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1. A MODERN MARKET MAKER
Mohammad AL Akkaoui – M2 Financial Economics
Paris 1 Pantheon Sorbonne

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Table of Contents
1. INTRODUCTION:...........................................................................................................3
1.0 ECONOMICS OF MARKET MAKING: .................................................................3
2.1 MICROSTRUCTURE OF MARKET MAKING:...........................................................4
2.2 THE ROLES PLAYED BY MARKET MAKERS..........................................................4
2.3 THE SUPPLY OF MARKET MAKING AND PROCESS.............................................5
2. ELECTRONIC MARKET MAKING: ..........................................................................7
A. LMSR PRICING MODEL:.............................................................................................8
B. MM PRICING MODEL:.................................................................................................8
3. EXAMINATION:.............................................................................................................9
4. ALTERNATIVES: .........................................................................................................12
5. CONCLUSION AND OPINION: .................................................................................13
6. BIBLIOGRAPHY ..........................................................................................................15

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1. Introduction:
Financial markets are often referred to as the fabric that holds our economy together.
They have allowed us to progress further in our evolutionary story, for example by financing
the discovery of new continents or curing fatal illnesses. Multiple players play different roles
in these markets, however only one of them is expected to always and under any circumstance
be available to respond to orders on the market, and that player is the market maker. Market
makers stand ready to buy or sell whatever the price was to ensure market liquidity. Liquidity
plays a key role in financial markets, and by providing liquidity, market makers ensure that the
music keeps on playing. Advances in the process of market making have a monumental effect
on the entire financial realm. During the last couple of decades, we have slowly moved towards
a more automatized financial system. As part of this transition, traditional market makers have
been replaced by computers that use complex algorithms and make decisions in fractions of
seconds.
These computer programs have arrived as a more efficient alternative to humans. They
operate in the same way as humans. They essentially provide a bid/ask spread they see fit
according to market conditions and they stand ready to accept any transaction sticking to that
spread. However, electronic market makers should theoretically provide a more stable pricing
mechanism since they are not subject to any personal preferences or other factors.
In this paper will provide with a brief overview of the current theoretical state of market
making and will mostly focus on the current drift to electronic market makers. We are mostly
interested in the pricing models used by these market makers. We will look in to a model
proposed by Brahma et Al (2012), the proposed model is dubbed a “Bayesian Market Maker”.
That model will be compared to the most prominent alternatives on the market. Furthermore,
we will …
1.0 Economics of Market Making:
Prior to further engagement with this topic, this essay will give a brief overview of the
economics that governs market making. The role of the market maker starts when the market
is in a state of imbalance, i.e. when buyers and sellers cannot be matched easily; in this case,
the market maker has to be active and correspond to every trade received. It can be inferred
that these agents provide liquidity to the market whenever needed. What’s more, providing

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liquidity is the market maker’s main objective. And seeing as liquidity is needed to ensure the
functioning of the financial system, market makers plays an important role. Furthermore,
liquidity is also needed to instil trust in investors that they can trade their assets as easily as
possible and move around their wealth. This capital mobility translates into the creation of
wealth in the real economy.
2.1 Microstructure of Market Making:
The field of market microstructure is interested in studying what rules and mechanisms
govern the market. And the most important aspect of this field is interested in the process of
price creation. The most straightforward representation of a market is the double auction one.
In this market buyers and sellers specify their quantities and prices and if there is a match, a
trade takes place. The problem with double auction markets is that these markets are only
efficient when there is enough liquidity. By enough liquidity we mean that matches between
the two isolated pools of buys and sells must occur rapidly It was quickly realized that
individual matches do not often occur and a new player must be create to fulfil that role.
As a result, exchanges employed market-makers, these induvials had the role of
ensuring immediate execution of orders and supplying liquidity to the market. These market
makers were assigned to specific asset. Additionally, market makers were required to post their
bid and ask spread to the general public. The introduction of electronic trading allowed
investors to observe quotes by different markers market makers on the same asset, as a result
competition in between these players rose and pushed efficiency upwards.
2.2 The roles played by market makers
The basic function of a market maker is to be a middle man between sellers and buyers
of financial assets but at different times. He does not do that for free though and makes a profit
by adjusting prices to his favour. However, by offering on the open market he risks loss to
informed traders (Hanson, 2009). To prevent that from happening market makers have to study
precisely the price and duration of their offerings. In a way to make the maximum profit from
uninformed traders and minimize their loss from the informed ones.
To fully understand how market makers work this essay will explain the process using
bond markets. Bond markets are mostly over the counter (OTC). Mainly because they hold a
lot of characteristics in common, such as: having a large and diverse set of assets, assets can be
restocked without the need to pass by the secondary market, and large trades that should not

