electronic market making - initial investigation

8/9/2019 Electronic Market Making - Initial Investigation

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Electronic Market Making: Initial Investigation

Yuriy NevmyvakaThe Robotics Institute

Carnegie Mellon UniversityPittsburgh, PA 15213

[email protected]

Katia SycaraThe Robotics Institute


[email protected]

Duane J. SeppiGSIA


[email protected]

Abstract

This paper establishes an analytical foundationfor electronic market making. Creating anautomated securities dealer is a challengingtask with important theoretical and practicalimplications. Our main interest is a normativeautomation of the market makers activities, asopposed to explanatory modeling of humantraders, which was the primary concern of

earlier work in this domain. We use a simpleclass of non-predictive trading strategies tohighlight the fundamental issues. Thesestrategies have a theoretical foundation behindthem and serve as a showcase for the decisionsto be addressed: depth of quote, quotepositioning, timing of updates, inventorymanagement, and others. We examine theimpact of various parameters on the marketmakers performance. Although we concludethat such elementary strategies do not solvethe problem completely, we are able toidentify the areas that need to be addressedwith more advanced tools. We hope that this

paper can serve as a first step in rigorousexamination of the dealers activities, and willbe useful in disciplines outside of Finance,such as Agents, Robotics, and E-Commerce.

1 Introduction

What is market making? In modern financial markets,market makers (or dealers) are agents who stand readyto buy and sell securities. The rest of marketparticipants are therefore guaranteed to always have acounterparty for their transactions. This renders marketsmore orderly and prices less volatile. Market maker areremunerated for their services by being able to buylow and sell high. Instead of a single price at whichany trade can occur, dealers quote two prices a bid(dealers purchase, customers sale) and an ask(dealers sale, customers purchase). The ask is higherthan the bid, and the difference between the two iscalled the spread the dealers source of revenue.

What are the benefits of automating this activity? Thisis a challenging decision problem: how can a machineupdate the bid-ask spread, anticipating or reacting tochanges in the supply and demand for a security? This

setting is also a great test bed for Machine Learning andStatistical techniques. Creation of an electronic dealer isa stab at the main goal of AI: replication of a humandecision process, which is notoriously difficult to modelor imitate. From a more pragmatic point of view,electronic market makers could render securitiesprofessionals more productive and markets more stable.Automated dealers, if designed properly, will notengage in market manipulations and other securitieslaws violations that recently resulted in a number of

dealer-centered scandals in both the NASDAQ [3] andNYSE [9]. Also, a more in-depth understanding of thedealers behavior will give us better guidance inextreme situations (market crises) and will facilitate theregulatory oversight. Finally, we expect automatedmarket making to have an impact on other disciplinesthat employ various market mechanisms to solvedistributed problems: Robotics [15], E-Commerce [7],Intelligent Agents [12], etc.

The goal of this paper is to establish an analyticalframework for electronic market making, using asimple class of strategies to highlight some centralissues and challenges in this domain. The paper is

organized as follows. Section 2 explains where thepresent effort is situated relatively to other research inthis area. In Section 3, we describe our experimentalsetup. Section 4 presents a simple model of electronicmarket making and a general taxonomy of possiblestrategies. Section 5 makes a case for so-called non-predictive market-making strategies, while Section 6presents the relevant experimental results. We concludewith a recap of important issues and a description offuture work.

2 Related Work Comparison

Automation of dealers activities was suggested morethan three decades ago [2] and is an important part ofMarket Microstructure an area that has evolved intoan independent subfield of Finance. The bulk ofprevious research on market making is mostlyconcerned with the sources and components of the bid-ask spread. A number of models have been developedto explain the evolution of the spread, incorporatingvarious factors that affect the market makers decisionprocess, such as inventory [13], information [4],volatility [6], risk aversion, competition [14], and manyothers [8]. The problem with such approaches is that


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they are mostly explanatory in nature. The relevantwork in the Computer Science community is morelimited. Market making has been adopted as a test-bedfor new Machine Learning techniques [11] with a goalto demonstrate the general effectiveness of a learningalgorithm, as opposed to treating market making as aproblem that requires solving. Also, empirical work hasdemonstrated the limitations of hard-coding market-

making rules into an algorithm [5]. The motivationbehind our approach is fundamentally different fromthat of previous research. Since we are interested increating an electronic market maker, we are much moreconcerned about future performance. Therefore, ourprimary goal is to optimally change the spread over thenext iteration instead of finding the best model for pasttransactions. We are trying to create something muchmore normative (as opposed to explanatory): todetermine which factors are important for making thespread update, and to capture the decision process of adealer.

3 Experimental Setup

In our experiments, we used the Penn ExchangeSimulator (PXS) software developed at the Universityof Pennsylvania, which merges actual orders from theIsland electronic market with artificial orders generatedby electronic trading agents [10]. Island is what iscalled an Electronic Communication Network (ECN).ECNs are somewhat different from traditional stockexchanges such as NYSE or the NASDAQ OTCmarket. NYSE and NASDAQ employ securities dealersto provide liquidity and maintain orderly markets, anduse both market and limit orders. A market order is aninstruction from a client to the dealer to buy or sell acertain quantity of stock at the best available price,whereas a limit order asks for a transaction at aspecified or more advantageous price. Therefore,market orders guarantee the execution, but not the priceat which transaction will occur, whereas limit ordersguarantee a certain price, but transaction may neverhappen. Island ECN is a purely electronic market,which only uses limit orders and employs no designatedmiddlemen. All liquidity comes from customers limitorders that are arranged in order books (essentially twopriority queues ordered by price) as shown in Figure 1a(limit price number of shares).

If a new order arrives, and there are no orders on theopposite side of the market that can satisfy the limitprice, then the order is being entered into the book. In

Figure 1b, a new buy order for 1000 shares at $25.20 orless has arrived, but the best sell order is for $25.30 ormore; thus no transaction is possible, and the new orderis entered into the buy queue. When another buy orderarrives for 250 shares at $25.40 or less, it getstransacted (or crossed) with the outstanding orders inthe sell queue: 150 shares are bought at $25.30 andanother 100 shares are bought at $25.35 (Figure 1c).This demonstrates that even though there are nodesignated market orders in ECNs, immediate and

guaranteed execution is still possible by specifying alimit price that falls inside the opposite order book. Allcrossing is performed by a computer respecting theprice and time priority, without any intermediaries.

Figure 1.

What PXS does is simple: at each iteration, it retrievesa snapshot of the Islands order book, gathers all of thelimit orders from trading agents in the simulation, andthen merges all the orders (real and artificial) accordingto the ECN rules described above: some orders transact

and some get entered into the book. When transactionshappen, agents are notified about the changes in theirinventory and cash, and the new merged order bookbecomes available to all the agents to study and makedecisions. This new order book is the staterepresentation of the simulators market, which can bedifferent from the Island market because the ordersfrom electronic traders are present only in thesimulator. The inherent problem with such setup is thatIsland (real-world) traders will not react to the actionsof the traders in the simulator, which can lead to adisconnect between the two markets. This implies thatin order for the experiment to remain meaningful, thesimulator traders have to remain low impact i.e.

their actions should not move the simulated pricesignificantly away from the Island price. We enforcethis property by prohibiting the participating agentsfrom accumulating a position in excess of 100,000shares either short or long. Such a simple rule gets thejob done surprisingly well. To put thing in perspective,daily volume in the simulator reaches many millionshares (actively traded MSFT is being used).

As stated before, PXS does not have market orders thatflow through the dealers, or any designated dealers atall, for that matter. This can lead to a conclusion thatsuch setup is ill-suited for studying the market makersbehavior. But we have to draw a distinction between

market making as an institution (as seen on the NYSEfloor) vs. market making as a trading strategy (used onproprietary trading desks and certain OTC dealingoperations). The former can be interpreted as publicservice, where the market maker has certainobligations. He is supposed to be compensated by thebid-ask spread, but because of heavy regulations thatprotect customers, the dealer often finds himself beingrestricted in trading opportunities, which limits hisprofits [9]. Alternatively, market making can be

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interpreted as a strategy where a trader tries to keep hisstock position around zero (being market neutral) andto profit from short-term price fluctuations. As far aslow profile trading goes, the market maker is notsupposed to move markets: the NYSE dealers areexplicitly prohibited from doing so by the negativeobligation principle. Thus, our setup is well suited forstudying market making as a strategy, which also

happens to be the main part of market making as aninstitution.

4 Market Making: A Model

We decompose the problem facing the electronicmarket maker into two components: establishing thebid-ask spread and updating it. We further subdividethe update methods into predictive and non-predictive.The primary objective of a dealer is to manage the bid-ask spread: it has to be positioned in such a way thattrades occur at the bid as often as at the ask, thusallowing the dealer to buy low and sell high. (We willexamine these mechanics in Section 5). In order for thisto happen, the quotes have to straddle the true price

of the security [6] and be positioned as close to it aspossible. However, the true price is an elusiveconcept, difficult to determine or model. Therefore, thefirst decision for the market maker (either human orartificial) is where to establish the initial spread.

Figure 2.

There are two ways to approach this decision. The first,hard way is to perform the actual valuation of thesecurity being traded: for a stock, try to determine thevalue of the company using discounted cash flows,ratios, etc.; for a bond, find the present value of thepromised payments, and so on. If there is no establishedmarket, or the market is very illiquid, then valuationmay be the only approach. Fortunately, the majority ofmodern securities markets employ limit orders in somecapacity. The two queues of the order book should bean accurate representation of the current supply (sellqueue) and demand (buy queue) for the security.Presented with such supply-demand schedule, themarket maker tries to determine the consensual value.In the simplest case, the dealer can observe the top ofeach book the best (highest) buy and the best (lowest)sell also known as the inside market. He thenassumes that the markets consensus about the price liessomewhere between these two numbers. In Figure 2a

the best bid is $25.21, and the best ask is $25.30 (theinside market is $25.21-30), and the true price of thestock is in this interval. Now, the market maker can usethe top of each book as a reference point for positioninghis initial quotes at $25.22-29, for example (Figure2b) and then update his spread as the book evolveswith new arrivals, transactions and cancellations.

Updating the spread is at the heart of market making.

While the order book is informative about theconsensus price of the security, it often fails to providesufficient liquidity, thus creating demand for marketmakers. We classify update strategies into twocategories. The first attempts to foresee the upcomingmarket movements (either from the order bookmisbalances or from short-term patterns), and adjust thespread according to these expectations. The secondgroup reasons solely on the information about thecurrent inside market. These non-predictive strategiesare inherently simpler, and, therefore, better suited forour introductory examination of electronic marketmaking.

5 Non-Predictive StrategiesIn order to make the case that the non-predictivestrategies are worth considering, lets examine in detailhow the market maker earns money. Following themovement of the stock price over several hours, it iseasy to discern some patterns: going up, down, back up,and so on. But if we take an extremely short time period(seconds or fractions of a second), it becomes apparentthat the stock constantly oscillates up and down arounda more persistent (longer-term) movement. If the pricerises consistently over an hour, it doesnt mean thateveryone is buying; selling is going on as well, and thetransaction price (along with the inside market) moves

down as well as up. Figure 3 illustrates this: while thereis an upward movement (the dotted line), we can seethe temporal evolution of the order book wheretransactions happen at the top of the buy queue, thenthe sell queue, then buy, then sell again. By maintaininghis quotes on both sides of the market, at or close to thetop of each order book, the market maker can expect toget hit at his bid roughly as often as at the askbecause of these fluctuations. This way, after buying atthe bid (low) and selling at the ask (high), the dealerreceives the profit equal to the bid-ask spread for thetwo trades, or half-the-spread per trade. In the contextof Figure 3, suppose that the top order in each queue isthe dealers; the dealer buys at $25.10, then sells at

$25.18 (8 cents per share profit), buys at $25.16 andsells at $25.26 (10 cents profit). If each transactioninvolves 1,000 shares, and all this happens over severalseconds, then market making can be quite profitable.

Having understood the nature of the dealers income,we can re-formulate his task: adjust the bid-ask spreadin such a way that the orders generated by other marketparticipants will transact with the dealers bid quote andthe dealers ask quote with the same frequency. In our

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example, we are looking for an algorithm to maintainthe dealers quotes on top of each queue to capture allincoming transactions. The stock price is steadily goingup overall, while fluctuating around this general climb,so if the market maker wants to maintain profitability,then his spread should also continuously move upstraddling the stock price.

Figure 3.

How can the dealer tell at any given point lookingforward that its time to move the spread up and by howmuch? The non-predictive family of electronic tradingstrategies would argue that he cannot and need not doso. It postulates that while there are some patternsglobally, the local evolution of the stock price is arandom walk. If this random walk hits the bid roughlyas often as it hits the ask, then the market maker makesa profit. This means that an uptick in the stock price isas likely to be followed by a downtick as by anotheruptick idea of efficient markets with short-termliquidity imbalances. If the above assumption holds,and if the dealer is able to operate quickly enough, thenthe trading strategy is very simple. All the dealer has todo is maintain his bid and ask quotes symmetricallydistant from the top of each book. As the book evolves,the market maker has to revise his quotes as quickly aspossible, reacting to changes in such a way thatprofitability is maintained.

In principle, the dealer should be market neutral i.e.he doesnt care what direction the market is headed heis only concerned about booking the spread. On theother hand, the dealer is interested in knowing how theinside market will change over the next iteration inorder to update his quotes correctly. The way the non-predictive strategies address this is by assuming that theinside market after one short time step will remainroughly at the same level (thats the best guess we canmake). Therefore, being one step behind the market isgood enough if one can react quickly to the changes.

Such is the theory behind this class of strategies, but inpractice this turns out to be more complicated.

6 Implementation and Results

Here is a general outline of an algorithm thatimplements the non-predictive strategy; at eachiteration:

(1) Retrieve the updated order book;(2) Locate an inside market;

(3) Submit new quotes (buy and sell limit orders),positioned relatively to the inside market;

(4) Cancel previous quote.

As it should be clear from this description and thetheoretical discussion above, there are three mainfactors, or parameters, that determine a non-predictivestrategy: position of the quote relative to the insidemarket, depth of the quote (number of shares in the

limit order), and the time between quote updates.6.1. Timing

Timing is, perhaps, the simplest out of the threeparameters to address. Our experimental results areconsistent with the theoretical model from Section 5:faster updates translate into higher profits. The dealerwants to respond to changes in the market as soon aspossible, and therefore, the time between the updatesshould be as close to zero as the system allows. Theimplication of this rule is that update time shouldcertainly be minimized when designing an electronicmarket maker. The computational cycle must beperformed as fast as possible, and the communication

between the dealer and the market should also be spedup. Our experiment shows that its the latter issue thatis a more important bottleneck, plus its the one harderto control. The computational cycle for a simplestrategy is inherently short (under 1 second), but it takesabout 3 5 seconds for a submitted order to show up inthe book, and about the same delay for the order to getcancelled (if not transacted) after it appears in the book.While these delays are not unreasonable by the realworlds standards, they are not negligible. This is oneof the frictions in market implementation, whichshould not be overlooked: the dealer wants to access themarket as quickly as possible, but such delays canprevent him from operating on a scale short enough to

capture the small fluctuations. Therefore, other systemswhere these delays can be decreased can potentially bemore effective and produce better results than oursimulated setup.

6.2. Quote Positioning

Position of the quote relative to the rest of the orderbook is the most important parameter. We use a simpledistance metric: number of cents by which the dealersquote differs from the top [non-dealer] order in theappropriate book. We started our strategyimplementation with a well-known, albeit controversialpractice of penny jumping. In general, penny jumpingoccurs when a dealer, after entering his customers

order into the order book, submits his own order, whichimproves the customers limit price by a very smallamount. The dealer effectively steps in front of hiscustomer: the customers potential counterparty willtransact with the dealer instead. Such practice is notillegal (because the dealer does provide a priceimprovement over the original order), but is consideredunethical, and became the center of the recent NYSEinvestigation [9]. In our case, we are simplyundercutting the current inside market (or the de facto

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bid-ask spread) by one cent on both sides. Figure 2ashows that if the inside market is 25.21-30, our marketmakers orders will make it 20.22-29 (the size of thebid-ask spread goes from 9 to 7 cents). This way, thedealer is guaranteed to participate in any incomingtransaction up to the size specified in the depth of hisquote. We expect the following behavior from thisstrategy: the revenue (P&L) should rise slowly over

time (since profit per share is tiny), while the inventory(I) ought to fluctuate around zero (see Figure 4a). Weobserve, however, that in our test set a typical tradingday looks like Figure 4b: the strategy gradually losesmoney.

Figure 4.

The fundamental problem is that while we base ourdecision on the book at time t0, our orders gets placed inthe book at t1, which may or may not be different fromthe original t0 book. The non-predictive strategy placesan implicit bet that the two books will be close at leastenough to preserve the profitable property of dealing.What actually happens in our tests, is that the insidemarket is already tight, plus the book changessomewhat over the 3 second delay, and thus,oftentimes, both the bid and the ask placed at t0 end upon the same side of the market at t1 (Figure 5a). Thenone of the orders transacts, and the other gets burieddeep in the order book. If we find ourselves in thissituation on a regular basis, we end up paying thespread instead of profiting from it. This explains whyour actual P&L pattern mirrors the pattern we expected.This experiment highlights the three challenges forelectronic market making in any setting: (1) makingdecisions in one book, acting in another; (2) marketfrictions aggravate this disconnect; and, (3) spreadsare extremely tight leaving little or no profit margin [1].

Does this mean that the non-predictive strategies areinherently money-losing? Not at all one modificationsolves the third issue and mitigates the first two. We

found that instead of undercutting the inside market, itis more profitable to put the quotes deeper in theirrespective books. The dealers spread is wider nowresulting in higher margins, plus even if the quotes getput into the book with a delay, they still manage tostraddle the inside market and preserve the buy low,sell high property. Figure 5b shows the exact samescenario as Figure 5a, but with wider dealer quotes.Wider spreads lead to higher profit margins, but lessvolume flowing through the dealer. One has to find a

balance between these two components of the revenue.We determined that putting the quotes 1-3 cents awayfrom the inside market works well, and alleviates theconcerns that make penny jumping unprofitable. Wealso determined that the third fundamental parameter the depth of quote can also increase the dealersvolume and thus his profitability: the deeper the quotethe more stocks will flow through the dealer with each

transaction. However, increasing the volume to anarbitrary level has consequences for dealers inventory.

Figure 5.

6.3. Inventory Management

In theory, the market maker should buy roughly asfrequently as he sells, which implies that his inventoryshould fluctuate around zero. In practice, however, thisdoesnt always work out. If a stock price is going upconsistently for some period of time, the dealers askends up getting hit more often than his bid. If thedealers quote is deep and/or close to the inside markethe winds up with a growing short position in a risingstock he is taking a loss. Plus, even the main

assumption behind the non-predictive strategies canfail: when a stock crashes, there are actually nobuyers in the marketplace, and our entire market-making model is simply not valid any more. Finally, ifa dealer accumulates a large position in a stock, hebecomes vulnerable to abrupt shifts in supply anddemand i.e. if he has a significant long position, andthe stock price suddenly falls, then hes taking a loss. Inbrief, there is a trade-off: on one hand, the dealer wantsto have a large inventory to move back and forth fromone side of the market to the other making profit, butthen he doesnt want to become exposed by having aposition that cannot be easily liquidated or reversed. Toreconcile these conflicting goals, some rules have to be

put in place to manage the dealers holdings. We haveimplemented and tested a number of such approaches.The distance to the inside market proved to be the moreeffective, since its tied both to the inventory andprofitability. If there is too much buying (the dealersask is being hit too often, and he accumulates a shortposition), then moving the ask deeper into the sell bookcompensates for this. Also, if the stock is going in onedirection consistently, this approach will force thespread to be continuously adjusted, using the inventory

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misbalance as a signal. We achieved good results withthe formula QuoteDistance = MinimumDistance +alpha * max(0, Inventory InitialLimit)/Inventory *MinimumDistance. When the position is within theInitialLimit, the quote is always set MinimumDistanceaway from the market, but if the inventory gets outsidethe limit, the quote moves further away, encouragingthe inventorys movement in the opposite direction.

7 Analysis and Conclusion

Implementing and testing the non-predictive market-making strategies, we arrived at a number ofconclusions: faster updates allow to follow the marketmore closely and increase profitability; to combatnarrow spread and time delays, we can put the quotedeeper into the book, although at the expense of thetrading volume; trading volume can be increased withdeeper quotes; inventory can be managed effectively byresizing the spread. However, non-predictive strategiesdo not solve the market-making problem completely.Figure 6 exemplifies one general shortcoming of non-predictive strategies: at the open, the price keeps going

up, the market maker cannot get his quotes out of theway fast enough, accumulates a large short position,and loses a lot of money. All this happens in 10minutes. This goes back to one fundamental problem:there are times when the short-term fluctuations inwhich the non-predictive strategies are rooted justarent there. The only way to address this is to use somepredictive instruments order book misbalances, pastpatterns, or both in order to be prepared for thesestreaks.

Figure 6.

Even with this inherent weakness, the non-predictivestrategies have some clear practical advantages. First,they are simple and computationally cheap, but, at thesame time, a human trader can never replicate them.Their performance can be improved by speeding up the

access to the market, or by applying them to less liquidstocks. Their use of the inside market as the onlydecision anchor makes them indifferent about thecomposition of the trading crowd. And, finally, theproblematic situations, described above can be handledby special cases to boost the overall performance.

In this paper, we have presented a structured frameworkfor reasoning about the electronic market making andanalyzed a number of fundamental issues in this domainusing a simple class of strategies as an example. While

we have not provided all the answers, our main goalwas to frame electronic market making as a coherentproblem and to highlight the points that must beaddressed in order for this problem to be solved. Webelieve that this is an interesting and promising area,and that advances in the electronic market making willbe useful in disciplines beyond Finance.

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