Order Imbalance Based Strategy in High Frequency Trading

1 Order Imbalance Based Strategy inHigh Frequency TradingCandidate Number: 275571 Linacre CollegeUniversity of OxfordA thesis submitted in partial fulfillment of the MSc inMathematical and Computational FinanceMay 27, 2015 AcknowledgementsI would like to thank my supervisor, Dr. Zhaodong Wang, for his as-sistance on this thesis and providing guidance throughout. Discussionsabout this project, high Frequency Trading , hedge funds, and the industryas a whole have been interesting and the MSc Mathematical and Computational Finance class, I wouldlike to thank Ivan Lam and Xuan Liu for their ideas and perspectives onhigh Frequency Trading , Trading strategies, and statistical would also like to thank a good friend in the industry, and all aroundgenius, Jethro , my sincerest gratitude to my fianc ee Emily and my parents fortheir unending thesis aims to investigate the performance of an Order imbalancebased Trading Strategy in a high Frequency setting.

2 We first analyze thestatistical properties of Order Imbalance and investigate its capabilities asa Trading Strategy motivated by ideas introduced in [4, 7, 11]. We try tounderstand how the Strategy performs on different futures contracts andits relationship with Trading volume. Finally, we attempt to improve thetrading Strategy by including other Imbalance - Based signals, adjusting forbid-ask spread, and optimizing the model and Trading High Frequency Trading .. Limit Order Books and Microstructure .. Stationarity .. Order Imbalance ..42 Order Imbalance Volume Order Imbalance .. Assumptions and Setup .. Statistical Analysis .. Results and Performance .. Summary and Considerations ..163 Improved Additional Factors and Analysis .. Imbalance Ratio .. Reversion of Mid-Price .. Spread .. Parameter Selection and Results .. Linear Model .. with Order Imbalance Strategy .

3 Analysis .. Selection Results .. Summary and Final Considerations ..324 Further Work ..34 Bibliography35iA Daily Strategy P& Volume Order Imbalance Strategy P&L: Main Contract .. Volume Order Imbalance Strategy P&L: Secondary Contract .. Final Improved Strategy P&L: Main Contract ..48B Daily P&L Heatmaps for Various Lag 2 P&L Heatmap .. Lag 3 P&L Heatmap .. Lag 4 P&L Heatmap ..57C Trading Simulation R Code58iiChapter High Frequency TradingTraditionally, financial markets operated on a quote-driven process where a few mar-ket makers provided the sole liquidity and prices for financial assets [6]. Recently,major developments have been made to electronify the financial markets which hasled to many Trading firms using computer algorithms to trade financial assets as re-ported by Wang [14] and Aldridge [1].High Frequency Trading (HFT), in particular,has been a major topic due to the features that distinguishes it from electronic andmanual Trading .

4 This includes the extremely high speed of execution (microseconds),multiple executions per session, and very short holding periods (usually less than aday).Many algorithmic Trading strategies have been developed on the advent of highfrequency Trading coming to the markets. According to Wang [14] and Aldridge [1],the advantages to having computers execute strategies include: higher accuracy, noemotion, lower costs, and technological innovation as the speed of Trading becomesgreater. Furthermore, by using the available market data, high Frequency traders areable to come up with strategies which identify and trade away temporary marketinefficiencies and price discrepancies. In this paper, we will be adapting and testingan existing Strategy for HFT and verifying its stability and Limit Order Books and MicrostructureLimit Order Books (LOB) allow any trader to become a market maker in the financialmarkets (Gouldet al.)

5 [6]). It is a mechanism which allows traders to submit limitbuy (sell) orders for the asset and the prices they wish to pay (receive). The limitorder book is a complex system and understanding it can give insight into traders 1intentions and a way to develop Trading strategies using the rich and granular datait stores. We will define a few technical terms relating to LOBs that will be usedthroughout the paper including fields specific to the dataset we will be LOB is essentially a matching engine for buyers and sellers in the market [6].Within a LOB, the bestbid(ask)priceis the highest (lowest) price a market maker iswilling to buy (sell) the asset at to market takers. The maximum number of contractsthat the market makers are willing to buy (sell) at the bid (ask) price is called thebest bid (ask)volume. Any market taker who wishes to buy (sell) at thecounterpartypricecan submit amarket orderto trade at the best ask (bid) price up to the ask(bid) volume available.

6 If the market Order to buy (sell) is larger than the ask (sell)volume, then they will walk the book; the market taker will continue buying (selling)at the next-best ask (bid) price until their entire market Order is this project, the data we will use is the China Financial Futures Exchange(CFFEX) CSI 300 Index Futures (IF). It comprises of snapshots taken every 500milliseconds. From this point on, every time step is in intervals of 500 ms. That is,timet+ 1 is 500 ms after timet. The tick size of the IF contracts is and thetick value is 300 Chinese Yuan (CNY). The Trading hours of the contracts on CFFEXis from 9:15 to 11:30 for the morning session, and 13:00 to 15:15 for the afternoonsession. A sample of the data for January 16th, 2014 is shown in Table dayIF14019:27 :27 :27 :27 :27 :27 : certain fields omitted to save spaceTable : Sample data set for IF1401 and IF1402 on Jan 16th, data provided is in comma separated values (CSV) format and each filepresents a single Trading day.

7 However, on the CFFEX, two different futures contractsare traded: the CSI 300 Stock Index Futures (IF) and the Treasury Bond Futures(TF). We will only be focusing on the IF contracts for this paper. IF contract maturityis on the third Friday of every month. Instrument ID: the unique identifier of the futures contract being traded. Itbegins with IF or TF and followed by a 4-digit integer. The first two digits2represents the year and the last two represents the month of contract example IF1401 is the IF contract maturing in January 2014. Update time: the exact time the LOB snapshot was taken, up to 500 millisec-ond precision. Volume: the transaction volume of contracts traded since market open (9:15) Turnover: the CNY-denominated volume traded since market open (9:15).This quantity is calculated by number of contracts price tick value. Open Interest: the number of contracts traded that create an open position(not trade to close) Bid/Ask price: the highest/lowest price a market maker is willing to buy/sellthe futures contract at.

8 Equivalently, it is the best price that a market takercan sell/buy the contract at. Bid/Ask volume: the number of contracts available at the current bestbid/ask price. Second of day: number of seconds (rounded down) since midnight of thetrading measure we will be using throughout the paper is the mid-price, denotedMt, which is the arithmetic average of the bid and ask prices at timet. More detailsregarding the structure and intricacies of the CFFEX can be found in Wang [14]. StationarityAs mentioned in Wang [14], high Frequency Trading and applications of their strategiesare closely related to the ergodic theory of stationary processes. We first explain thetwo types of stationarity for a time seriesXtas defined by Tsay [12] and Wang [14].A time-seriesXtisstrongly stationaryif (Xt1,Xt2,..,Xtn) has the same distribu-tion as (Xt1+a,Xt2+a,..,Xtn+a) for allaand any arbitrary integern >0.

9 A lessstrict definition of stationarity for the time-seriesXtis calledweakly stationaryifthe first two moments do not change over time. That is,E[Xt] =E[Xt+a] = andCov(Xt,Xt+a) = afor all timetand arbitrary a. The covariance for any intervalashould only depend onafor the process to be weakly stationarity is difficult to verify empirically and therefore any hypothesistests we conduct in this paper will be to verify weak stationarity, including boththe Augmented Dickey-Fuller test and the KPSS test. It is sufficient for the datato be weak stationary for traders to build an algorithmic Trading Strategy whichgenerates positive expected profits to be applied repeatedly and steadily accumulatepositive returns [14]. Further theory regarding stationary processes, the strong ergodictheorem, and its applicability in high Frequency Trading can be found in [10, 14]. Order ImbalanceMany studies have been conducted to describe the relationship between trade activity(volume) and price change and volatility (see Karpoff [8] for example).

10 As traderssubmit limit orders to buy (sell), they impact the bid (ask) volumes of the limitorder book and thereby gives us a view of the traders intentions. Categorizing tradevolume as either taking the bid (ask) would allow us to gain insight into the directionof the upcoming price changes. To quantify this intent to trade, we look at thedifference between the bid and ask volume, called Order Imbalance . Chordia andSubrahmanyam [4] have found the positive relationship between Order Imbalance anddaily returns on a sample of stocks from the New York Stock Imbalance is an important descriptor that allows us to understand thegeneral sentiment and direction the market is headed. If informed traders have infor-mation that has not been incorporated into the asset price yet, they can take a long(or short) position given the positive (or negative) news and subsequently increasingthe Imbalance on the asset [7].