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pass on a central limit order book. Since this is not a two-way market large players attempt to
assist trades, by either trading on behalf of their customers or by looking for matches of them.
As a result, market makers are expected to service their customers immediately and as a result
supporting liquidity and price discovery. Additionally, they are expected to maintain liquidity
even if it means that they have to absorb adverse shocks and quote prices that support market
continuity.
With regards to government bonds a lot of banks have implemented a primary dealer
system, in which one player (or consortium) is allowed to act as a market maker and is given
incentives to maintain his obligation. As for the majority of bonds issued by publicly traded
firms they require liquidity on the secondary market so they pay a fee on a deal to deal basis
(Nielsen, et al., 2012).
2.3 The supply of market making and process
Market makers take part in diverse markets leading to slight variations in their expected
roles, however overall, they share similar business models. Their business models usually
depict a large base of customers to ensure an abundant flow of trades and large stock of assets
to trade if needed. Additionally, they must ensure access to international markets; but the most
important aspect needed is professional personal to set the quotes on the market (Madureira &
Underwood, 2008).
As stated previously market makers are expected to act on both sides of the market and
as a result are at risk of incurring a loss. Their profit and loss account can be divided in to two
main categories, facilitation revenues that show the spread made on setting bid and ask prices
minus the cost of the trade. The second category is trades that were counteracted by other
incoming trades and are stated as inventory revenues. From these streams one variable pops up,
the price quoted by the market makes can provide them with the power to manipulate or even
stall down markets.
Market makers set a two-sided price, on one side the bid price that they are willing to
buy assets at and at the other one the ask price that they are willing to sell assets on. The
difference between these two represents the spread of the market. This two bracket pricing
system used by the market maker provides the ability to predict on markets immediately in a
proper stock exchange (Desmsetz, 1968). As for the bid and ask prices themselves, they are set
under the assumption of perfect competition. Overall the market maker’s main role is to set his

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prices according to how he observes the market is going. It should be noted that the spread
provides market participants with valuable information on the intent of the market maker and
the general condition of the market.
That spread will move narrower if the market maker can rapidly balance trades out, this
also decreases the costs incurred. Hence in a highly liquid market the market maker will move
towards a narrower spread due to a lower cost of operations and subsequently not as much
revenue per trade (Schultz, 2003). As for less liquid markets the opposite prevails as the market
make has to keep a large inventory of securities increasing his cost and making him demand a
larger spread. As a result of this relationship market makers provide their quotes as a function
of the markets liquidity; for highly liquid markets two way prices are continuously quoted with
a tight spread as the market maker demands a large volume of trades to generate a sizable
bottom line. Meanwhile on less liquid markets the market maker will quote on demand, i.e.
quotes are not shared openly, as this market is more order driven. Generally, quotes in these
markets are high as the volume of trades does not make for a sizable bottom line using the rates
charged on the other end of the spectrum (Praet & Herzberg, 2008). Hence liquidity plays a key
role in the market making process.
It should be noted however that liquidity is a function of market conditions and investor
sentiment, as a result a relationship between the market makers quote and the rest of the market
prevails. By so market makers adjust their prices and strategies according to prevailing market
conditions just by observing their level of liquidity. Let us take the case of a volatile market as
an example; the increase in volatility will decrease the market makers desire to hold on to assets.
As a result, a market maker will widen his spread and the quantities set at the best prices on the
market (BIS Committee on the Global Financial System, 2014).
What has been stated in this section is a general characteristic of all market makers;
however even though market makers still have similar business models the market has evolved
drastically. Since the last decade of the twentieth century finance has been slowly progressing
towards more and more digitalization. Traditional market makers have been able to stand
against this tide of change as they adjusted their business models however that has changed
over the years. As a larger share of volume moves towards electronic trading platforms market
makers across the world are being forced to also automate their services. The movement though
to electronic market making has not been able to catch up to the demand for such a service, as

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a result online trading platforms have started to perform basic market making activities (BIS
Markets Committee , 2016).
2. Electronic market making:
Ever since electronic trading first kicked off in the end of the last century the demand
to provide real time quotes on line rose, and with the entirety of global exchanges now providing
services online the demand has never been higher. Multiple models have and still exist
attempting to provide the best formula for electronic market making, in the upcoming sections
we will take Euronext Paris as our prime example.
Euronext Paris is by design an automated order driven market; in other terms, all orders
from members are sent automatically from individuals on the market to a central limit order
book. Additionally, for the public the top five bid and quote prices and their corresponding
quantities are constantly available for purchase. As for execution, all incoming orders are
performed automatically with the best match limit orders available in the book. Meanwhile for
large block trades they can removed from the top five quote list.
To ensure liquidity Euronext Paris allows some stocks to have active liquidity providers
on the market (named ALs standing for apporteurs de liquidite). These liquidity providers play
a role in taming market volatility by actively trading any gaps in the market or counteracting
liquidity shocks. They are also needed to guarantee transactions always pass through and at the
most optimum price. Lastly, they play a role in increasing the volume of transactions passing
through the system.
Euronext Paris is not the only example of an electronic market maker and other
examples exist. Multiple attempts have been made to find the perfect model for an automated
market maker. One proposal by Garman (1976) proposed a monopolistic market maker that sets
prices by maximizing his expected profit in each unit of time. That model however is function
of the market makers ability to keep a steady inventory of liquid money and will collapse if it
fails to meet its cash based needs. Meanwhile another attempt by Ho & Stoll (1981) also
specifies a single market maker per instrument but faces random demand and maximizes its
profits by based on the utility of its final bottom line obtained from its activities. However, the
most advanced of them all is the LMSR market maker developed by (Hanson, 2007) and we
will use it as a reference to the prevailing technology used by electronic market makers.

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a. LMSR Pricing model:
As stated previously we will use the LMSR as our reference model and compare the rest
of the models tested to it. This model uses a scoring rule in a prediction market setting to make
its decisions. The scoring rule used by the authors is based on logarithmic equations and is
believed to be the most efficient method when electronic market making is concerned. In this
model, the market makers price setting mechanism is dependent on one special variable named
b. We will get to that variable later before that it should be noted that according to LMS the
market maker sets its price to insure a constrained loss whatever the level of liquidity is.
The spot price is function of the market makers current inventory using a logarithmic
transformation, and b decides the size of the spread. It is used to set the adaptively level of the
market maker. A smaller b indicates a more adaptive market maker as a result small losses are
allowed and a larger spread is resulted due to lower liquidity. In other words, the smaller is b
the smaller are he losses incurred by the market maker but that comes at the cost of a less liquid
market. As a result, it also bounds its loss, hence to minimize market maker loss a less liquid
market is required. This is one of the main drawbacks of the LMS.
To adjust to this fact the model was altered and another liquidity variant version of the
model was created (LMSR). In this model, the price response of the model is the same whatever
the level of liquidity is (Othman, et al., 2010). This is achieved by transforming b in to an
endogenous variable in the model increasing as the market volume does to. On the other hand,
the model still has a bounded loss that can eliminate losses if demanded.
This model is considered to be one of the ground-breaking techniques in setting an
algorithm for an electronic market maker. For that reason, it will be used as a base to test the
model referenced in the upcoming section.
b. MM Pricing Model:
Participants on the open market do reach their decisions using a set of rational rules but
they also do incorporate their own believes on the task in front of them. That belief is how much
they think the value of that asset should be and thus driving them to perform the trade in the
first place. Additionally, according to them believes investors drive up or down the price of the
asset they are actively trading. To incorporate for this an electronic market maker should also
have its own belief system. The solution comes in the form of an information based market
maker first proposed by Das and Magdon Ismail (2008).

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This solution incorporates an electronic market maker which holds a belief about the
true value of the traded security. That belief is adjusted every time the market maker makes a
trade and it is proxied for by the previous probability density (Brahma, et al., 2012). Combined
this creates market asymmetry as the market maker and most other traders have different sets
of beliefs about the true value of the traded asset. As such the market makers sets the spot price
and the traders respond each acting based on their own sets of beliefs with that of the market
maker evolving per trade. It should be noted that under a perfectly competitive market the
market maker sets its prices to receive no expected profits.
After every trade, the market maker observes the trader’s response and whether they
bought, sold, or did not trade any shares. This information is used as the investors trigger point
representing approximation of his true belief what the value of the asset should be. This
information is fed back again in to the market makers own belief of the assets value (Brahma,
et al., 2012).
This model operates based on two corner stones; the first one is that the market maker
always has its own belief on the true value of the asset represented by the density distribution.
The other corner stone is setting prices to achieve a given goal, most probably that goal is the
amount of profit it is expected to extract from the market. Brahma et al (2012) use this proposed
model a market making algorithm named the Bayesian Market Maker Algorithm (BMM).
The BMM benefits from two traits supplied by Das and Magdon Ismail’s (2008) model;
the capacity to take on sizable trades and the rapid adaptability to adverse market events. Other
than the two tasks provided by the previous model it also observes the investors reaction and
makes count for it in the upcoming trade.
3. Examination:
With the two models now introduced they can be compared, however we will not
compare the mathematical basis of the models and will be sufficient with comparing the data
obtained from simulated trading. We will turn to the tests done by Brahma et al (2012) in our
explanation. The authors ran a trading simulation made up of 200 time periods with the true
value of the underlying asset moving according to a Gaussian distribution with the probability
of jumping to a new price being 1%, additionally uniform shocks were also used. The figure
bellow represents a simulated trading experiment performed on the two algorithms (one
simulation 100 time periods).

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These three figures can provide us with an initial comparison between the LMSR and
BMM algorithms. The initial results show that the BMM can adopt faster to changes then it’s
counterpart and stably assigning quotes around the equilibrium. Notice also that when large
shocks occur and the price moves instantaneously the BMM is better equipped than the LMSR
in adjusting to the new true value of the asset. Overall the BMM seems to be more capable of
adjusting to changes in the true market value of an asset, this is explained by the spread set by
the algorithm. The spread set initially widens whenever it detects a significant shift and then
slowly tightens towards the equilibrium.
The table above is from the same experiment (1000 simulations each covering 200 time
periods) and summarizes empirically the performance of the tow algorithms. The first thing that
pops up is that the BMM was able to generate a profit whatever the type of shock was

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meanwhile LMSR continuously made a loss. However, this does come at a cost as these
simulations show that the BMM is more likely to have wider spreads then it’s counterparty.
As much as the previous experiment gains in terms of empirical soundness (Alwin fix
this please) human experimentation can provide us with better results. For that reason, the two
algorithms will be tested using a live trading experiment obtained from Brahma et al (2012).
The experiment uses the same test group to simultaneously compare both market makers to
limit biasness; it consists of a simple exercise in which a trader states what quaintly he demands
to buy or sell, based on that information the algorithm provides him with its price and he has to
decide whether to accept it or not. It should be noted that the price moves according to a random
walk which traders comprehend slowly overtime as in real markets. Additionally market shocks
will be simulated during the exercise to test the algorithm’s response. Overall six individual
experiments were run and the results came in as follows (one chart per experiment):

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As with the previous experiment this one also shows (5 out of 6) that BMM is cable of
generating a higher profit than LMSR. It was also capable of surpassing LMSR in obtaining the
true value of the underlying asset, as measured by RMSD in the table above. As with market
shocks the experiments show that BMM is at least as fast if not faster in adapting to shocks than
LMSR. However, it should be noted that in equilibrium 4 the LMSR was more capable of
reaching the true value of the asset than BMM, it also demonstrates a substantial monetary loss
for BMM.
To further ratify the relative superiority of BMM over LMSR an agent based experiment
was conducted; agents were split as fundamental (half assuming rational expectations including
price history and the other half only using information it receives from its trials) and technical
traders playing the role of noise traders. The results came in as follows:
This experiment shows that BMM is more capable assigning a lower spread than LMSR
while also generating a lower expected loss. Raising LMSR’s b value tightens the spread but
increases its loss. This more realistic experiment (with rational agents) shows us BMM’s edge
over LMSR as it increases LMSR’s loss and increases BMM’s stability.
4. Alternatives:
While BMM and LMSR both seem to present an efficient way to the problem at hand,
they can be improved greatly. The problem with BMM and LMSR is that they are static and
fail to evolve with respect to the market and learn from the actions of market participants. At
the time of their development this was not possible but now with the recent advancements in

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the field of artificial intelligence a new approach to the problem can be used. In their paper Li
et al (2013) introduce a new market maker that nor only adjusts his price based on the past but
also attempts to forecast the future price of the asset he is responsible for. Their market maker
utilizes all the information he has in his order book in addition to any available market news to
predict the price. That information is then used to steer the market towards it’s true value and
it is also used to limit losses due to unexpected trends. In core, this model does not differ that
much from BMM, since it also holds a belief system about the true value of the underlying
asset. However, the origins of this belief differ drastically as the BMM attempts to extract it
from the action of traders rather than from market news; incorporating a fact-based belief
system would drastically improve BMM’s performance and should be the point of interest of
future researchers.
5. