

inven

tory

-70,7

79

(4,0

67.8

7)

-412,2

51

(25,3

40)

-154,8

99

(10,9

91)

-372,2

55

(13,8

29)

e-o-d

pro

fit

(x1,0

00)

86,3

71

(181.4

3)

468,6

69

(34,0

71)

173,5

31

(12,0

95)

424,2

22

(22,5

49)

OPP.

Tra

din

gvolu

me

136,8

16

(13,5

59)

473,2

44

(48,6

48)

308,6

92

(70,1

92)

419,6

60

(37,3

75)

Tra

din

gm

ark

etsh

are

(%)

52.7

3(1

.95)

24.5

7(2

.17)

44.7

1(4

.03)

25.2

4(2

.31)

Volu

me

mark

etsh

are

(%)

50.1

7(2

.20)

22.4

4(2

.28)

42.3

6(4

.03)

23.7

9(2

.19)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

56.5

9(0

.93)

89.3

1(1

.33)

64.2

5(3

.97)

87.5

6(1

.64)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

53.5

0(1

.06)

88.2

7(1

.36)

62.1

7(3

.95)

85.9

4(1

.87)

e-o-d

inven

tory

17,8

64

(3,9

96.8

9)

210,2

73

(13,0

78)

46,8

66

(16,3

30)

192,3

15

(13,5

63)

e-o-d

pro

fit

(x1,0

00)

-15,1

31

(20,5

85)

-238,3

40

(22,2

22)

-53,4

12

(24,0

33)

-218,9

18

(18,3

95)

SMALL

Tra

din

gvolu

me

4,8

65.8

8(2

40.2

9)

7,9

14.1

8(3

38.4

6)

6,6

09.1

3(5

18.9

2)

7,4

47.6

7(2

75.1

5)

Tra

din

gm

ark

etsh

are

(%)

6.1

9(0

.37)

1.3

4(0

.11)

3.3

2(0

.24)

1.4

1(0

.11)

Volu

me

mark

etsh

are

(%)

1.0

3(0

.17)

0.0

00

(0.0

00)

0.1

4(0

.35)

0.0

00

(0.0

00)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

10.7

4(0

.73)

70.7

1(1

.62)

22.7

0(2

.09)

64.6

9(2

.48)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

10.6

5(0

.79)

70.9

8(1

.67)

22.8

5(2

.14)

64.9

9(2

.51)

e-o-d

inven

tory

-3,9

63.6

2(2

22.0

6)

-3,8

39.4

8(1

67.8

3)

-4,5

58.8

3(3

10.6

1)

-3,7

48.5

5(1

35.3

6)

e-o-d

pro

fit

(x1,0

00)

27.5

9(9

.56)

-3.9

8(3

.81)

-22.7

2(3

1.2

0)

2.2

8(2

.14)

ELP

Tra

din

gvolu

me

978,9

83

(232,8

39)

129,7

91

(18,1

41)

750,6

48

(135,9

85)

Tra

din

gm

ark

etsh

are

(%)

46.9

1(3

.90)

18.7

6(3

.55)

44.5

1(4

.09)

Volu

me

mark

etsh

are

(%)

46.1

9(4

.40)

18.0

5(3

.65)

42.5

7(3

.89)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

6.0

1(5

.59)

0.0

(0.0

)4.8

0(5

.63)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

6.5

3(6

.03)

0.0

(0.0

)4.5

7(5

.31)

e-o-d

inven

tory

-115.3

9(1

15.4

6)

-571.2

4(4

27.1

4)

-117.4

8(7

7.9

0)

e-o-d

pro

fit

(x1,0

00)

244.7

8(3

1.1

6)

40.9

5(2

6.2

6)

252.2

1(1

3.8

1)

Tab

le5:

Age

nt

stat

isti

csunder

nor

mal

condit

ions

Th

een

d-o

f-d

ayp

rofi

tsre

flec

tth

ein

trad

ayca

shfl

owas

soci

ate

dw

ith

trad

ing,

as

wel

las

the

vir

tual

pro

fit

from

mark

ing

tom

ark

etth

een

d-o

f-d

ayin

vento

ry.

28

LF

Ton

lyL

FT

w.

hom

.E

LP

sL

FT

w.

het

.E

LP

sn

on

tran

sact

ion

tax

tran

sact

ion

tax

non

Fla

shC

rash

Fla

shC

rash

BUY

Tra

din

gvolu

me

56,9

09

(4,3

14.6

4)

213,5

99

(19,8

25)

570,3

61

(124,2

16)

108,8

42

(20,2

73)

188,9

64

(13,8

08)

Tra

din

gm

ark

etsh

are

(%)

18.2

8(0

.45)

9.0

6(0

.73)

4.2

1(0

.62)

13.1

4(0

.70)

9.5

7(0

.76)

Volu

me

mark

etsh

are

(%)

21.1

8(0

.70)

9.6

8(0

.93)

4.9

8(1

.00)

14.5

7(0

.90)

10.4

2(0

.91)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

71.2

3(6

.03)

96.2

1(0

.96)

31.7

9(1

0.3

2)

92.8

3(2

.32)

94.8

5(0

.36)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

67.5

0(7

.26)

95.4

1(1

.14)

25.6

2(9

.59)

91.9

6(2

.78)

93.3

1(0

.54)

e-o-d

inven

tory

56,9

09

(4,3

14.6

4)

213,5

99

(19,8

25)

570,3

61

(124,2

16)

108,8

42

(20,2

73)

188,9

64

(13,8

08)

e-o-d

pro

fit

(x1,0

00)

-60,1

87

(20,8

72)

-239,8

06

(25,4

77)

-177,3

82

(10,9

59)

-126,3

93

(27,9

19)

-214,2

48

(13,6

55)

SELLT

rad

ing

volu

me

68,7

27

(4,6

52.8

6)

405,9

34

(23,5

76)

460,4

37

(31,0

10)

153,2

27

(12,5

41)

366,4

16

(12,5

65)

Tra

din

gm

ark

etsh

are

(%)

23.3

1(1

.47)

17.8

0(1

.25)

3.9

3(0

.61)

19.3

9(1

.31)

19.0

7(1

.31)

Volu

me

mark

etsh

are

(%)

25.7

5(1

.82)

18.8

4(1

.55)

4.0

7(0

.61)

21.0

1(1

.43)

20.6

7(1

.39)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

28.0

6(7

.51)

81.4

8(1

.61)

62.0

4(6

.67)

44.8

8(5

.28)

76.5

1(1

.64)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

30.0

2(8

.15)

79.5

4(1

.84)

55.5

8(7

.52)

43.8

2(5

.45)

72.5

6(2

.19)

e-o-d

inven

tory

-68,7

27

(4,6

52.8

6)

-405,9

34

(23,5

76)

-460,4

37

(31,0

10)

-153,2

27

(12,5

41)

-366,4

16

(12,5

65)

e-o-d

pro

fit

(x1,0

00)

86,1

38

(5,9

35.7

4)

460,8

49

(30,6

47)

680,8

72

(273,4

46)

175,6

67

(13,4

78)

413,6

76

(22,6

53)

OPP.

Tra

din

gvolu

me

129,4

48

(12,9

91)

488,1

02

(48,1

53)

841,0

34

(146,7

60)

283,6

57

(59,8

19)

429,6

25

(37,7

52)

Tra

din

gm

ark

etsh

are

(%)

51.9

1(1

.96)

25.0

5(2

.23)

7.5

8(0

.40)

41.4

4(3

.14)

25.7

6(2

.31)

Volu

me

mark

etsh

are

(%)

48.8

0(2

.21)

22.7

7(2

.29)

7.9

5(0

.61)

38.7

8(3

.09)

24.2

7(2

.22)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

56.1

0(0

.93)

88.1

0(1

.22)

46.1

9(1

0.5

8)

66.5

4(3

.18)

86.5

2(1

.65)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

53.0

6(1

.10)

87.1

0(1

.26)

37.6

9(1

0.8

5)

64.4

9(3

.17)

84.8

6(1

.83)

e-o-d

inven

tory

18,0

63

(3,8

22.3

0)

219,4

97

(12,7

46)

-46,5

13

(131,7

86)

56,8

69

(11,6

87)

199,9

80

(12,9

81)

e-o-d

pro

fit

(x1,0

00)

-14,8

60

(20,4

65)

-250,4

41

(21,1

47)

719,3

48

(556,5

39)

-65,7

15

(22,5

45)

-224,6

10

(19,8

57)

SMALL

Tra

din

gvolu

me

4,4

80.5

9(2

64.2

9)

8,0

43.1

8(3

15.3

2)

12,8

99

(1,6

20.1

7)

6,0

68.3

3(4

62.9

9)

7,5

35.4

3(2

67.9

0)

Tra

din

gm

ark

etsh

are

(%)

5.9

4(0

.35)

1.3

6(0

.12)

0.3

5(0

.028)

3.0

6(0

.20)

1.4

3(0

.11)

Volu

me

mark

etsh

are

(%)

1.0

0(0

.000)

0.0

00

(0.0

00)

0.0

00

(0.0

00)

0.0

10

(0.1

0)

0.0

00

(0.0

00)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

11.3

0(0

.82)

67.3

9(1

.76)

42.5

7(6

.74)

25.0

8(2

.01)

60.7

7(2

.12)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

11.2

3(0

.87)

67.7

6(1

.82)

33.7

4(9

.78)

25.2

4(2

.05)

61.0

9(2

.14)

e-o-d

inven

tory

-3,5

94.6

7(2

31.2

6)

-3,8

22.2

3(1

80.3

3)

-2,9

61.7

6(1

,101.7

3)

-4,0

65.6

7(2

44.9

7)

-3,7

34.4

3(1

25.2

8)

e-o-d

pro

fit

(x1,0

00)

61.2

0(2

1.7

2)

-4.5

9(3

.59)

9,0

74.9

4(1

,214.6

8)

38.2

9(1

4.1

7)

4.3

1(1

.23)

ELP

Tra

din

gvolu

me

977,3

59

(239,8

19)

8,0

86,4

57

(694,6

88)

156,6

49

(14,8

27)

729,2

56

(134,8

53)

Tra

din

gm

ark

etsh

are

(%)

46.0

1(4

.09)

83.6

2(0

.66)

22.1

7(2

.66)

43.3

1(4

.12)

Volu

me

mark

etsh

are

(%)

45.2

0(4

.48)

80.1

0(1

.53)

21.6

1(2

.71)

41.1

9(3

.88)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

6.2

3(5

.83)

50.5

6(1

.89)

0.0

(0.0

)4.8

9(5

.71)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

6.6

6(6

.23)

52.3

6(2

.28)

0.0

(0.0

)4.6

8(5

.41)

e-o-d

inven

tory

-563.2

3(2

61.1

1)

341.2

3(1

76.5

5)

190.6

1(7

06.0

7)

-362.3

6(1

36.3

0)

e-o-d

pro

fit

(x1,0

00)

268.2

1(2

9.7

5)

-979,7

29

(2,0

07,8

15)

39.5

1(2

7.4

4)

265.1

8(1

4.7

3)

POV

Tra

din

gvolu

me

2,6

49

(440.9

3)

22,7

77

(1,8

69.7

9)

60,7

90

(12,0

66)

8,6

08

(1,6

84)

18,4

32

(1,1

24.9

0)

Tra

din

gm

ark

etsh

are

(%)

0.5

7(0

.062)

0.7

2(0

.066)

0.3

0(0

.034)

0.8

1(0

.074)

0.8

5(0

.083)

Volu

me

mark

etsh

are

(%)

0.5

3(0

.50)

0.8

5(0

.36)

0.0

00

(0.0

00)

0.9

7(0

.17)

0.8

5(0

.36)

Tra

de

aggre

ssiv

enes

sra

tio

(%)

100.0

0(0

.000)

100.0

0(0

.000)

100.0

0(0

.000)

100.0

0(0

.000)

100.0

0(0

.000)

Volu

me

aggre

ssiv

enes

sra

tio

(%)

100.0

0(0

.000)

100.0

0(0

.000)

100.0

0(0

.000)

100.0

0(0

.000)

100.0

0(0

.000)

e-o-d

inven

tory

-2,6

50

(441)

-22,7

77

(1,8

69.7

9)

-60,7

90

(12,0

66)

-8,6

08

(1,6

84)

-18,4

32

(1,1

24.9

0)

e-o-d

pro

fit

(x1,0

00)

14.5

7(1

0.1

4)

40,6

03

(9,6

97.0

4)

4,6

13.3

9(1

7,1

51)

42.6

0(2

1.7

6)

12,8

86

(19,7

81)

Tab

le6:

Age

nt

stat

isti

csunder

stre

ssm

arke

tco

ndit

ions

(incl

udin

gP

OV

)

29

0

10

20

30

40

50

60

70

80

90

100

%

10 10 10

20

20

30

40

50

90

100

50 100 150

20

40

60

80

100

Flash crash probability

ELPs Number

Max

imum

Inve

ntor

y

0

10

20

30

40

50

60

70

80

90

100

%

10

20

30 40

60

70

80

100

500 1000 1500 2000

0

50

100

150

200

250

Flash crash probability

Time frame

Spr

ead

Figure 2: Flash crash probabilities for various model configurations and pol-icy options

The upper plot reflects the outcomes of different number of homogenous ELP agents vs.their maximum threshold inventory levels (their activity time frame is fixed to one secondand their quote size to seven). The lower plot shows the impact of varying the activitytime frames (milliseconds) vs. the minimum spread (ticks) on the flash crash probability.

30

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offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch offELPs switch off

1135

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seed: −1462441651

0500

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Time

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Inst

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Figure 3: Price, volume and market quality time series – LFT w. hom. ELPsuntil 11:00

31


0

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Dep

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Figure 4: Other market quality time series (ctd.) – LFT w. hom. ELPs until11:00

32


0

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dep

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Gap

s w

ithin

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Figure 5: Other market quality time series (ctd.) – LFT w. hom. ELPs until11:00

33

Sell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program startSell program start

1164

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050

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long

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09:00 10:00 11:00 12:00 13:00 14:00 15:00

ELP

sho

rt h

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ngs


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10

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09:00 10:00 11:00 12:00 13:00 14:00 15:00ELP

−E

LP v

olum

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are


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1.0

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Spr

ead


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0.006

09:00 10:00 11:00 12:00 13:00 14:00 15:00

Inst

ant v

olat

ility

Figure 6: Price, volume and market quality time series – LFT w. hom. ELPs,POV (no flash crash)

34


0

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Dep

th w

ithin

100

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Figure 7: Other market quality time series (ctd.) – LFT w. hom. ELPs, POV(no flash crash)

35


7.5

10.0

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ELP

dep

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Dep

th w

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6

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dep

th s

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Gap

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Gap

s w

ithin

200

bps

Figure 8: Other market quality time series (ctd.) – LFT w. hom. ELPs, POV(no flash crash)

36


030

060

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ELP

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long

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ELP

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09:00 10:00 11:00 12:00 13:00 14:00 15:00ELP−

ELP

vol

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shar

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Spr

ead


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Inst

ant v

olat

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Figure 9: Price, volume and market quality time series – LFT w. hom. ELPs,POV (flash crash)

37


0

20

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09:00 10:00 11:00 12:00 13:00 14:00 15:00

Dep

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09:00 10:00 11:00 12:00 13:00 14:00 15:00ELP

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Dep

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Dep

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09:00 10:00 11:00 12:00 13:00 14:00 15:00

Dep

th w

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Figure 10: Other market quality time series (ctd.) – LFT w. hom. ELPs,POV (flash crash)

38


0

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ELP

dep

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dep

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09:00 10:00 11:00 12:00 13:00 14:00 15:00

Gap

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Gap

s w

ithin

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bps

Figure 11: Other market quality time series (ctd.) – LFT w. hom. ELPs,POV (flash crash)

39

Documents

Joint Discussion Paper Series in Economics...ventory control and simulated the 2010 Flash Crash (May 6, 2010) scenario, where a sudden market drop was triggered by a volume-inline