Impact of High-Frequency Trading LatencyOn Market Quality

A DISSERTATION SUBMITTED TO THE UNIVERSITY OF MANCHESTERFOR THE DEGREE OF MASTER OF SCIENCE IN THE FACULTY OF

ENGINEERING AND PHYSICAL SCIENCES

2015

By

Ogunsakin Rotimi Samuel

School of Computer Science

Contents

1 Introduction 121.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3 Report Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Background and Related Work 162.1 High Frequency Trading (HFT) And Algorithmic Trading (AT) . . . . . 162.2 High Frequency Trading (HFT) Strategies . . . . . . . . . . . . . . 18

2.2.1 Impact of HFT Strategies On Market Quality . . . . . . . . 202.3 High Frequency Trading (HFT) And Latency . . . . . . . . . . . . 22

2.3.1 Impact of HFT Latency On Market Quality . . . . . . . . . 252.4 High Frequency Trading (HFT) Simulation . . . . . . . . . . . . . 28

3 Research Design And Methodology 303.1 Theoretical Methodology - Mathematical Modelling . . . . . . . . . 303.2 Experimental Methodology - Simulation Modelling . . . . . . . . . 31

3.2.1 Discrete-Event Simulation (DES) . . . . . . . . . . . . . . . 333.2.2 Agent-Based Simulation (ABS) . . . . . . . . . . . . . . . . 343.2.3 Simulation Tool - Simulink and SimEvents . . . . . . . . . . 353.2.4 Summary of Simulation Assumptions . . . . . . . . . . . . . 36

4 Mathematical Modelling 374.1 Price Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3 Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Simulation Modelling 485.1 Discrete-Event Modelling - SimEvents . . . . . . . . . . . . . . . . . 485.2 High Frequency Trading and Latency . . . . . . . . . . . . . . . . . 51

5.2.1 Order Generation and Exchange . . . . . . . . . . . . . . . . 535.2.2 Exchange, CEP and ZI . . . . . . . . . . . . . . . . . . . . . 545.2.3 Order Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2.4 Trade Confirmation and Announcements . . . . . . . . . . . 575.2.5 Sample Simulation Run . . . . . . . . . . . . . . . . . . . . 575.2.6 Market Data Feed . . . . . . . . . . . . . . . . . . . . . . . 59

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6 Evaluation and Results 616.1 Scenario 1: HFTs With Same Latency . . . . . . . . . . . . . . . . 616.2 Scenario 2: HFTs With Varied Latency . . . . . . . . . . . . . . . . 656.3 Scenario 3: HFTs With Same Latency to Exchange But Varied

Market Data Latency . . . . . . . . . . . . . . . . . . . . . . . . . . 726.4 Scenario 4: HFTs With Varied Latency to Exchange And Varied

Market Data Latency . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7 Conclusions and Future Works 797.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

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List of Figures

2.1 Common Characteristics of AT and HFT [19] . . . . . . . . . . . . 172.2 Specific Characteristics of AT Excluding HFT [19] . . . . . . . . . . 172.3 Specific Characteristics of HFT [19] . . . . . . . . . . . . . . . . . . 182.4 Common High Frequency Based Strategies - Adapted from Gomber

et al (2011) [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Percentage of Latency-Related US Equity Exchange Revenues [24] . 242.6 Percentage of US Institutional Equity Exposed to Latency Risk . . 252.7 Latency Impact and Order Book Probability Estimate [27] . . . . . 263.1 Simulation System Dynamics . . . . . . . . . . . . . . . . . . . . . 354.1 Graph of Price Discovery Index (P ) Against Speed (S) . . . . . . . 384.2 Graph of Liquidity Index (L) Against Latency Lag (θ) . . . . . . . 414.3 Graph of Volatility Index (V ) Against Latency Lag (θ) . . . . . . . 445.1 Exchange Design: Trader, Exchange, Order Book and Data Vendor 525.2 Simulation Model: Order Generation and Exchange . . . . . . . . . 535.3 Exchange, CEP and ZI . . . . . . . . . . . . . . . . . . . . . . . . . 545.4 Order Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.5 Trade Confirmation and Announcement . . . . . . . . . . . . . . . . 575.6 Snap-shot: Sample Simulation Run . . . . . . . . . . . . . . . . . . 585.7 Market Data Feed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.1 Two HFTs with equal latency to the Exchange . . . . . . . . . . . . 626.2 Multiple HFTs with equal latency to the Exchange . . . . . . . . . 646.3 Multiple HFTs with varied latency to the Exchange (10 fHFTs and

10 sHFTs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.4 VWAP for multiple HFTs with varied latency to the Exchange(10

fHFTs and 10 sHFTs) . . . . . . . . . . . . . . . . . . . . . . . . . . 676.5 Multiple HFTs with varied latency to the Exchange (70% fHFTs

and 30% sHFTs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.6 VWAP for multiple HFTs with varied latency to the Exchange (70%

fHFTs : 30% sHFTs) . . . . . . . . . . . . . . . . . . . . . . . . . . 696.7 Multiple HFTs with same latency to the Exchange but varied mar-

ket data deed latency . . . . . . . . . . . . . . . . . . . . . . . . . . 726.8 Multiple HFTs with varied latency to the Exchange and to the Data

Vendor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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6.9 Multiple HFTs with varied latency to the Exchange and to the datavendor (Reverse Test) . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.10 Multiple HFTs with varied latency to the Exchange and to the DataVendor (Extreme Test) . . . . . . . . . . . . . . . . . . . . . . . . . 77

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List of Tables

3.2 Roadmap for Simulation Method - Adopted from [42] . . . . . . . . 326.2 Summary of Simulation Results for Scenario 2 . . . . . . . . . . . . 706.4 Simulation Results for 21:9 HFTs Ratio Scenario . . . . . . . . . . . 706.6 Simulation Results for 18:12 HFTs Ratio Scenario . . . . . . . . . . 716.8 Summary of Simulation Results for Scenario 3 . . . . . . . . . . . . 746.10 Summary of Simulation Results for Scenario 4 (Extreme) . . . . . . 78

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AbstractThis project work evaluates the impact of High Frequency Trading (HFT) Latencyon market quality which are Liquidity, Price Discovery and Volatility. To achievethis, a Mathematical and Simulation Model were developed. The MathematicalModel provides an in-depth analysis of HFT Latency and its resulting impacts onmarket quality which correlate with empirical results from literatures and providecausal explanation to some observed impact of HFT Latency. The result of theSimulation Model shows that (1) HFTs volatilise security prices due to their latencydominance and later reverse their strategy to push prices back to their efficientlevel by trading in opposite direction and thus, profiting from the Bid/Ask spread.(2) Latency between HFTs and the exchange (for Order submission) is most para-mount compare to Market Data-feed latency when investigating latency impact onmarket quality and (3) The impact of the Data-feed latency is recoverable giventhat (i) The latency-lag is very small - approximately 5ms (ii) Provided that thespecific order under consideration is large enough to last for a duration proportionalto the Data-feed latency-lag (4) The impact of latency-lag for order submission isnot recoverable within a trading window. Finally, we conclude that HFT Latencypositively impact Liquidity; contributes positively to Price efficiency for the fastHFTs while the slow HFTs in-cured a latency-cost for pricing information ineffi-ciencies; contribution to Volatility depends on which side of the market we analyse- considering the opening and closing of a security price, it was observed that HFTpositively impact volatility. But looking at the intermediaries, that is, in-betweenthe opening and closing price, volatility is introduced and cleared before the endof the trading window.

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DeclarationNo portion of the work referred to in this dissertation has been submitted insupport of an application for another degree or qualification of this or any otheruniversity or other institute of learning.

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Copyright1. The author of this dissertation (including any appendices and/or schedules

to this dissertation) owns certain copyright or related rights in it (the “Copy-right”) and s/he has given The University of Manchester certain rights to usesuch Copyright, including for administrative purposes.

2. Copies of this thesis, either in full or in extracts and whether in hard orelectronic copy, may be made only in accordance with the Copyright, Designsand Patents Act 1988 (as amended) and regulations issued under it or, whereappropriate, in accordance with licensing agreements which the Universityhas from time to time. This page must form part of any such copies made.

3. The ownership of certain Copyright, patents, designs, trade marks and otherintellectual property (the “Intellectual Property”) and any reproductions ofcopyright works in the dissertation, for example graphs and tables (“Repro-ductions”), which may be described in this dissertation, may not be ownedby the author and may be owned by third parties. Such Intellectual Propertyand Reproductions cannot and must not be made available for use withoutthe prior written permission of the owner(s) of the relevant Intellectual Prop-erty and/or Reproductions.

4. Further information on the conditions under which disclosure, publicationand commercialisation of this dissertation, the Copyright and any IntellectualProperty and/or Reproductions described in it may take place is available inthe University IP Policy (see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant Thesis restriction declarations depos-ited in the University Library, The University Library’s regulations (seehttp://www.manchester.ac.uk/library/aboutus/regulations) and in The Uni-versity’s policy on presentation of Dissertations.

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AcknowledgementsI would like to say a special thank you to my supervisor, Dr. CharalamposTheodoulidis (Babis) for his mentorship and support through out my dissertationperiod.

Special thanks to the School of Computer Science and Manchester BusinessSchool, most especially my lecturers: Dr. Gavin Brown, Prof. Christopher Hol-land, Dr. Yu-wang Chen, Dr Nadia Papamichail, Prof Peter Kawalek, Prof. JohnKeane and Dr. Daniel Dresner for offering me the foundation needed to carry outthis research.

Special thanks to my government, The Federal Republic of Nigeria for its sup-port via the TETFund Scholarship and the University of Port Harcourt, my almamater and the institution I am committed to serve.

Profound gratitude to Prof. Joseph Ajienka and Prof. Henry Njoku for theirmentorship, love and support. And a heart felt gratitude to Joe and Stella Ogun-sakin for always there for me.

A big thank you to my siblings, for their prayers, unswerving love, care andsupport and of course “Lizy” for her love, prayers and troubles.

A big thank you to my friends: Vignaraja, Alan and Farouk. You guys mademy Manchester experience a memorable one.

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DedicationFrom the deepest depth of heart...

To the Almighty God...To my late Father...To my lovely and caring Mother...To my Siblings...To my Family and Friends...

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Chapter 1

1 Introduction

The arrival of automation in the exchanges gradually brings to an end the involve-ment of human professional floor brokers and market makers. Over time, theseprofessional tasks were fully replaced with high speed computers and sophisticatedalgorithms (Algorithms for large order processing and automated market making)and the resulting savings from high wages and commission paid to human profes-sional brokers and market makers were passed onto investors and traders in formof lowered trading fee and rebate.

High Frequency Trading (HFT) as a consequence of this automation, the prolif-eration of HFT in the present day equity market, and the unboundedness of tech-nology innovation both in communication, microprocessor design and the abilityto manage complex algorithms more efficiently had contributed to pushing HFTactivities to its limit. HFT employs different trading strategies which are majorlyElectronic liquidity provisioning, Statistical arbitrage, Liquidity detection and Dir-ectional strategies (Market inference and News) among others. These strategiesand their underlying algorithms are gradually becoming homogenous across theHFTs and have shifted competition to latency (Speed) instead of strategies. Thisaccount for the high investment by “Top HFT Firms” into reducing latency frommilliseconds to micro-second, including the exchanges [1].

High Frequency Trading (HFT) is a primary form of Algorithmic Trading (AT)characterised by the use of sophisticated technology tools and computer algorithmsto rapidly trade securities [2]. According to the United States Security and Ex-change Commission (SEC), High Frequency Traders (HFTs) are proprietary trad-ing firms that use high speed (very low latency) systems to monitor market data,submit large amount of orders to the market, and utilise quantitative and al-gorithmic methodologies to maximise the speed of their market access and trad-ing strategies [3]. Other characteristics attributed to HFTs are: (1) The use ofhigh-speed and sophisticated computer programs to generate, route, and executeorders; (2) The use of co-location services and individual data feeds offered byexchanges and other service providers to minimise network and other types oflatencies (like processing speed); (3) Very short time-frames for establishing andliquidating positions; (4) Submission of numerous orders that are cancelled shortly

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after submission; and (5) Ending a typical trading day in as close to a flat positionas possible (that is, not carrying significant, unhedged positions overnight) [3].

HFT accounts for market share of over 70% in the Unites States equity marketin 2013 [4], 40% of Europe equity market [5], and according to TABB Group,HFT accounts for 77% of the UK equity market [2]. With the largest share ofthe equity market dominated by HFTs, it is evident that HFT activities wouldbe a predominant trading activity exhibiting the highest impact on equity marketquality, which are liquidity, price discovery and volatility. Thus, a detailed analysisof the impact of HFT trading activities which include trading strategies and latencyarm-race on market quality is highly imperative and beneficial to the equity marketand the global economy.

Research works in this domain have examined the impacts of HFT Strategieson market quality: Empirically using trading data or theoretically by buildingMathematical Models [5, 7, 8, 10].There are also research works that have examinedthe impact of latency on market quality with main focus on exchange latency [9] orHFT Latency[12, 13, 14] using trading data. None of the researches on the effectof latency on market quality has explored a simulation approach to examine theimpact of latency on market quality using different scenarios and varied latencylag between Fast HFTs and Slow HFTs or between HFTs and non-HFTs to gaininsight into the fierce latency competition taking place among the HFTs and theircorresponding impact on equity market quality.

In this research work, a Mathematical Model is developed based on valid as-sumptions from empirical and theoretical results in research literatures, to analyseand evaluate the impact of HFT latency on market quality - Liquidity, Price dis-covery and Volatility. With the result of the Mathematical Model as a proposed“Hypothesis”, a Simulation Model is used to simulate the interaction of minimumof two HFTs with an exchange using Discrete Event Simulation (DES) Model-ling. Agent Based Simulation (ABS) Modelling is used to model the interactionof the different HFTs with the order book. These HFTs are configured to tradeusing “same strategy” based on the principle of “Zero Intelligence” [15, 16] butwith varied latency to the exchange. Since our interest is in examining the effectof latency on market quality, it is natural to keep strategy constant by allowing allmarket participants (HFTs and non-HFTs) to trade with same strategy and varythe parameter we wish to evaluate (Latency). The result of each simulation epochare visualised and analysed to evaluate the impact of latency on Liquidity, Price

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discovery and Volatility. The final results of these simulations are juxtaposed withthat of the Mathematical Model “Proposed Hypothesis” and empirical results fromresearch literatures.

1.1 Aim

Analyse and evaluate the impact of HFT latency on equity market quality - liquid-ity, price discovery and volatility, using Mathematical and Simulation Modelling.

1.2 Objectives

• Learning Objectives

– Identify and understand the different HFT strategies and their under-lying mathematical, statistical, quantitative and qualitative models

– Understand the microstructure of the equity market and latency in thecontext of HFT

– Have an in-dept understanding of the equity market architecture, in-formation (Market order, limit order and trade announcement) pathwayand trader-to-exchange interconnection

– Understand Mathematical Modelling and Simulation Modelling (Dis-crete Event simulation (DES) and Agent Based Simulation (ABS)) andtheir application in the domain of financial intelligence

• Deliverable Objectives

– Develop a Mathematical Model based on empirical results from researchliteratures to theorise the impact of latency on market quality - Liquid-ity, Price discovery and Volatility

– Use Discrete-Event Simulation (DES) to model the interaction of mul-tiple traders (HFTs with varied latency) with an Exchange

– Use Agent-Based Simulation (ABS) to model the interaction of thevarious traders (HFTs and non-HFTs) with the order book

– Collect, analyse and visualise data during the simulation run and aftereach simulation epoch to examine the impact of latency variation (highand low) on market quality - Liquidity, Price discovery and Volatility

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1.3 Report Outline

This research work is structured as follows: In Chapter 2, a literature review ofthe evolution of HFT as a subset of Algorithmic Trading (AT) [17]; The differentHFT strategies and their impact on equity market quality; Effect of HFT latencyvariation on market quality; And the application of theoretical model (Mathem-atical Model) and simulation model (Discrete-Event Simulation and Agent BasedSimulation Model) in the domain of financial intelligence is done. Chapter 3 con-tains the Research Design and Methodology where the theoretical and simulationmodel are discussed in detail, including the underlying assumptions, theoreticallogic and approach used in developing the simulation model. Chapter 4 and 5contain the implementation of the Mathematical Model and the Simulation Modelrespectively. In Chapter 6, the simulation model is evaluated using different scen-arios, and the results of these different scenarios are analysed and discussed. Thisresearch work is concluded in Chapter 7 which also include recommendation forfurther work and immediately followed by references.

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Chapter 2

2 Background and Related Work

This research work investigates the Impact of HFT latency on market quality usingtheoretical and simulation approach. There are existing research in this area but aspointed out earlier, none has explored a simulation approach. However, It is veryimperative that the results of these research works be reviewed. This will form thebasis on which the results of both the Mathematical and Simulation Models in thisresearch will be evaluated. Some assumptions will be made in the Mathematicaland Simulation Model based on the results from empirical research in this domain.

HFT will first be reviewed as a subset of Algorithmic Trading (AT) [17], toclearly differentiate between HFTs and non-HFTs. The different HFT strategiesas available in the literatures will be reviewed next, followed by the theoretical andempirical research on the effect of HFT strategies on market quality. The conceptof latency in the context of HFT will also be reviewed followed by the impact oflatency on market quality and finally, research works where simulation approachhave been used to investigate the effect of HFT strategies on market quality willbe reviewed and formed the basis for the simulation model.

2.1 High Frequency Trading (HFT) And Algorithmic Trading (AT)

In algorithmic trading (AT), computers are directly interfaced with trading plat-forms and submitting orders to the exchange without immediate human interven-tion, these computers possesses inbuilt sophisticated algorithms that make tradingdecision based on the result of observes historical market data and other informa-tion at very high frequency, often in milliseconds [18]. HFT as a subset of AT alsopossesses similar characteristic as AT, that is, the use of sophisticated algorithmsto make trading decision at milliseconds. However, the difference between AT andHFT is that ATs mostly have longer holding period that are minutes, days, weeks,months or even longer, whereas HFTs hold a very short position, mostly in secondsor less and attempt to close the trading day in a neutral position[5].

To further differentiate between ATs and HFTs, Characteristics common to ATand HFT and those specific to AT and HFT are presented below: Figure 2.1 showsthe common characteristics of AT and HFT.

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Figure 2.1: Common Characteristics of AT and HFT [19]

There are characteristics that are specific to AT and not commonly associatedwith HFT. The specific focus is usually on intelligently working an order throughtime and across market to minimise market impact of large orders relative to apre-defined benchmark[19]. The Table in Figure 2.2 shows those characteristicsspecific to AT which are commonly not associated with HFT.

Figure 2.2: Specific Characteristics of AT Excluding HFT [19]

HFT strategies are naturally geared towards a high liquid instrument and asa prerequisite, HFTs rely on high speed (low latency) access to market, achievedby high investment in high-speed communication link to the exchange; usage ofco-location/proximity service; and dedicated/individual data feed. The Table inFigure 2.3 shows characteristics specific to HFT which are usually not associatedwith AT.

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Figure 2.3: Specific Characteristics of HFT [19]

2.2 High Frequency Trading (HFT) Strategies

While the diversity and opaqueness of the HFT universe makes it difficult to beable to examine all strategies, there are well known strategies, most of whichwere in existence before the advent of HFT but were made more effective throughthe use of high-speed computing infrastructures, communication networks, andsophisticated algorithms. Figure 2.4 below shows the list of some of the popularHFT Strategies as identified in the research domain.

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Figure 2.4: Common High Frequency Based Strategies - Adapted from Gomber etal (2011) [19]

Electronic Liquidity Provision (Market Making)

Market making refers to a strategy in which a market maker (in this case an HFTTrader) simultaneously post both buy and sell limit orders for a financial instru-ment on both side of the electronic order book in order to profit from the bid-askspread and at the same time providing liquidity to market participants [6, 19]. Toencourage provision of liquidity in the equity market, HFTs who provide liquidityare given rebate as a compensation for the risk involve in liquidity provisioning,thereby ensuring all market orders are converted to trade at the market bid-askprice at any given time during the trading hours.

(Statistical) Arbitrage

Statistical Arbitrage refers to a strategy in which two closely related financialinstruments whose prices should move on-a-pair with each other, for example, theS&P 500 features and SPY (the ticker symbol that tracks S&P 500). If the priceof S&P 500 goes up due to the arrival of a buy order and the SPY do not goup immediately, an HFT can buy the low price SPY and sell the high price S&P500, profiting from the bid-ask spread [6]. Opportunity for this type of strategies

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only exist in the market for a very short period (in micro or milli seconds) andthus the fastest HFTs will always win it all. Other forms of arbitrage exist andpredominantly benefits from price inefficiencies either across asset or across market[19].

Liquidity Detection

This is a type of strategy in which HFTs employs sophisticated algorithms todiscern patterns left by other market participants in the market and adjust theiractions (to buy or to sell) accordingly. HFTs most time focus attention on largeorders and employ various strategies to detect sliced orders or gain informationabout electronic order book - This is sometimes refers to as “sniffing out” otheralgorithms or “Ping” in order books to retrieve information [19].

Directional Trading

This is a type of strategy where HFTs placed orders based on order flow signals.This can also be in form of news, where news are automatically parsed using textanalytics and trade (buy or sell financial instrument) based on knowledge inferredfrom the parsed news [6].

2.2.1 Impact of HFT Strategies On Market Quality

Hendershott et al. [7] conducted a study on the New York Stock Exchange (NYSE)automated quote dissemination in 2003, using the change in the market structurethat lead to increase in Algorithmic Trading (AT) activity to measure the causaleffect of HFT on liquidity. Found out that for large stocks, HFT narrows spreads,reduces adverse selection and reduces trade-related price discovery. In general,they concluded that HFT improves liquidity and enhances the informativeness ofquotes.

The study of Menkveld [11] in 2007 on the entry of HFT into the trading ofDutch Stocks found out that the market makers (AT and HFT) inventory revert tothe mean position numerous times within a trading day, which implies the presenceof high rate of liquidity within the market compared to the Belgian Stock Market(Used as a control since there was no AT or HFT presence). In comparison to theBelgian stock Market, bid-ask spread was 15% narrower, adverse selection was 25%less and volatility is unaffected. This implies that the presence of HFT increases

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liquidity, reduces adverse selection and have no observable influence on volatility.Menkveld observation shows that bid-ask spread and volatility are not correlatedcontrary to theoretical observations.

Hendershott and Riordan [20] measured the contribution of HFT and non-HFTliquidity supply and liquidity demand to price change components and found outthat HFTs trades in opposite direction to the market price movement. Whenprices deviate from fundamental value, HFTs push prices back to their efficientlevel by initiating trade in opposite direction. Contributing to price efficiency andincreasing liquidity.

Biais and Foucault [21] analysed trading equilibrium for a given level of HFTand discovered that when some HFT becomes very fast, it leads to increasedadverse selection cost for the slower traders and generate negative externalities.This is probably due to the ability of the faster HFTs to process bid-ask quoteinformation and adjust their trading strategies accordingly before the slower HFTs,leading to adverse selection for the slower HFTs.

Boehmer et al. [22] studied the effect of HFT intensity on market liquidity,short-term volatility, and price discovery between 2001 and 2011 in 42 equitymarket around the world and found out that on average - HFT improves liquidityand price discovery but increases volatility. In contrast to the average effect, theydiscovered that increase in HFT intensity reduces liquidity and increase volatilityfor the small cap stocks. The reason for this variation was not explicit in theliterature. This research work will attempt to provide a causal explanation tothe resulting effect of HFT intensity (HFT intensity can also be attributed to lowlatency) on market quality.

The flash crash event that occurred in May 6, 2010 is one of the major extern-alities attributed to HFT activities. But Kirilenko et al. [8] empirically showedthat HFTs did not cause the Flash Crash, but contributed to it by demandingimmediacy ahead of other market participants. This immediacy absorption activ-ity of HFTs results in price adjustment that are costly to the slower HFTs andthe traditional market makers, thereby resulting in adverse selection. They alsoobserved that at times of market stress and high volatility which might be due to alarge buy or sell order resulting into an order flow imbalance. HFTs exacerbate thisdirectional move by demanding liquidity in the the direction of price movement,increasing the speed in which the best bid and ask queue get depleted leading toa spike in trading volume and setting the stage for a flash-crash-type event.

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In summary, most of the research showed that HFT Strategies contributed toincreased liquidity in the equity market but at the same time generate adverseselection for the slower HFTs leading to negative externalities. Improvement in li-quidity is attributed to reduction in the bid-ask spread and volatility but Menkveldobservation shows that bid-ask spread and liquidity are not correlated [11]. Otherempirical results supported Menkveld observation, Boehmer et al. [22] shows thatHFT improves liquidity and price discovery but increases volatility. The effect ofHFT on volatility seems to be inconsistent consistent in the research literature,but in general, most of the research agreed that HFTs increase volatility but alsocontributed to stabilising the market bid-ask quote under extreme price imbal-ance. The proposed Mathematical and Simulation Model is intended to clarifythese observed discrepancies.

The contribution of HFT to price discovery is consistent in both theoretical andempirical research. HFT improves price discovery for the faster HFTs but worsenfor the slower HFTs leading to adverse selection for the slower and non-HFTs.The causal explanation for this is also provided in the developed Mathematicaland Simulation Model.

2.3 High Frequency Trading (HFT) And Latency

The assumed speed limit for the trading world is said to be the speed of lightwhich is almost impossible to achieve considering the natural limitation set by thephysical component used in transmitting market data from exchange to trader andback to the exchange. Even in the case of co-location where HFTs systems areconnected directly to the exchange, the connection medium still pose a barrier toachieving this speed of light. The clock speed of the hardware on which tradingalgorithm are executed is also another barrier.

Despite these natural barriers in achieving the speed of light, in the tradingworld where trading decision are made and executed in milli-seconds, such sphereof operation have no space for human traders [23]. Latency “The time it takes toaccess, process and respond to market information [24]” is a relative term sinceyesterday’s ultra-low latency can be today’s low latency. However, low-latency canbe classified as those with sub-ten (single digit) milli-seconds round trip [23]. Inthe exchange market, latency exist in two forms which are Exchange latency andMarket players latency which are the HFTs (Agency and Proprietary), non-HFTs

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and Human traders. These two forms of latency exhibit considerable impact onmarket quality. This research work is focused on the impact of latency variationof market participant on market quality but reviewing the two forms of latencywill be beneficial.

Exchange And Latency

The business model of exchanges is such that its functionality depends on itsability to receive, aggregate, manage, match orders and generate resulting tradeinformation. Contrary to the old traditional exchange model which is totallyreliant on humans known as specialist for trade execution. The newer modelengaged the speed and sophistication of modern microprocessors and computeralgorithms which are faster, better and more accurate than a human specialist tomatch orders according to a very simple procedure: “Price and Time priority”.

The newer model of exchange is best represented by Electronic CommunicationNetwork (ECN) - with the simple mantra of “Who has the best price?” followedby “Who put the best price out first” [23]. This simple mantras has led to adrastic change in the the quote execution landscape putting the latency at whichexchanges receive, execute, manage and relay order book information at the forefront of the exchange business model.

The latency difference between execution venue give rise to several opportun-istic strategies directed at Latency Arbitrage, where predatory algorithms executetrade in one execution venue and offset in another for instant profit. The growinglatency lag between the respective liquidity pool has been on the rise and accord-ing to TABB Group, cash trading and market data revenue, which are the mostsusceptible trade to low-latency competition have been on a steady increase from2003 to 2007 in the United State equity market and represent over 50% of the totalrevenue of the US equity market as shown in Figure 2.5 below [23].

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Figure 2.5: Percentage of Latency-Related US Equity Exchange Revenues [24]

Market Players and Latency

The race to zero [25] has become a common term in the financial market, whichmeans the absence of latency ⇒ Latency = 0. The competition for zero latencyis more prominent among those market participants that execute market makingstrategy (Liquidity providers) of which majority of HFTs belong. These are HFTswho generate profit by capturing the spread between the supply and demand fora particular security.

The agency execution providers are also affected by the latency arm-race. TheSOR (Smart Order Router) used to make order route decision relies on real-timemarket data and thus, a cost is attached to any buy or sell decision if it arrives ata later time than that of a competitor. The best scenario for this case is the onepresented by Budish et al [26]:

Considering latency from the perspective of a liquidity provider, if thepresence of an observable news in the public domain makes his quoteto become stale. It immediately enters a race competition where: 1)Trying to adjust his stale quote and 2) Many others trying to snaphis stale quote. Considering that in a continuous limit order book,messages are processed one at a time in serial and so, even with acutting-edge speed, one will always loose against many.

The scenario above do not quantify the cost of latency i.e the cost implication ofbeing latent, but only present one of the numerous scenarios where the cost of

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being latent can lead to a severe adverse effect. The report from TABB Groupattempt to put a cost on latency from the perspective of liquidity providers [23]:

In 2008, 16% of US institution are exposed to latency risk, totalling$2 Billion in revenue as shown in Figure 2.6 below. If a broker’selectronic trading platform is 5 milliseconds behind the competition,it could loose at least 1% of it’s order-flow which is equivalent to $4

Billion in revenue permillisecond, up to 10ms could result in at least10% drop in revenue. And finally, “If a broker is 100ms slower thanthe fastest broker, it may as well sell his FIX (Financial InformationeXchange) engine and become a floor broker” [23 p.8].

Figure 2.6: Percentage of US Institutional Equity Exposed to Latency Risk

2.3.1 Impact of HFT Latency On Market Quality

Ende et al.[27] provides a performance measure of the effect of latency in thecontext of competitive advantage of a trader’s Information Technology (IT) infra-structure over another based on a historical dataset of Deutsche Börse’s electronictrading system “Xetra”. Using trading data from DAX30 instrument traded atXetra, they used a probability approach to estimate the impact of latency from atrader’s perspective and observed the following:

That the length of latency delay has a considerable impact on the probabilityof an order book situation changing unfavourably for a submitted order as shownin Figure 2.7(a).

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(a) Day pattern for E.ON and latencies of 10 – 100 ms (b) Scaling of hit probability due to latency

Figure 2.7: Latency Impact and Order Book Probability Estimate [27]

The graph in Figure 2.7(a) shows the intra-day patterns for 10 to 100ms for abuy market order in E.ON. It can be observed that in the morning, the probabilityof the order book alteration is high and decreases continuously due to the fiercecompetition usually experienced by the exchange during market opening time -“DAX instruments continuous trading takes place from 9:00 till 13:00 o’clock inthe morning and 13:02 till 17:30” [27 p.6].

The probability is observed to reach the minimum just after the midday-auctionand increase again. The observed striking increase is congruent with the openingtime of the US markets, which is at 15 : 30 [27]. From this empirical result it canbe observed that the cost of latency is higher when competition are high in themarket, in the opening of the market; after the midday-auction; during openinghour of other market; or during such event like news.

Furthermore, to estimate the cost of being latent, Ende et al. [27] fitted a log-linear regression to the graph of average increase of probabilities for a buy marketorder in E.ON as shown in Figure 2.7(b). From the slope of the regression theydeduced a simple rule of thumb.

“A 1 % increase in latency leads to a 0.9 % increase in the probabilityof unfavourable order book changes. Thus reducing latency about 1 mshas a greater effect on the probability” [27 p.8]

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Other empirical observations from the historical dataset of Deutsche Börse’s elec-tronic trading system “Xetra” as presented by Ende et al. [27] are summarisedbelow:

• Most latency demanders of which majority of HFTs belong, concerns onlythe top of the order book i.e most market orders issued either exactly matchthe best/bid price and volume or deleted immediately from the order book.This is due to the low latency at the disposal of the HFTs and thus, it is amore optimal strategy to delete unfulfilled order from order book and replacethem frequently than leaving them to go stale.

• Highly capitalised stocks exhibit higher probabilities of encountering orderbook change than the low capitalised one from a market participant per-spective.

• The impact of latency is higher on those HFTs whose business model is suchthat they seek a very low spread, usually the liquidity providers who executesthe market making strategy by quoting both side of the order book to profitfrom the spread, compare to those institution who follows a long-time profitbusiness model - this are usually ATs that are non-HFTs, and of course,human traders or investors.

Furthermore, using the publicly available data from NASDAQ order-level data,identical to those supplied to subscribers and provide real-time information aboutorders and execution with each entry (order submission, cancellation and execu-tion) time-stamped to milliseconds. Hasbrouck and Saar [28] observed that thefastest trader have an effective speed of 2 − 3ms, while the slowest speed is ob-served to be 200ms which are thought to be human traders and not the tradesgenerated by algorithms. They concluded that in the current equity market struc-ture, increased low-latency activities improves liquidity and short time volatility.The causation explanation for the above observation will be provided later in thisresearch work using the result of the mathematical and simulation model.

It is observed in the reviewed research work that latency impact and cost areestimated based on market data which do not provide an insight into what goes onbeyond the exchange. Knowing that in most rapid strategies - those involving low-latency, order only last a few milliseconds and thus are not executable by majorityof market participants [29]. These failed attempts by relatively slower traders are

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not captured in the trading data and thus, analysing latency impact using tradingdata may be a seemingly-bias approach. But using a simulation approach do notonly allow for testing different scenarios by varying latency and number of marketparticipants, but also allow us to analyse what is happening beyond the exchangeby examining and analysing the exchange queue.

2.4 High Frequency Trading (HFT) Simulation

There are existing research work in the domain of financial intelligence wheresimulation approach have been explored. We will only review those closely relatedto this research work - where simulation approach have been used to examine theeffect of related HFT strategy on specific market quality.

Wah and Wellman [24] developed a Discrete Event Simulation (DES) Systemto capture the fragmentation that exist in cross-market communication due toinformation transfer delay which are being utilised by low-latency HFTs to executearbitrage strategy, while Agent Based Simulation (ABS) was used to simulate theinteraction between HFT and Zero Intelligence trading agent at millisecond levelto examine the effect of Latency Arbitrage on market quality. The simulationapproach used in this research work was adopted from that of Wah and Wellmanwork. That is, using Discrete-Event Simulation (DES) to model the interactionof multiple traders (HFTs with varied latency and non-HFTs) with an Exchangeand Agent-Based Simulation (ABS) to model the interaction of the various traders(HFTs and non-HFTs) with the order book.

The concept of Zero Intelligence as used by Wah and Wellman [24] was firstproposed and used by Gode and Sunder [30] in an experiment at the Universityof Carnegie Mellon where human traders were replaced by Zero Intelligence pro-gram that submit random bid and ask orders to investigate the determining factorof market allocative efficiency. The result of the experiment showed that alloc-ative efficiency in a double auction market derives largely from its structure andindependent of traders motivation, intelligence or learning.

Farmer et al. [31] in their work “The predictive power of zero intelligence infinancial markets” also adopted the principle of Zero Intelligence trader to test thestatistical mechanism of price formation and the accumulation of stored supplyand demand under the simple assumption that orders are placed at random withno underlying motivation or intelligence. The resulting model makes an excellent

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prediction for transaction cost, price diffusion rate and quantity closely related tosupply and demand under natural market condition, which suggest price formationmechanism is constrained by market rather than the strategic behaviour of agentsas previously thought.

The Zero Intelligence principle was adopted in this research since the aim ofthe research is to investigate effect of latency and thus, it will be logical to keep thevariable (Strategy) constant while we vary latency to test different scenarios. UsingZero Intelligence traders will help to achieve this and also, since traders motivationand intelligence does not have any effect on price formation and allocative efficiencyof the financial market [24, 30, 31]. The resulting impact of latency on marketquality will not be affected by the use of Zero Intelligence traders.

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Chapter 3

3 Research Design And Methodology

Lacking suitable data to empirically study the effect of latency on market quality,a theoretical and simulation approach is pursued, which enable incorporation ofcausal premises and specifically, presumptions of how trading behaviour is shapedby environmental conditions [24].

This research project is divided into Two, which are Theoretical and Experi-mental. The theoretical part involve the development of a Mathematical Modelbased on theoretical observation from available empirical results from researchwork in the areas of HFT latency and its impact on market quality. The Mathem-atical Model is proposed as an “Hypothesis” to be validated by providing analysisand explanation consistent with those found in empirical research. The SimulationModel which is dedicated to the experimental part of the research will be validatedby testing different scenarios of varied latency and number of market participantsand juxtaposed the results with those available in empirical research.

3.1 Theoretical Methodology - Mathematical Modelling

Models are abstraction of reality, characterised by assumptions about variables(things which change), parameters (things which do not change) and functions(the relationship between them) [32]. There are different types of mathematicalmodels but we shall focus mainly on those used in the research which are de-terministic and stochastic model. Deterministic models have no component thatare inherently uncertain, meaning no parameter of the model is characterised byprobability distribution unlike stochastic models. A stochastic model will producemany different results depending on the actual value a random variable takes ineach realisation [32] which makes it a suitable choice for modelling a financialmarket where order arrivals and execution are stochastic and not deterministic.

In reality, there exist a large element of compromise in mathematical modellingand modelling in general. Majority of interacting systems in the real world likethe financial market including its different interacting agents are very complex andcomplicated to model in their entirety and thus requires a compromise. Accordingto Dym [33]

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“The best model is the simplest model that still serves its purpose, thatis, which is still complex enough to help us understand a system and tosolve problems. Seen in terms of a simple model, the complexity of acomplex system will no longer obstruct our view, and we will virtuallybe able to look through the complexity of the system at the heart ofthings” [33 p.4]

The following steps will be followed in building the mathematical model:

1. Identify the most important part of the real system (the financial system andtrader agents) to be included in the modelled system to achieve just the rightlevel of complexity to give a mathematical expression that is worth while.

2. Formulate valid assumptions based on the empirical results obtained fromresearch work in the areas of Financial Market modelling and High-FrequencyTrading and Latency

3. Identify variables (things which change), parameters (things which do notchange) and functions (the relationship between them)

4. Build a flow diagram and established a relationship between (3) above basedon (2) above

5. Validate the model by testing it against observations from empirical resultsas available in research journals.

3.2 Experimental Methodology - Simulation Modelling

The simulation part of the research is divided into two logical parts which are:Discrete-Event Simulation (DES) used to model the interaction of multiple traders(HFTs with varied latency and non-HFTs) with an Exchange and Agent-BasedSimulation (ABS), used to model the interaction of the various traders (HFTs andnon-HFTs) with the order book. The simulation modelling roadmap is shown inTable 3.2 below

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SN Steps Activities

1Research question • What are the effects of HFT Latency on market

quality - Liquidity, Price discovery and Volatility

2

Identify simple theorythat addresses theresearch question

• Competition is predominantly based on Speed(latency reduction) and less of strategy

• Low-latency HFTs activities impact market qualityand generate externalities for slower HFTs and nonHFTs

3

Chose a simulationapproach that fits theresearch question

• Use Discrete-Event Simulation (DES) to model theinteraction of multiple traders (HFTs with variedlatency and non-HFTs) with an Exchange

• Use Agent-Based Simulation (ABS) to model theinteraction of the various traders (HFTs andnon-HFTs) with the order book

4Create computationalrepresentation

• Specify valid assumptions based on results ofempirical research in literature

• Operationalise constructs by building acomputational algorithms based on assumptionsand real life system

5Verify computationalrepresentation

• Replicate simple theory to verify computation andalgorithm logic for correctness, like running thesimulation with just 2 HFTs.

• If failed, debug by correcting theory and/or designlogic and/or software coding

6Experiment to buildnovel theory

• Create experimental design, for example; varyconstruct like latency, number of traders, ZI orderdistribution and so on

• Add new features if necessary based on likelytheoretical realism

7Validate with empiricalresult • Compare result of Simulation with empirical results

Table 3.2: Roadmap for Simulation Method - Adopted from [42]

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3.2.1 Discrete-Event Simulation (DES)

Discrete-Event Simulation models are described at a level of abstraction where thetime base is continuous, but during a bounded time-span, only a finite number ofrelevant events can occur - These events can cause the state of the system to changebut the system’s state remains unchanged in-between events [34]. A Discrete-EventSystem can either be Deterministic or Stochastic. Modelling a financial marketrequire the use of both Deterministic and Stochastic System.

In a financial market, each market participants (HFTs, non-HFTs or a Humantrader) generates order deterministically. Meaning every market or limit bid/askorders from each traders have a constant speed which is dependent on the latencyof the inter-connection between the trader and the exchange. If the departure timeis known, the arrival time can be estimated.

Let the Departure time of an order from an HFT = Td

Let the Arrival at the Exchange = Ta

Let the Latency of the link between the HFT and the Exchange = δ

Thus, the relationship between Td, Ta and δ can be express as follows:

Ta = Td + δ + d(τ) (3.1)

Where τ is the position of the order at the exchange queue and d(τ) is therate at which the order advances in the exchange queue. If there is no queue atthe exchange at the time of order arrival or the order is the first to arrive at theexchange then d(τ) = 0 , then:

Ta = Td + δ : When d(τ) = 0 (3.2)

Even if we assume that the Latency δ = 0. The existence of a queue at theexchange means the order will not be executed at the Time Ta = Td as shownbelow:

Ta = Td + d(τ) : When δ = 0 (3.3)

It can be observed from above that even though the departure of orders from amarket participant is deterministic (The speed of its connection to the exchange),the execution of the order at the exchange is stochastic and not deterministic dueto the likeliness of an exchange queue and the existence of “price” competition

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among various traders.Another stochasticity that also exist is the bid/ask quote attached to each order

as attribute. We apply the principle of Zero Intelligence as previously elucidated.Meaning each trader generates bid/ask quote at random with no underline in-telligence or strategy, taking from a sets of Uniform Distribution. Therefore, atthe time an order departs from a trader’s system, it has both deterministic andstochastic attributes attached to it, which are the speed (Latency) and quotes(Bid/Ask) respectively. As soon as the order arrives at the exchange queue, allattributes becomes stochastic - This is the areas we are interested in investigating.Thus, a deterministic and stochastic approach is required to successfully build aDES model of acceptable complexity and representation of a real exchange system.

3.2.2 Agent-Based Simulation (ABS)

Agent-Based Simulation (ABS) or Agent-Based Modelling (ABM) is a modellingapproach for simulating actions and interactions of autonomous individual refersto as agents, with the view of assessing their effect on the system as a whole [37].Complex systems like the financial market with thousands of market participants(ATs, HFTs, non-HFTs and Human traders) can best be understood as a systemof autonomous agents that follows set of rules of interaction with other agents andtheir environment - in this case, the order book [38].

The interaction of HFTs with the order book is modelled based on the prin-ciple of Agent-Based Modelling where the agents in this case represents the dif-ferent traders with specific attributes which are latency, order and quotes. Eachindividual trader agent is autonomous and self contained in that they act inde-pendently. Each trader generates and submits order to the exchange at discreteintervals, which is both deterministic and stochastic as explained in the previoussection.

The interaction of individual trader-agent with each other is done on the orderbook. A bid/ask order submitted by one trader-agent is being executed by anotheragent and as a result changes the system dynamics. Each time an agent interactwith the order book, the depth of the order book either increases or decreaseswhich in turns changes the probability distribution of the outcome of the nexttrader-agent interaction with the order book [27]. Summarily, the dynamics of theSimulation Model changes from the perspective of an entity (orders) in the systemat each point in the simulation depending on entity’s state and position as shown

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in figure 3.1 below.

Figure 3.1: Simulation System Dynamics

3.2.3 Simulation Tool - Simulink and SimEvents

Simulink is a product of Mathworks, a block diagram environment for multi-domain simulation and Model-Based Design with support for simula-tion, automatic code generation, and continuous test and verificationof embedded systems [41]. In addition, Simulink provides a graph-ical editor, customisable block libraries, and solvers for modelling andsimulating dynamic systems that integrate seamlessly with MATLAB,enabling incorporation of MATLAB codes and algorithms into modelsand export of simulation results to MATLAB for further analysis[41].This flexibility of being able to manipulate Simulink block librariesamong other inbuilt libraries suitable for model-based design made ita tool of choice for modelling the Agent-Based Simulation (ABS) partof this research work.

SimEvents is a sub component of Simulink which provides a discrete-event sim-ulation engine and component library for Simulink which can be usedto model event-driven communication between components to ana-lyse and optimise end-to-end latencies, throughput, packet loss, andother performance characteristics [36]. The inbuilt libraries of pre-defined blocks, such as queues, servers, and switches, enables accuratepresentation of system and customise routing, processing delays, pri-oritisation, and other operations which make it a choice modelling toolfor the Discrete-Event Simulation (DES) part of the research work.

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3.2.4 Summary of Simulation Assumptions

The following assumptions are made in the developed Discrete-Event Simulation(DES) and Agent-Based Simulation (ABS):

1. Order submission per discrete time interval is 1 (i.e quantity of each submit-ted order per a discrete time interval = 1).

2. Orders are exclusively processed based on “Time priority” without consider-ation for price “Price priority” - This is because we assume all traders usessame strategy “Zero Intelligence” and therefore, there is no price superiority.

3. The principle of “Zero Intelligence” is used to randomly generates Bid/Askquotes in the Simulation System to exclusively restrict the simulation totesting impact of latency by keeping the “Strategy” variable constant.

4. The exchange’s latency is set to 1microsecond to allow the Exchange exhaustthe milliseconds generated orders in the order queue during a simulationwindow of 1 second.

5. Simultaneous events that occur during entity (Order) generation are pro-cessed round-robinly, i.e the respective position of such generated orders atthe Exchange queue is determined by the round-robin algorithm as imple-mented in SimEvents. However, Order processing by the Exchange is exclus-ively sequential, based on the position of each order at the exchange queueusing the First-In First-Out (FIFO) standard data structure as implementedin SimEvents.

6. All through the Simulation and its evaluation, we refer to Slow HFTs, ATsand Human Traders as Slow HFTs (Abbreviated as sHFTs), While the HFTsassumed to be trading at ultra-low latency are referred to as Fast HFTs(Abbreviated as fHFTs).

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Chapter 4

4 Mathematical Modelling

The Mathematical Model is developed based on assumptions derived from theresults of empirical research as available in the research literatures. The resultingmodel is discussed under the following sub sections, which are Price discovery,Liquidity and Volatility.

4.1 Price Discovery

As observed from the results obtained from research literature. The contributionof HFT to price discovery is consistent in both theoretical and empirical research.HFT improves price discovery for the faster HFTs but worsen for the slower HFTsleading to adverse selection. The causal explanation for this is provided in thedeveloped Mathematical Model.

Price discovery is assumed to be a function of bid-ask activities in the exchangeon a financial instrument. With increase in speed, price discovery become moreefficient. Naturally we expect all HFTs to have access to market bid-ask quoteat the same time, but in reality this is not the case due to the difference in theconnection speed between HFT traders and the exchange.

Let the speed between a trader and the exchange = St : Where t is the latency(assume to be the time to receive, process, and respond to quote)

Let the highest speed between a Trader T and the Exchange E = S0 =⇒ t = 0

(latency = 0)

Let the fastest HFT trader in the market be TS0

Let the delay between the fastest HFT trader TS0 and an HFT trader TSt =

S0 − St = δ: Where δ = Latency − Lag

The relationship between Price Discovery Index P , Speed S , Latency t, andLatency-lag δ be:

Pt = exp (St−δ) (4.1)

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At the maximum connection speed between the trader T and the ExchangeE, TSt = S0 − St = δ = 0 (Meaning the Latency Lag δ = 0). Thus, the PriceDiscovery Index P0 at latency t = 0 can be represented as follows:

P0 = exp(S0−0) = expS0 (4.2)

The graph of Pt and P0 against St and S0 respectively is shown in Figure 4.1below:

Figure 4.1: Graph of Price Discovery Index (P ) Against Speed (S)

From the above graph, as the speed between HFTs and the Exchange increases,the Price Discovery Index P increases exponentially. From the graph, the Latency-lag between the fastest HFT T0 and a slower HFT Tt = δ = 1. But as the speed Sincreases from Sa to Sb (from a to b) it can be observed the the margin betweenthe price discovery index of the faster HFT trader and the slower HFT traderwidened (P0 − Pb � P0 − Pa). This implies that as the speed between HFTs andthe exchange increases, Price discovery improves relatively for the faster HFTsand worsen for the slower HFTs and thus leading to higher transaction cost andadverse selection. This is very logical, for example: If the Latency-lag in terms oftime between a faster HFT and a slower HFT is 1ms. An upgrade dat reduces thelatency at the exchange from 50ms to 10ms like the upgrade of Deutsche Boerse’s

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trading system on April 23, 2007 [1] will imply an increase in Latency-lag betweena fast HFT and slow HFT from 1ms to 5ms.

This means the slower HFTs will always be 5ms behind as against the initial1ms. This leads to decrease in price efficiency for the slower HFTs while simul-taneously leads to improved price efficiency for the faster HFTs. This agreed withthe discovery of Biais and Moinas [39] that when some HFT becomes very fast,it leads to increase in adverse selection cost for the slower traders and generatenegative externalities which is due to the ability of the faster HFTs to processbid-ask quote information and adjust their trading strategies accordingly beforethe slower HFTs, leading to adverse selection for the slower HFTs.

Another observation from the Mathematical Model is that as the speed of thefaster HFTs increases relative to the slower HFTs, the slower HFTs are swept underthe carpet and if intraday trading data are analysed, price discovery will appearto be becoming more efficient as illustrated in the equation below

From Equation 1 above, Pt = exp (St−δ)

As St→∞

=⇒ Pt = exp (St−δ) = exp (St) (4.3)

This implies that the slower HFTs with the Latency-lag δ will no longer berelevant and would most time withdraw from the market as observed by Biaisand Moinas [39] that in equilibrium, smaller institution (slower HFTs) are lessinformed than their large counterpart (faster HFTs) and exit the market whenHFTs become more prevalent to avoid adverse selection cost.

Under the assumption of predominant speed-based competition, we can con-clude that the relationship between Price Discovery Index P , Speed S , Latency tand Latency-lag δ can be express as an exponential function

f(St) = exp(St−δ) = Pt (4.4)

Where δ is the latency-lag between the fastest HFT and a slower HFT underconsideration.

4.2 Liquidity

The assumption of predominant speed-based competition implies all HFTs willwant to buy or sell a financial instrument at almost the same time. A good

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example is the release of a negative news about a stock, where we would expect allHFTs to initiate a sell order with no HFT initiating a buy order at the other endof the market, thus liquidity should disappear instantaneously. But this does nothappen due to disparity in the different HFT’s speed. Instead, the slower HFTswill initially provide liquidity due to the delay in receiving the news, but reverttheir position as soon as such HFTs become aware of the news. This continuesuntil the slowest HFT receive the news. At this point liquidity will momentarilydisappear unnoticeably because the faster HFT will immediately start liquidatingtheir position by buying back from the slower HFTs at a lower price than theyinitially sold, profiting from the bid-ask spread. While the slower HFTs will beselling to the faster HFT at a price lower than they bought, thereby recording aloss and leading to adverse selection.

Let L be the Liquidity Index

Let the latency between any HFT and the Exchange be = t

Let the latency for the fastest HFT in the market be = δt = δ0 = 0

Let the latency for the slowest HFT in the market be = δt = δ∞ = 1

Let the Latency-lag between the fastest HFT and any slower HFT be = δ0−δt = θ

Let the relationship between L, δ0, δt be express as follows:

L = − log[1− (δ0 − δt)] = − log(1− θ) : Where, θ = δ0 − δt (4.5)

The graph of L against θ is shown in Figure 4.2 below:

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Figure 4.2: Graph of Liquidity Index (L) Against Latency Lag (θ)

As shown above, Liquidity for a particular financial instrument reduces as thelatency-lag (θ) reduces (The difference between the time it takes a slower HFT toreceive an information from the market minus that of the faster HFT) meaningmore HFTs are getting informed. For example, this could be a case of a negativenews, a large market order by a big AT firm or as a result of large market movementin a particular direction. At the point where Latency lag (θ) = 0 , Liquiditymomentarily = 0 as shown in Figure 4.2 below. This signifies a point of maximuminformation circulation. At this point, the faster HFTs starts liquidating theirposition - since they will be the first to be aware of the illiquidity, and start tostabilise the price and thus making profit from the bid-ask spread while generatingadverse selection cost for the slower HFTs.

Hendershott and Riordan [40] observation when measuring the contribution ofHFT and non-HFT liquidity supply and liquidity demand to price change com-ponents and found out that HFTs trades in opposite direction to the market pricemovement can be explained from the above model. HFTs in general consumesliquidity before providing it. This makes it seems HFTs are actually stabilisingprice but in reality, the faster HFTs uses its speed advantage to momentarily takeaway liquidity and quickly liquidate its position, making profit from the bid-ask

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spread which shall be proved experimentally by simulation modelling in the nextchapter.

Hendershott and Riordan [40] also observed that HFTs consume liquidity whenbid-ask spread is low and provide liquidity when bid-ask spread is wide. As shownin the graph of the Mathematical Model above, when the latency-lag θ is maximum,bid-ask spread is at the minimum. But as soon as the faster HFTs start reactingto market information, for example by selling - in the case of a negative news,they began to take away liquidity and introducing volatility. At the point whereliquidity momentarily = 0, bid-ask spread = Maximum, and thus the faster HFTsstart providing liquidity. This is a better causal explanation for Hendershott andRiordan [40] observation - be proved experimentally by simulation modelling inthe next chapter.

The Model also provide an explanation for the flash crash that occurred inMay 6, 2010. The Mathematical Model shows that the faster HFTs wait untilthe momentary time where liquidity equals zero before liquidating their position.But in the presence of a large order as witnessed in the flash crash [8], HFTs willcontinue to consume liquidity as long as it is available, driving down the price andat the same time increasing volatility until a point of illiquidity is reached beforeliquidating their position. The presence of a very large order will make HFTs notto liquidate their position and this may lead to a crash if no mechanism is in placeto manually pause trade on such stock.

The correlation of the result of the Mathematical Model with empirical resultsshows that the assumption of HFT predominant speed based-competition holdsand that Latency positively impact liquidity but at thesame time generate negativeexternalities for the slower HFTs. Thus, the relationship between Liquidity IndexL and the Latency lag θ can be express as follows:

f(δ0−δt) = − log[1− (δ0 − δt)] = L (4.6)

Since δ − δt = θ

f(θ) = − log(1− θ) = L (4.7)

Furthermore:

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θ→0⇒ f(θ) = − log(1− 0) = 0⇒ L = 0 (4.8)

This shows that if the latency lag θ equals 0, meaning that all HFTs have equallatency, and thus liquidity will be equal to Zero. Even though it is not possiblefor latency to be equal, but if the slower HFTs withdraw from market as HFTsintensity increases leaving the faster HFTs [8], a condition close to this may occur.To overcome this, exchanges provides rebate to liquidity providers to encourageliquidity and also, some HFTs are registered as liquidity providers to avoid thiscondition.

Also:

θ→1⇒ f(θ) = − log(1− 1)⇒ L = ”Undefined” (4.9)

This means that, at the point of maximum latency lag θ = 1 there is virtuallyno activity in the market and thus Liquidity L does not exist. This implies a crashas witnessed on 6th May, 2010.

4.3 Volatility

As shown from the empirical results from literature, Boehmer et al. [22] studiedthe effect of HFT intensity on market liquidity, short-term volatility, and pricediscovery between 2001 and 2011 in 42 equity market around the world and foundout that on average - HFT improves liquidity and price discovery but increasesvolatility. Biais and Moinas [39] also analyse trading equilibrium for a given levelof HFT and discovered that when some HFT becomes very fast, it leads to in-creased volatility and thus increased adverse selection cost for the slower tradersand generate negative externalities.

This shows that when HFTs intensity in the market increases, this lead tovolatility. This condition of HFTs intensity leading to increase in volatility isonly possible if most of the HFTs are trading on the same strategy, meaningbuying or selling at the same time. This create a condition of price imbalance andresult in volatility. This agreed with the assumption of predominant speed basedcompetition. Volatility can be modelled under this assumption as follows.

Let V be the Volatility Index

Let the latency between any HFT and the market be = t

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Let the latency for the fastest HFT in the market be = δt = δ0 = 0

Let the latency for the slowest HFT in the market be = δt = δ∞ = 1

Let the latency difference between the fastest HFT and any slower HFT be =

δ0 − δt = θ

Let the relationship between V, δ0, δt be express as follows:

V = − log(δ0 − δt) = − log(θ) : Where, θ = δ0 − δt (4.10)

The graph of V against θ is shown in Figure 4.3 below:

Figure 4.3: Graph of Volatility Index (V ) Against Latency Lag (θ)

It can be observed from the graph that, as the Latency lag θ decreases, volatilityincreases. The Latency lag θ is the latency difference between the fastest HFTtrader and a slower Trader, as this differences reduces, meaning that the slowerHFTs are becoming more informative and thus executing trade in same directionas the faster HFTs and thus leading to increased volatility. Take for example:The arrival of a large market bid order to buy a financial instrument. The faster

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HFTs will be the first to be aware, assuming that the firm placing such order mayhave access to private information and start issuing a market buy order. The otherHFTs will be providing liquidity until they become aware of the trends and start toliquidate their acquired position by buying back which lead to increased volatilityon the particular security. This agreed with the result of Biais and Foucault[9] that when some HFT becomes very fast, it leads to increased volatility andthus increased adverse selection cost for the slower traders and generate negativeexternalities.

At the point of highest volatility, that is, when all traders are now fully aware ofthe market trend (when latency lag θ = 0). The slower HFTs withdrawn from themarket to avoid adverse selection cost, at this point the faster HFT start liquidatingtheir position by selling. This agreed with the result of Hendershott and Riordan[40], they observed that HFTs consume liquidity when bid-ask spread is low (lowvolatility) and provide liquidity when bid-ask spread is wide (high volatility).

From Equation 4.13 above, it can be observed that:

θ→0⇒ f(θ) = − log(0)⇒ V = ”Undefined” (4.11)

This implies that, at the point of highest volatility - when θ ≈ 0, if the fasterHFTs do not liquidate their position after the withdrawer of the slower HFTs, themarket could be heading for a crash. There is usually a mechanism in place tocheckmate this in the security market.

Also:

θ→1⇒ f(θ) = − log(1)⇒ V = 0 (4.12)

This means that, at the point of highest latency, volatility V = 0. This impliesa trade off between low latency θ ≈ 0 and high latency θ ≈ 1 and thus the optimumlatency should lie in between. That is, for Optimum Volatility V0 and OptimumLatency θ0

V0 = f(θ0) : (0 < θ0 < 1) (4.13)

There have been numerous proposition both from the academic and the fin-ancial sectors about what the optimum latency should be. Budish et al. [26]proposed a discrete-time frequent batch as a replacement for the continuous-timelimit order book where market and limit Bid/Ask Orders are processed in batches

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by the Exchanges based on a fixed-time interval. The fixed-time interval at whichan Exchange processes an order is the respective “induced-latency” of the exchangeas proposed by Budish et al [26]. Thus, the optimum speed, which is the minimumspeed an HFT must possess to be able to compete without negative externalitiesas a result of being latent will be the fixed-time interval at which the Exchangeprocesses Bid/Ask Orders.

Let δi = Induced-latency ( Latency at which the exchanges processes Orders basedon the proposed discrete-time frequent batch by Budish et al [26].

Let the latency of an HFT under consideration be = δHFT

Let the Optimum-latency based on the proposed discrete-time batch be the latencyat which δHFT ≥ δi

Thus:

δOptimum ⇒ δHFT ≥ δi (4.14)

The above condition will allow for a bounded latency competition where HFTswill only strive to achieve the optimum latency to remain competitive and not theunbounded latency competition as we have today in the financial market wherethe fastest wins it all. The term “fastest” is a very relative term in the contextof HFT, since yesterday’s fastest speed could mean today’s slowest. The onlylimitation of HFT latency in today’s competition is the natural barrier poised bynature to achieving Zero latency and the limitation of innovation in the areas ofdata transmission and communication.

The value of the optimum-latency based on the proposed Mathematical Modeland Budish et al [26] could best be determined empirically which is beyond thescope of this research work. However, we are able to show theoretically that theoptimum latency should be between the highest and lowest latency obtainable inthe market where Volatility is optimum as shown below.

V0 = f(θ0) ⇒ (0 < θ0 < 1) (4.15)

Where θ0 ⇒ Optimum Latency

And based on Budish et al proposal [26]

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δOptimum ⇒ δHFT ≥ δi (4.16)

Where δOptimum = Optimum Latency

δHFT = Latency of HFT under consideration andδi = Induced Exchange latency based on the proposed discrete-time frequent

batch by Budish et al [26].

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Chapter 5

5 Simulation Modelling

Following from the Roadmap for Simulation Method as highlighted in section3, Table 3.1. Discrete-Event Simulation (DES) is adopted in modelling the in-teraction of multiple traders (HFTs with varied latency and non-HFTs) with anExchange. While Agent-Based Simulation (ABS) is used to model the interactionof the various traders (HFTs and non-HFTs) with the order book.

This section is structured as follows: The block libraries and other computa-tional routines as available in Simulink and SimEvents will be defined followed bya description of the functionality and logic of each of the block libraries used inthe simulation.

5.1 Discrete-Event Modelling - SimEvents

A static description of the DES simulation will be done by describing the compon-ent of the DES model followed by the working logic. Descriptions of the compon-ents are given below [36]

• Entity: Any object or component in the simulation system which requiresexplicit representation in the model, for example: a trader which could eitherbe an HFT, AT or non-HFT. These entities can pass through a network ofqueues, servers, gates, and switches during a simulation and can carry data,known in SimEvents software as attributes.

• Entity generator: The Entity Generator block is used to generate entitiesin response to either a signal-based events that occur during the simulation -signal-based entity generator or based on specified time interval - time-basedentity generator. It is also possible to generate entities at random usinga statistical distribution. The signal-based entity generator is used in thissimulation since orders (bid/ask) are generated based on market signals fromthe exchange in real life. The logic used to achieve this will be discussed inthe next chapter

• Event-based sequence: The Event-based sequence block generates anevent-based signal using data provided, the provided data in this case is

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the Latency - the time lapse between each entity generation. The latencyare specified in seconds, for example: 0.001 ⇒ 1ms , meaning that entities(orders) will be generated every 1ms.

• Attribute: Attributes in SimEvents are data attached to generated entities.We represent entities as orders and attach attributes to each orders whichare Bid and Ask attributes. The values of these attributes (Bid and Askattributes) are set by the Set attribute block

• Set attribute: The set attribute block accepts an entity, assigns data toit, and then outputs it. Assigned data (Bid price or Ask price) is stored inentity attributes i.e in the Bid and Ask attributes.

• Get attribute: The Get attribute block outputs signals using data fromentity attributes. For each arriving entity, the block updates the signal atthe signal output ports using values from attributes (Bid price or Ask price)while outputting the entity unchanged.

• Attribute function: The attribute function block accepts an entity (Or-ders), manipulate its attribute (Bid price or Ask price) if necessary and thenoutputs it via the Get attribute block. The attribute function block is usedto implement the Zero Intelligence module of the simulation where Bid priceor Ask price for each generated entity (Order) are randomly assigned froma set of uniformly distributed data.

• Signal scope: The signal scope block is used to create plots using data froman event-based signal. The data for the vertical axis comes from the signalconnected to the block’s signal input port. This block is used to analyse andvisualise movement of entities (Orders) in the simulation.

• Attribute Scope: The attribute scope block is used to create plots usingdata from a real scalar-valued attribute of arriving entities. This block isused to analyse and visualise the movement, state and values of (Bid andAsk Orders) in the simulation.

• Path combiner: The part combiner block accepts entities (Orders) throughany entity input port and outputs them through a single entity output port.This is used to simulate an Exchange FIX engine in the simulation, where

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all market and limit orders (Entities) are retrieved and forward to the CEPengine before being crossed by the order book. If multiple entities (Orders)arrive at the Path Combiner block simultaneously while the entity outputport is not blocked, the sequence in which the entities depart from the Pathcombiner and placed in the exchange queue depends on the sequence ofdeparture-events from blocks that precede the Path Combiner block (Whichare the entity generating blocks) or can be treated randomly or using around-robin approach - The rand-robin approach is used to process simul-taneous events in the simulation where priority is assigned interchangeablyfor simplicity. However, Execution of Orders by the exchange is exclusivelysequential based on the position of each order at the exchange queue usingthe First-In First-Out (FIFO) standard data structure as implemented inSimEvents.

• FIFO Queue: The FIFO queue block stores up to N entities simultaneously,where N is the Capacity parameter value. The block attempts to output anentity through the OUT port, but retains the entity if the OUT port isblocked. If the block is storing multiple entities and no entity times out,then entities depart in a first-in, first-out (FIFO) fashion. This block is usedto simulate an exchange queue in the simulation

• Server: The server block serves one entity (Order) for a specified periodof time, and then attempts to output the entity through the OUT port.If the OUT port is blocked, then the entity stays in this block until theport becomes unblocked. This block is used to model the Exchange in thesimulation, where each arriving order are processed based on a first-in, first-out (FIFO) fashion.

• Matlab function block: The MATLAB Function block allows addition ofMATLAB functions to Simulink (SimEvents) models for deployment. Thiscapability is useful for coding algorithms that are better stated in the textuallanguage of the MATLAB software than in the graphical language of theSimulink/ SimEvents product. This block is used to implement the Orderbook which involve explicitly writing MATLAB codes using the Agent-BasedSimulation paradigm.

• System State: System state is a collection of variables (entities and its

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corresponding attributes and other simulation parameters) that contains theinformation necessary to describe the system at any time.

• Event: Generally, an event is an instantaneous occurrence that changesthe state of a system while in a discrete-event simulation, an event is aninstantaneous discrete incident that changes a state variable, an output,and/or the occurrence of other events

• Event Notice: A record of an event to occur at the current or some futuretime, along with any associated data necessary for the execution of the event.At minimum, the record should include event type and the correspondingevent time

• Event List: Event lists are event notices for future events usually orderedby time of occurrence - also known as Future Event List (FEL)

• Activity: A duration of specified length with a known beginning time whichcan be statistical, functional or time based. A good example is order gen-eration of which time interval between order generation can be statistical(drawn randomly from a statistical distribution), functional (Dependent onother activities or conditions) or time-based (A fixed time interval).

5.2 High Frequency Trading and Latency

As a first step, the description of the real system we wish to model will be presen-ted, before the description of the system under consideration will be presented.The financial market is a complex system of interacting independent systems andagents, of which their collective activities determine the state of the system. Mod-elling the overall financial system will be overly complex for the research, butmodelling only part of the financial system under consideration, which are thoseareas of the financial market where HFT latency have direct or indirect influence,and with an acceptable and sufficient level of complexity to investigate the impactof HFT latency on market quality will be best.

Figure 5.1 below shows the structure of the modelled financial market usingSimulink and SimEvents.

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Figure 5.1: Exchange Design: Trader, Exchange, Order Book and Data Vendor

As elucidated previously, all traders in the simulation has no intelligence andthus all market and limit orders are randomly generated - following the principleof Zero Intelligence as used in simulation where the focus of the research is noton strategy [24]. All generated orders are submitted to the Order Queue of thestock exchange market. The exchange order queue is an infinite First-in First-out(FIFO) queue and so the queue is always available to receive and store arrivingorders using the FIFO data structure. Orders are made available to the exchangeon a discrete time-space which is dependent on the exchange’s latency and memorycapacity. Orders are route to the Order Book from the exchange for storage andprocessing, this is usually done by the CEP.

The Order Book receives, stores, crosses orders and submits trade records to theExchange. The exchange buffers and processes corresponding trade records fromthe Order Book, sends trade confirmations to all traders connected to the exchangeand trade announcements to Data Vendors. Data Vendors are responsible for

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notifying traders of reported trades. Order Wrapper wraps orders when availablefrom Order Queue and add the property SizeLeft while OrderHeap is a priorityqueue storing either market-buy, market-sell, limit-buy or limit-sell orders.

This is an overview of the simulation design. To give a more technical detail,the simulation model as implemented in SimEvents are divided into modules forclarity and explained under the following subsections.

5.2.1 Order Generation and Exchange

Figure 5.2: Simulation Model: Order Generation and Exchange

As shown in Figure 5.2 above, the Event-based-entity-generator-block named FastHFT generates entities (Orders) based on the signals received from the signal port(named: fcn). The signalling source where the time interval between each entity(Order) generation is generated and send to the Event-based-entity-generator-block named Fast HFT is the event based sequence block named Fast HFT SpeedSignalling Source. In-between the Fast HFT Speed Signalling Source and Fast HFTblock is the Signal-based-function-generator named Fast HFT Trade GeneratingSource which determines how many entities are generated in each event time.

For example: if the signal output of Fast HFT Speed Signalling Source is setto 0.001 which implies 1ms, this means that the Fast HFT will generate entities(Orders) at an interval of 1ms which is the Latency of the Fast HFT. However,

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the number of entities (Orders) generated at each 1ms time stamp is determinedby the Fast HFT Trade Generating Source. If the output of the Fast HFT TradeGenerating Source is set to 50, this means the Fast HFT will generate 50 entities(Orders) per 1ms. In the simulation, order size is assumed to be equal to 1 forsimplicity and thus, the Fast HFT Trade Generating Source is used to signifies thenumber of Fast HFT traders we are considering - which means an output of 50⇒ 50 Fast HFTs. Due to the limitation of the working computer, a maximumof 200 HFTs in total were successfully simulated, considering that the simulationtime-stamp is in milli-seconds. The same analogy as elucidated above applies tothe Slow HFT section of the model.

The Fast HFT Trade Counter and Slow HFT Trade Counter are Entity-scope-blocks used to count and visualise the number of entities (Order) generated by eachHFTs. The fHFT Trade Attribute and sHFT Trade Attribute are Set-attribute-block use to set the Bid and Ask attributes for the respective HFTs. The ExchangeSwitch is a Path-combiner used to route all the Orders to the Exchange Queuewhich shall be discussed in the next subsection.

5.2.2 Exchange, CEP and ZI

Figure 5.3: Exchange, CEP and ZI

The Exchange Switch as shown in Figure 5.3 above, is a Path-combiner used toroute all the Orders to the Exchange Queue. The Exchange Queue is an infin-ite First-in First-out (FIFO) queue used to hold all generated orders for pro-cessing by the exchange. The infinite Exchange Queue enables all HFTs to gen-erate orders without interruption through-out the simulation time. The Exchange

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Server is a SimEvent-single-server-block that extract entities (Orders) from theExchange Queue for processing, and forward to the Trade Extractor which is anAttribute-function-block. The Exchange Server’s Latency is configured to be inmicro-seconds - this allows the Exchange Server to be able to process all orders inthe queue during the simulation time.

The Trade Extractor is an Attribute-function-block which represent the CEP(A minimal implementation of the CEP, since the real CEP performs more func-tions than extracting and forwarding Bid/Ask Orders). The Trade Extractor isused to extract Order-attribute information which are the respective Bid and Askorders from the different HFTs before sending to the Order Book for crossing. In-between the CEP (Trade Extractor) and the Order Book is the ZI Trade Generator,this is used to randomly assign Bid and Ask prices to the respective separated Bidand Ask orders to be extracted and cross by the Order Book.

The simulation functions slightly different from the real system. In reality, theexchange holds Orders in a temporary memory in a batch, and process them basedon Price-Time-Priority. Which means Orders are first sorted based on best pricefollowed by order arrival time. But in this research work, we assume there is nobest or worse prices since our traders have no intelligence - our focus is not onstrategy but on Latency, and so it is logical to process Orders solely based on timepriority to investigate the effect of latency. More so that competition is assumedto be predominantly speed based and not strategy [13].

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5.2.3 Order Book

Figure 5.4: Order Book

The Order Book Simulator as shown in Figure 5.4 above is a MATLAB Func-tion block used to simulate the Order Book. The Order Book Simulator containsMATLAB codes and ABS Algorithms where each arriving Bid and Ask Ordersare treated as individual and independent agents, whose arrival changes the stateof the Order Book - Either decreasing the depth of the Order Book by removing anOrder (Successful execution) or increasing the depth by adding Order that couldnot be instantly executed to the Order Book.

The Order Book Simulator is placed in-between two SimEvents blocks whichare Get Attribute and Set Attributes respectively. The Get Attribute is used toparameterise the resulting Bid and Ask Order prices from the ZI Trade Generatorfor the Order Book Simulator for crossing as shown. While the Get Attribute isused to parameterise the Order Book Simulator execution output. The outputcontains additional information which are a Boolean parameter that representsuccessful execution and an execution price parameter. The Boolean parameter of”1” and price ”P” indicates that the Order is successfully executed at price ”P”.

While a boolean parameter of ”0” and price ”P” indicates that the Order couldnot be executed at price ”P” but appended to the Order Book.

The Matlab Function naturally runs based on the Matlab function call time-stamp which is higher than the simulation time - i.e the function block is naturally

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slower than the milliseconds rate at which orders are generated and expected tobe processed in the simulation and therefore creating a lag. This necessitate theaddition of an additional SimEvent single-server-block with a Zero Latency. Thisalters the natural latency of the function block and enables it to process Ordersat Zero latency.

Resulting output of all Order crossing from the Order Book are sent out throughthe Get Attribute block.

5.2.4 Trade Confirmation and Announcements

Figure 5.5: Trade Confirmation and Announcement

The Analyser block attached to the Order Book via the Set Attribute block isan Attribute Scope block used to extract the resulting output of each orders asthey exit the Order Book. The Analyser block automatically stores, computeand output the statistics of each Ask and Bid orders originating from each of theFast and Slow HFTs which can be visualised graphically. The Stock Price blockautomatically computes and output the Volume Weighted Average Price (VWAP).The simulation is terminated by an Entity Sink block, a block where all the entitiesin the simulation go to rest.

5.2.5 Sample Simulation Run

The debug window shown in figure 5.6 below is a snap-shot of the simulation-runshowing the System state, Event list, Event time, Entity advancement and so on.

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Figure 5.6: Snap-shot: Sample Simulation Run

As shown in Figure 5.6 above, the first order or entity (en1) in the simulationwas generated at time 0.01s ⇒ 10ms and originated from the Fast HFT. Theorder (en1) advances from Fast HFT to the Fast HFT Trade Counter, a block thatkeep track of the number of trades originating from the Fast HFT. Advance fromthere to the fHFT Trade Attribute where Bid and Ask attributes are assignedto each order. The attribute value of 1 is assigned to the Fast HFT which willbe used to uniquely identify all Orders originating from the Fast HFT by the ZIOrder Generator which randomly assigns prices to the Ask and Bid orders beforebeing crossed by the Order Book. Then proceed to the Exchange Switch followedby the Exchange Queue until the Order is crossed by the Order Book and finallyended up at the Entity Sink block.

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5.2.6 Market Data Feed

Figure 5.7: Market Data Feed

The Market Data Feed is a direct connection between a Trader and a Data Vendor.The link is utilised by the Data Vendor to send market data to all traders connectedto its Data Feed, such as price, volume traded, sizes, latest bid and ask price andthe time of the last trade reported by a trading venue. These market data are veryimportant to traders (HFTs, AT, and non-HFTs) in making trade decision (buyingand selling decision). Thus, the latency between an HFT and a Data Vendor maygenerate externalities and thus should be considered in the research.

For example:

Let there be a Data Vendor D

Let the Fast HFT’s Latency to D = λf

Let the Slow HFT’s Latency to D = λs

Let the Latency difference between λs and λf = λs − λf = δ

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Where δ is the Latency of λs relative to λf

If the Fast HFT receives a Best Ask Price P1 from a Data Vendor D for a securityat time tλf and instantly make a decision to sell at the Best Ask Price P1. Let usassume the Sell order is large enough to drive the Best Ask Price down to P0 attime tλs = tλf + δ : where P1 > P0. The Slow HFT will receive the Best Ask PriceP1 at tλf + δ and if the Slow HFT make a decision to Sell would be incurring acost P1 − P0. Thus, we can say that the cost of latency δ for the Slow HFT is:

δ = P1 − P0 (5.1)

To model the latency difference and experimentally investigate the impact ofHFT Latency on market quality with respect to the latency between HFTs andData Vendors we use the Signal Latch and Initial Value Block. The Initial ValueBlock sends a time delay to the respective HFTs, that is, the time to generatethe first entity (Order). After the first entity is generated at this initial latency,the HFT starts receiving Latency signals from the Signalling Source via the SignalLatch which is the speed used to send order to the exchange.

For example: If the Latency for Order generation is 1ms and the value of theinitial value is 5ms. Then the first entity (Order) is generated at 5ms and the nextOrder generation is at 10ms and continue to generate at 1ms henceforth. Thisimplies that a delay of 10ms has been introduced for the particular HFT compareto other HFTs in the market. This enables us to simulate and examine the effectof latency between an HFT Trader and a Data Vendor. Various scenarios will besimulated in the next Chapter to examine effect of Data-feed latency on marketquality.

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Chapter 6

6 Evaluation and Results

The developed Simulation model investigates the impact of latency on marketquality which are Liquidity, Volatility and Price discovery, and evaluated usingdifferent market setup scenarios. Four major fundamental scenarios are identifiedand tested, the result of each scenarios are documented, analysed and evaluatedbased on the proposed mathematical model and results of empirical research inthe domain of financial market and High Frequency Trading (HFT). The result ofthe simulation provides novel explanation to HFT activities and resulting latencyimpact on market quality. It provides causal explanation for already establishedfacts and new insights on HFT activities and impacts as related to Latency.

6.1 Scenario 1: HFTs With Same Latency

Two HFTs With Same Latency

The first evaluation to be performed in the simulation is that of Two HFTs with thesame latency to the Exchange (Latency = 5ms). This allows us to ensure accurateworking of the simulation model. Since one-to-one scenario is very simple to predictin term of outcome, this will allow us to identify any logical error or misplacedassumption that will negatively impact the result of subsequent simulations whichare critical to the research. A simulation time of 1 Second was chosen for thesimulation and subsequent simulation. The result of the simulation is shown inFigure 6.1 below.

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(a) HFT 1 (b) HFT 2

(c) HFT 1 (d) HFT 2

(e) ZI Orders (f) VWAP

Figure 6.1: Two HFTs with equal latency to the Exchange

As seen in Figure 6.1 (a) and (b), HFT 1 was able to successfully execute 93

Orders while HFT 2 successfully executes 85 Orders each. While the percentageof executed orders are 11.7% and 10.68% respectively as shown in Figure 6.1 (c)and (d). Despite the fact that orders were randomly generated based on theZero Intelligence principle as shown in Figure 6.1 (e) and given that both HFTshave same latency of 5ms to the Exchange, HFT 1 still execute more trades than

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the HFT 2 with different execution pattern as shown in Figure 6.1 (c) and (d).This shows that even though the Order price is generated from a set of uniformdistribution with the boundaries a = 200 and b = 300 as shown in Figure 6.1 (e),where the probability of selecting a value within the boundaries a and b is equalas shown in Equation 6.1 below.

f(x) =

1b−a for a ≤ x ≤ b,

0 for x < a or x > b(6.1)

Where x in the equation above is the Order Price generated by the ZI, whichcan be referred to as the probability function f(x) in the above equation.

The number of executed trades are not equal because the order crossing pro-cess is stochastic and the probability of a trade being executed is independent ofthe prior probability in the distribution from which the order is selected. Thisconfirms that order crossing at the Exchange is exclusively stochastic just as thereal Exchange order book. The VWAP as shown in Figure 6.1 (f) shows that therewas a little volatility in price at the beginning of the market and become stableshortly after at approximately 0.6s. This correlates with empirical results of pricevolatility at the opening of the market [27].

The result of the simulation is as expected, this shows that all assumptionsmade in the implementation are valid. Thus, subsequent simulation should produceresult with acceptable approximation of the real live exchange. Finally, we canconclude that: With equal latency to market, and relatively similar strategy, onetrader will always surpass the other given the minutest advantage.

Multiple HFTs With Same Latency

The next evaluation is multiple HFTs with the same latency to the Exchange(Latency = 5ms). The HFTs are grouped into two groups of 10 HFTs each, makinga total of 20 HFTs. The result of the simulation shows that the performance ofthe different HFTs are similar in terms of the number of executed orders as shownin Figure 6.2 (a) and (b) below. However, The presence of multiple HFTs lead toa reduction in volatility compare to when there are just Two HFTs as shown inFigure 6.2 (c). In Figure 6.1 (f) above, the VWAP started returning to the meanat 0.6 Seconds while in the case of multiple HFTs, the VWAP is already at the

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mean at 0.3 Seconds. This is consistent with empirical results, that the presenceof more HFTs lead to reduced volatility and improved price discovery [20].

(a) (b)

(c)

Figure 6.2: Multiple HFTs with equal latency to the Exchange

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6.2 Scenario 2: HFTs With Varied Latency

For clarity and consistency, the following are observed in the rest of the simulationscenarios:

1. We we refer to Slow HFTs, ATs and Human Traders as slow HFTs (Abbrevi-ated as sHFTs) . While the HFTs assumed to be trading at ultra-low latencyas Fast HFTs (Abbreviated as fHFTs).

2. From Hasbrouck and Saar [28], they observed that the fastest trader havean effective speed of 2− 3ms, while the slowest speed observed to be 200msin their research on the impact of milliseconds on security trading. In thesimulation, a Latency of 2.5ms will be assigned to the Fast HFTs while theSlow HFTs will be assign Latency range of 7.5ms to 102.5ms [23, 28].

3. From the result of empirical research, HFT constitutes on average 70% of theequity market. A ratio of 7 : 3 will be used in all scenarios that investigatesimpact of HFTs prevalence in term of latency and numbers in the financialmarket.

Multiple HFTs With Varied Latency

A total of Three scenarios are used to evaluate the impact of HFT Latency whenwe have multiple HFTs trading at different speed. Figure 6.3 shows the result ofthe simulation when there are 10 Fast HFTs (fHFTs) and 10 Slow HFTs (sHFTs)with Latencies 2.5ms,7.5ms ; 2.5ms, 22.5ms; and 2.5ms, 102.5ms respectively.The latency-lag in each of the simulations are 5ms, 20ms and 100ms respectively.

It can be observed that the percentage of executed trades (Orders) for thefHFTs and sHFTs at Latency 2.5ms and 7.5ms are 18.7 and 6.2 respectively asshown in Figure 6.3 (a) and (b). Comparatively, The sHFT percentage orderexecution at 1s is 66.8% lesser compare to the fHFT - This is a very huge cost,which can run into Billion of Dollars based on the TABB Group Estimate [23].Also, making an estimation of the cost of latency from the result shows that thecost of 1ms ⇒ 0.236% loss in Order flow, which implies a loss of 1.18% of sHFTOrder-flow for 5ms latency behind the fHFT. This is close to the estimate made byTABB Group [23] That if a broker’s electronic trading platform is 5 millisecondsbehind the competition, it could loose at least 1% of it’s order-flow.

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(a) Latency = 2.5ms (b) Latency = 7.5ms

(c) Latency = 2.5ms (d) Latency = 22.5ms

(e) Latency = 2.5ms (f) Latency = 102.5ms

Figure 6.3: Multiple HFTs with varied latency to the Exchange (10 fHFTs and 10sHFTs)

The latency difference is increased from 5ms to 20ms, The percentage of ex-ecuted trades for the fHFT improve by 20% while that of sHFT worsened by 18%

as shown in Figure 6.3 (c) and (d) respectively. We assume the maximum latencydifference to be 100ms. Thus, increasing the latency difference by a 100ms lead toan improvement of 9% of total execution trade for the fHFT while that of sHFTworsened by 12% as shown in Figure 6.3 (e) and (f) respectively.

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An observation of the impact of latency on the Slow HFT shows that at max-imum latency lag of 100ms, only 0.49% of its total Orders were executed compareto the fHFTs whose total percentage of order executed is 24.3%. This confirmthe dominance of the fHFTs when latency-lag is very large. The slower HFTs areswept under the carpet, because the market direction is predominantly determ-ined by the fHFTs at this instance. According to Biais and Moinas [39], that whenthe HFTs becomes prevalent, the non-HFTs (Slower Traders) withdraw from themarket to avoid negative externalities.

With the fHFT dominance, there was no observable difference in volatility asshown in Figure 6.4 (a) and (b). Which means that the dominance of fHFTs basedon only latency have no observable effect on volatility as shown by Menkveld [11].However, if we have more fHFT than sHFT, volatility may worsen or improve -This scenario will be observed in the next simulation.

(a) Latency-lag = 5ms (b) Latency-lag = 100ms

Figure 6.4: VWAP for multiple HFTs with varied latency to the Exchange(10fHFTs and 10 sHFTs)

Multiple HFTs With Varied Latency ( 70% fHFT and 30% sHFT)

From empirical analysis, HFTs account for market share of 70% on average [2, 4, 5].Therefore, it is assumed that the maximum trading capacity of HFTs in term ofnumbers will be 70% of the total market participants and the remaining 30% willbe ATs, and non-HFTs. In the simulation, the ratio of fHFT to sHFT is configuredto be 7 : 3 based on the above analysis to investigate what happened in the marketwhen we have more fHFTs than sHFTs. The latency-lag between the fHFTs andsHFTs remains 5ms, 20ms and 100ms respectively as shown in Figure 6.5 (a) -(f).

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(a) Latency = 2.5ms (b) Latency = 7.5ms

(c) Latency = 2.5ms (d) Latency = 22.5ms

(e) Latency = 2.5ms (f) Latency = 102.5ms

Figure 6.5: Multiple HFTs with varied latency to the Exchange (70% fHFTs and30% sHFTs)

The result of the simulation shows that when fHFTs are dominant in term ofnumbers and latency, the cost of latency to the sHFTs is higher compare to onlylatency dominance. When the latency-lag is 100ms, the sHFTs were only ableto execute 0.23% of their trades compare to the 0.49% in the previous simula-tion. This shows that the fHFTs generate more negative externalities when theydominate the market in both dimension - Latency and Number. The notion that

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Slower HFTs and non-HFTs withdraw from the market at this point of dominanceis questionable, from the result of the simulation, the Slower HFTs which representthe Slower HFTs, ATs and non-HFTs in reality did not withdraw from the market.But over 90% of their orders did not get executed and thus, when trading data areanalysed, it would appear they are in-active.

Secondly, as shown in Figure 6.6 (a) and (b), Volatility seems to disappeartotally when the fHFTs dominate in both directions. In the previous result whenHFTs dominate in term of latency only, we observe volatility with no visible im-provement as the latency-lag increases. But when fHFTs dominate in both num-bers and latency, Volatility disappears. This implies that we can assumed theobserved volatility is caused by the fHFTs - meaning that in reality, due to thedominant power of the Fast HFTs, they introduce volatility into the market andreverse their strategy to re-stabilise the market and thus profit from the spread.According to Hendershott and Riordan [20], when prices deviate from fundamentalvalue, HFTs push prices back to their efficient level by initiating trade in oppositedirection and contributing to price efficiency and increasing liquidity. The result ofthe simulation agreed with the HFTs contribution to price efficiency and increasingliquidity, and in addition, provide a causal explanation for the cause of volatilitywhen HFTs are prevalent.

(a) Latency-lag = 5ms (b) Latency-lag = 100ms

Figure 6.6: VWAP for multiple HFTs with varied latency to the Exchange (70%fHFTs : 30% sHFTs)

Table 6.2 below shows the summary of the simulation output for scenario 2.

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SimulationLatency-lag(ms)

Number offHFTs

Number ofsHFTs

% of fHFTsExec.Trades (%)

% of sHFTsExec.Trades (%)

1 5 10 10 18.7 6.2

2 50 10 10 22.5 2.7

3 100 10 10 24.3 0.5

4 5 14 6 21.7 3.2

5 50 14 6 23.8 1.2

6 100 14 6 24.7 0.2Table 6.2: Summary of Simulation Results for Scenario 2

The number total number of HFTs was increased from 20 to 30 using the 7 : 3

ratio. Meaning 21 fHFTs and 9 HFTs were used and the result of the simulation isthe same as that of 14 fHFTs and 6 sHFTs as shown in Table 6.4 below includingthe effect on Volatility. This shows that the percentage of Order execution ismainly dependent on the percentage of fHFTs relative to the percentage of thesHFTs and not on the total number of HTFs.

SimulationLatency-lag(ms)

Number offHFTs

Number ofsHFTs

% of fHFTsExec.Trades (%)

% of sHFTsExec.Trades (%)

1 5 21 9 21.7 3.2

2 50 21 9 23.8 1.2

3 100 21 9 24.7 0.2Table 6.4: Simulation Results for 21:9 HFTs Ratio Scenario

To confirm the above deduction, that is, that the percentage of Order executionis mainly dependent on the percentage of fHFTs relative to the percentage of thesHFTs and not the total number of HFTs. A 6 : 4 ratio was used, meaning 60%

of fHFTs and 40% of sHFTs with a total number of 30 HFTs (18 fHFTs and 12

sHFTs) as shown in Table 6.6 below. The percentage of executed Orders differsfrom the result obtained in the 7 : 3 HFTs ratio scenario despite the fact that wehave the same total number of 30 HFTs. This confirms the earlier deduction ofthe dependence of percentage total Order execution on the percentage of fHFTsrelative to the percentage of the sHFTs and not the total number of HFTs.

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SimulationLatency-lag(ms)

Number offHFTs

Number ofsHFTs

% of fHFTsExec.Trades (%)

% of sHFTsExec.Trades (%)

1 5 18 12 20.4 4.4

2 50 18 12 23.0 1.8

3 100 18 12 24.5 0.4Table 6.6: Simulation Results for 18:12 HFTs Ratio Scenario

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6.3 Scenario 3: HFTs With Same Latency to Exchange But

Varied Market Data Latency

The next scenario run on the developed simulation model is that of multiple HFTswith same latency to the Exchange but varied latency in their market data-feedlatency - the latency of the link from the trader to the Data Vendor. The resultof the simulation is shown in Figure 6.7 (a) to (f).

(a) Data-Feed Latency-lag = 0ms (b) Data-Feed Latency-lag = 5ms

(c) Data-Feed Latency-lag = 0ms (d) Data-Feed Latency-lag = 50ms

(e) Data-Feed Latency-lag = 0ms (f) Data-Feed Latency-lag = 100ms

Figure 6.7: Multiple HFTs with same latency to the Exchange but varied marketdata deed latency

The HFTs with higher Data-feed latency are referred to as Slow HFTs and whilethe HFTs with lower Data-feed latency are referred to as Fast HFTs. In reality,HFTs speed are predominantly determined by their order submission latency i.e

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their respective latency to the Exchange. Mostly, Faster HFTs usually have lowerlatency both ways. The purpose of this scenario is to examine the effect of Data-feed latency on market quality and to be able to evaluate the effect of Data-feedlatency, the order submission latency variable need to be kept constant.

As shown above, there are 10 Fast HFTs and 10 Slow HFTs, both with alatency of 2.5ms to the Exchange. The market-data feed latency-lag between thefHFTs and the sHFTs varies as follows: 5ms, 50ms and 100ms respectively. Itcan be observed from Figure 6.7 (a) and (b) that the fHFTs (in term of Data-feed latency) started at 15% but suddenly dropped below 10% at 5ms when thesHFT enters the market. But at the end of the 1sec simulation time, both sillfinishes at approximately 12.5%. However, looking at Figure 6.7 (c) and (d), asharp downward trend is observed at 50ms in (c) as a result of the sHFT orderplacement. The two HFTs did not end the 1sec trade window with same executionpercentage (fHFT ended at 12.7% while sHFT ended at 12.2% ) due to the largelatency-lag of 50ms. The same applies when the latency lag is 100ms as shownin Figure 6.7 (e) and (f). This shows that the impact of the data-feed latency isrecoverable given that

1. The latency-lag is very small - approximately 5ms and

2. Provided that the order is large enough to last for a duration proportionalto the data-feed latency-lag.

For example: In Figure 6.7 (e), if the order is to last for just 100ms, the fHFTswould have taking a price advantage and execute the orders before the sHFTssubmit orders for the same security at 100ms later. And at this time the sHFTwould have in-cured a cost as shown in Equation 5.1. Because the best Bid/Askprice at that instance (at 100ms later) will either be lesser or greater than theBest Bid/Ask possessed by the sHFTs [14]. Thus, this position is un-recoverableeven thought the order last a life-time due to the large information gap. Table 6.4below shows the summary of the simulation output for scenario 3

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SimulationExchange Latency[All] (ms)

D-V Latency lag[sHFTs] (ms)

% of fHFTs Exec.Trades (%)

% of sHFTs Exec.Trades (%)

1 2.5 5 12.45 12.45

2 2.5 50 12.7 12.2

3 2.5 100 13.2 11.6

Table 6.8: Summary of Simulation Results for Scenario 3

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6.4 Scenario 4: HFTs With Varied Latency to Exchange

And Varied Market Data Latency

The last scenario run on the simulation is that of Fast HFTs and Slow HFTs(both with varied latency to the exchange and Data Vendor). The result of thesimulation as shown in Figure 6.8 (a) to (d) shows that when an HFT has a highlatency-lag, both to the exchange and to the data vendor, such has no place in theworld of HFT. As shown in Figure 6.8 (a) and (c), the submission of Orders by thesHFTs at 50ms and 100ms has no effect on the percentage of executed orders ofthe fHFTs and thus, just as emphasised by Viraf “If a broker is 100ms slower thanthe fastest broker, it may as well sell his FIX (Financial Information eXchange)engine and become a floor broker” [23 p.8].

(a) Exchange Latency = 2.5ms, Data-Vendor Latency-lag = 0ms

(b) Exchange Latency-lag = 50ms, Data-VendorLatency-lag = 50ms

(c) Exchange Latency = 2.5ms, Data-Vendor LatencyLag = 0ms

(d) Exchange Latency = 100ms, Data-Vendor LatencyLag = 100ms

Figure 6.8: Multiple HFTs with varied latency to the Exchange and to the DataVendor

However, the latency variation is reversed to observe the difference, meaningthat a data-vendor latency-lag of 100ms is assigned to the Fast HFTs with Ex-

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change latency of 2.5ms while a data-vendor latency-lag of 0ms is assigned tothe Slow HFTs with Exchange latency-lag of 5ms and 100ms. The result of thesimulation is as shown in Figure 6.9 (a) to (d).

(a) Exchange Latency = 2.5ms, Data-Vendor Latency-lag = 100ms

(b) Exchange Latency-lag = 5ms, Data-Vendor Latency-lag = 0ms

(c) Exchange Latency = 2.5ms, Data-Vendor Latency-lag= 100ms

(d) Exchange Latency = 100ms, Data-Vendor Latency Lag= 0ms

Figure 6.9: Multiple HFTs with varied latency to the Exchange and to the datavendor (Reverse Test)

The result of the simulation shows that even though the fast HFTs started ex-ecuting orders at 100ms, less than 100ms mark into the trade, they were alreadyahead of the Slow HFTs. This shows that the Exchange latency is most paramountcompare to Data-Vendor latency when considering latency impact on market qual-ity. To further investigate if Exchange latency really matter most, a data-vendorlatency-lag of 500ms is assigned to the fHFT, which means the fHFT will starttrading half way into the order execution window. The result of the simulation isas shown in Figure 6.10 (a) to (d).

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(a) Exchange Latency = 2.5ms, Data-Vendor Latency Lag= 5000ms

(b) Exchange Latency-lag = 5ms, Data-Vendor LatencyLag = 0ms

(c) Exchange Latency = 2.5ms, Data-Vendor Latency-lag= 500ms

(d) Exchange Latency-lag = 50ms, Data-Vendor Latency-lag = 0ms

(e) Exchange Latency = 2.5ms, Data-Vendor Latency Lag =500ms

(f) Exchange Latency = 100ms, Data-VendorLatency Lag = 0ms

Figure 6.10: Multiple HFTs with varied latency to the Exchange and to the DataVendor (Extreme Test)

The result of the simulation shows that irrespective of when HFTs that areconsiderably fast wishes to execute orders, such will always sweep under the carpetall HFTs whose latency-lag between them (The fHFTs under consideration) and

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the HFTs (The sHFTs) is greater than or equal to 5ms. As shown in Figure 6.10(a), (c) and (e), the fHFTs finishes the 1sec trading window with a higher executedorder percentage than the sHFTs despite starting half-way into the trade. Thiswill also result in negative externalities for the slower HFTs, such as large loss inorder-flow, price inefficiency, and above all huge loss of revenue. Table 6.6 belowshows the summary of the simulation output for scenario 4 (Extreme)

SimulationExchangeLatency[fHFTs] (ms)

Data-VendorLatency-lag[fHFTs] (ms)

ExchangeLatency-lag[sHFTs] (ms)

Data-VendorLatency-lag[sHFTs] (ms)

% of fHFTsExec.Trades (%)

% of sHFTsExec.Trades (%)

1 2.5 500 5 0 15.4 9.8

2 2.5 500 50 0 22.6 3.0

3 2.5 500 100 0 23.1 1.2Table 6.10: Summary of Simulation Results for Scenario 4 (Extreme)

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Chapter 7

7 Conclusions and Future Works

This section of the research work present the summary, findings, conclusion andrecommendations for future research.

7.1 Conclusions

This research work is focused on the analysis and evaluation of the impact of HFTLatency on market quality which are Liquidity, Price discovery and Volatility.To achieve this, Two objectives were explicitly defined at the beginning of theresearch work which are The Learning Objectives and The Deliverable Objectives.This form the basis for evaluating the research work. The following milestoneswere achieved in relation to the learning and deliverable objectives:

The Learning Objectives

• The different HFT Strategies were presented in a structured hierarchicaldiagram which was later analysed and discussed.

• HFT Latency in relation to the market microstructure was analysed fromboth the perspective of the exchange and that of market participants whichare the High Frequency Traders (HFTs), Algorithmic Traders (ATs) and theInvestors and Human Traders.

• The equity market dynamics was analysed, that is, the anatomy of the equitymarket dynamic in relation to order movement from Trader’s system to theexchange queue; the exchange; CEP; the Order Book; and finally, how tradeconfirmation and announcement are generated and transmitted. A struc-tured model of the financial market model used in the simulation was alsopresented in Section Five.

• Mathematical Modelling theory and application was reviewed, including itsapplication in financial intelligence. Furthermore, Simulation was reviewed,which are Discrete-Event Simulation (DES) and Agent-Based Simulation(ABS) and their application in the domain of financial intelligence whichinclude financial system modelling.

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The Deliverable Objectives

• A Mathematical Model was developed based on the empirical result fromresearch literatures. Certain assumptions were made to theorise the impactof latency on market quality (Liquidity, Price discovery and Volatility) basedon the result of empirical research as elucidated in Section 4.

• A Simulation Model was built using Simulink and SimEvents from Math-Works. MATLAB Codes and Functions were also written to perform taskthat are not already explicitly defined in Simulink and SimEvents modules inother to ensure the dynamics of the model is close enough to the real system(Financial Market). Discrete-Event Simulation (DES) paradigm was usedto model the interaction of multiple traders (HFTs with varied latency andnon-HFTs) with an Exchange. While Agent-Based Simulation (ABS) wasused to model the interaction of the various traders (HFTs and non-HFTs)with the order book.

• Zero Intelligence principle was used to generate Orders by Traders in thesimulation. This enable us to focus on the main variable under consideration(Latency).

• Results of the simulation were presented, analysed and discussed in the “Eval-uation and Results” Section of the project - Section 6.

Novel Findings Results of the simulation show that:

• Contrary to what is obtainable in the research literature that HFTs reducesvolatility. According to Hendershott and Riordan [20] that when prices de-viate from fundamental value, HFTs push prices back to their efficient levelby initiating trade in opposite direction and thereby contributing to priceefficiency and increasing liquidity. Through the result of the Simulation, it isobserved that HFTs volatilise security prices due to their latency dominanceand later reverse their strategy to push prices back to their efficient level bytrading in opposite direction and thus, profiting from the Bid/Ask spread.

• The latency between HFTs and the exchange (for Order submission) is mostparamount compare to the Market Data-feed latency when investigatinglatency impact on market quality.

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• The impact of the data-feed latency is recoverable given that.

– 1. The latency-lag is very small - approximately 5ms.

– 2. Provided that the order is large enough to last for a duration pro-portional to the data-feed latency-lag.

• The impact of the latency-lag for order submission is not recoverable withina trading window due to in-cured latency-cost as shown in equation 5.1.

In summary, from the results of the Mathematical and Simulation Modelling, weconclude as follows, that HFT latency:

1. Positively impact liquidity, but do so by volatilising price and later re-stabilising it. Menkveld[11] empirically confirms that inventory revert tothe mean position numerous times within a trading day, which implies thepresence of high rate of liquidity. The result of the simulations shows thepresence of volatility when fHFTs are dominant “latency wise” - The ob-served volatility can only be caused by the dominant HFTs which are thefHFTs, but no sign of volatility when fHFTs dominate in terms of “latency”and “number” which implies that the volatility is caused and cleared by thefHFTs which are the dominant party.

2. Contributes positively to price efficiency, but only to the fast HFTs whilethe slow HFTs in-cured a latency-cost for pricing information inefficienciesproportional to the latency-lag between the sHFTs and the Market Data-feedVendors.

3. Contribution to Volatility depends on which side of the market we analyse,which is actually the reason for the conflicting results in the research liter-atures [22]. Considering the opening and closing of a security price, it wasobserved that HFT positively impact volatility. But looking at the interme-diaries, that is, in-between the opening and closing price as shown in Section5. Volatility is introduced and cleared before the end of the 1 sec simula-tion window. Thus, from the result of the simulation we can not arrive at aconclusion.

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7.2 Future Works

For further work on the research, the following are recommended:

1. We were only able to model one order submission per a discrete time interval(i.e quantity of each submitted order per a discrete time interval = 1). This isadopted for simplicity and due to the limitation of the physical system used torun the simulation. A future work should include multiple order submissionper trader per discrete event time. This will allow for a simulation modelthat is closer in resemblance to the real system with a possibility of a betterresult than we have obtained.

2. All orders in the simulation were executed using a single exchange, a futureresearch should incorporate multiple exchanges to evaluate the impact ofmultiple exchanges’ latency difference on market quality. Both from themarket participant perspective and the Exchanges perspective.

3. The principle of Zero Intelligence was used to exclusively restrict the simu-lation to testing impact of latency. A future work should include strategy inorder to evaluate the correlation between strategy and latency in the contextof their respective impact on market quality.

4. Orders were exclusively processed based on “Time priority” without consid-eration for price. This is because we assume all traders uses same strategy“Zero Intelligence” and therefore, there is no price superiority. A future workthat incorporate strategy should include “Price priority” to be able to arriveat a better conclusion of latency impact on market quality with considerationfor strategy.

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References

[1] Riordan, R., & Storkenmaier, A. (2012). Latency, liquidity and price discov-ery. Journal of Financial Markets, 15, 416–437.

[2] CFA Magazine: The Impact of High-Frequency Trading on Markets [Online].Available at: https://www.rbccm.com/globalequity/file-569694.pdf [Accessedon: 20 June 2015].

[3] United States Commodities and Futures Trading Commission and Securitiesand Exchange Com mission (2010), “Findings regarding the market eventsof May 6, 2010,” Report of the Staffs of the CFTC and SEC to the JointAdvisory Committee on Emerging Regulatory Issues, September 30, 2010.

[4] Gomber, P., Arndt, B., Lutat, M., & Uhle, T.(2011) High-Frequency Trading [Online]. Available at:http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1858626 [Accessedon: 1 June 2015].

[5] Brogaard, J. A. (2010). High frequency trading and its impact on marketquality. Northwestern University Kellogg School of Management WorkingPaper [Online]. Available at: http://heartland.org/sites/default/files/htf.pdf[Accessed on: 20 June 2015].

[6] Jones, C. M. (2013). What do we know about high-frequency trading? CharlesM. Jones* Columbia Business School Version 3.4: March 20, 2013. ColumbiaBusiness School.

[7] Hendershott, T., Jones, C. M., & Menkveld, A. J. (2011). Does AlgorithmicTrading Increase Liquidity? Journal of Finance, 66(1), 1–33.

[8] Kirilenko, A., Kyle, A., & Samadi, M. (2010). The flash crash:The impact of high frequency trading on an electronic mar-ket [Online]. Available at: http://www.ftm.nl/wpcontent/ up-loads/content/files/Onderzoek%20Flash%20Crash.pdf [Accessed on: 20June 2015].

[9] Ye, M. (2012). The Externalities of High Frequency Trading, 1–48 [Online].Available at: http://www.sec.gov/divisions/riskfin/seminar/ye031513.pdf[Accessed on: 20 June 2015]

83

[10] Zhang, X. F. (2010). The Effect of High-Frequency Trading onStock Volatility and Price Discovery, 1–53. [Online]. Available at:http://mitsloan.mit.edu/groups/template/pdf/Zhang.pdf [Accessed on: 20June 2015]

[11] Menkveld, A. J. (2013). High frequency trading and the new market makers.Journal of Financial Markets, 16(4), 712–740.

[12] Moallemi, C. C., & Sağlam, M. (2013). OR Forum—The Cost ofLatency in High-Frequency Trading. Operations Research, 61(5), 1070–1086.doi:10.1287/opre.2013.1165

[13] Viraf, W. (2008). The Value of a Millisecond: Finding the Op-timal speed of a Trading Infrastructure [Online]. Available at:http://www.tabbgroup.com/PublicationDetail.aspx?PublicationID=346[Accessed on: 20 June 2015]

[14] Ende, B., Uhle, T., & Weber, M. C. (2011). The Impact of a Millisecond: Measuring Latency Effects in Securities Trading. Proceedings of the 10thInternational Conference on Wirtschaftsinformatik (WI), (February), 27–37.

[15] Dhahahjay, K.D. & Shyam, K. (n.d.). Allocative Efficiency of Markets WithZero-Intelligence Traders: Market as a Partial Subtitude for Individual Ra-tionality. The Journal of Political Economy, 101(1), 119–137.

[16] Farmer, J. D., Patelli, P., & Zovko, I. I. (2005). The predictive power ofzero intelligence in financial markets. Proceedings of the National Academyof Sciences of the United States of America, 102, 2254–2259.

[17] Brogaard, J. (2010). High Frequency Trading and its Impact on Mar-ket Quality, 5th Annual Conference on Empirical Legal Studies Paper.http://ssrn.com/ paper=1641387.

[18] Chaboud, A., Erik, H., Clara, V., & Ben, C. (2009). Rise of the Machines:Algorithmic Trading in the Foreign Exchange Market. [Online]. Available at:http://ssrn.com/ paper=1501135 [Accessed on: 21 June 2015]

[19] Gomber, P., Arndt, B., Lutat, M., & Uhle, T.(2011) High-Frequency Trading [Online]. Available at:

84

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1858626 [Accessedon: 12 July 2015]

[20] Hendershott, T., & Riordan, T. (2011), “High frequency trading and pricediscovery” working paper, UC Berkeley.

[21] Biais, B., & Moinas, S. (2011). Equilibrium High Frequency Trading [Online].Available at: http://www.lse.ac.uk/fmg/events/conferences/pastconferences/2012/PWC-Conference_7-8June/Papers-andslides/ Bruno_Biais_paper.pdf[Accessed on: 22 July 2015].

[22] Boehmer, E., Fong, K., &Wu, J. (2012). International evidence on algorithmictrading. Available at SSRN 2022034, 2012, 49.

[23] Viraf, W. (2008). The Value of a Millisecond: Finding the Op-timal speed of a Trading Infrastructure, (April). Retrieved fromhttp://www.tabbgroup.com/PublicationDetail.aspx?PublicationID=346

[24] Wah, E., & Wellman, M. (2013). Latency arbitrage, market fragmenta-tion, and efficiency: a two-market model. Proceedings of the FourteenthACM Conference on Electronic Commerce, 1(212), 855–872. Retrieved fromhttp://dl.acm.org/citation.cfm?id=2482577

[25] Barr, D., Benos, E., Braun-munzinger, K., Butterworth, E., Chich-kanov, P., Cornelius, M., Meeks, R. (2012). Financial arms races,(April). Based on a speech delivered at the Institute for NewEconomic Thinking, Berlin 14 April 2012. [Online]. Available at:http://www.bankofengland.co.uk/publications/Documents/speeches/2012/speech565.pdf [Accessed on: 20 June 2015]

[26] Budish, E., Cramton, P., & Shim, J. (2014). A Market Design Approachto the HFT Debate : The Case for Frequent Batch Auctions. [Online].Available at: http://faculty.chicagobooth.edu/eric.budish/research/HFT-FrequentBatchAuctions.pdf [Accessed on: 20 June 2015]

[27] Ende, B., Uhle, T., & Weber, M. C. (2011). The Impact of a Millisecond: Measuring Latency Effects in Securities Trading. Proceedings of the 10thInternational Conference on Wirtschaftsinformatik (WI), (February).

85

[28] Hasbrouck, J., & Saar, G. (2013). Low-latency trading. Journal of FinancialMarkets, 16(4), 646–679.

[29] Goldstein, M. A., Kumar, P., & Graves, F. C. (2014). Computerized andHigh-Frequency Trading, 49(2), 1–35.

[30] Gode, D. K. and Sunder, S. (1993). Allocative efficiency of markets with zero-intelligence traders: Market as a partial substitute for individual rationality.Journal of Political Economy 101, 1, 119–137.

[31] Farmer, J. D., Patelli, P., & Zovko, I. I. (2005). The predictive power ofzero intelligence in financial markets. Proceedings of the National Academyof Sciences of the United States of America, 102, 2254–2259.

[32] Bokil, V. A. (2009). Introduction to Mathematical Modelling. [Online]. Avail-able at: http://www.mesacc.edu/~davvu4111/IntroToModel.pdf [Accessedon: 20 June 2015].

[33] Dym, C. L. (1980). Principles of Mathematical Modelling. American Journalof Physics, 48(11), 994.

[34] Morgan, C. B., Banks, J., & Carson, J. S. (1984). Discrete-Event SystemSimulation. Technometrics, 26(2), 195.

[35] Karnon, J., Stahl, J., Brennan, A., Caro, J. J., Mar, J., & Möller, J. (2012).Modelling using Discrete Event Simulation: A Report of the ISPOR-SMDMModelling Good Research Practices Task Force-4 Background to The TaskForce. Value in Health, 15(6), 821–827.

[36] Mathworks SimEvents User’s Guide for R2015a (2015). [Online]. Availableat: http://cn.mathworks.com/help/pdf_doc/simevents/simevents_ug.pdf[Accessed on: 20 June 2015]

[37] Zheng, H., Son, Y.-J., Chiu, Y.-C., Head, L., Feng, Y., Xo, H., . . . Hickman,M. (2013). A Primer for Agent-Based Simulation and Modelling in Transport-ation Applications.

[38] Maidstone, R. (2012). Discrete Event Simulation, System Dynamics andAgent Based Simulation: Discussion and Comparison. System, 1–6.

86

[39] Biais, B., & Moinas, S. (2011). Equilibrium High Frequency Trading [Online].Available at: http://www.lse.ac.uk/fmg/events/conferences/pastconferences/2012/PWC-Conference_7-8June/Papers-andslides/ Bruno_Biais_paper.pdf[Accessed on: 22 April 2015]

[40] Hendershott, T., & and Riordan, T. (2011), “High frequency trading and pricediscovery” working paper, UC Berkeley

[41] Mathworks Simulink Intro R2015a (2015). [Online]. Available at:http://uk.mathworks.com/products/simulink/ [Accessed on: 20 June2015]

[42] Davis, J. P., Bingham, C. B., & Eisenhardt, K. M. (2007). Developing The-ory Through Simulation Methods. Academy of Management Review, 32(2),480–499.

[43] Bonabeau, E. (2009). Decisions 2.0 : The Power of Collective Intelligence.MIT Sloan Management Review, 50(50211), 45–52.

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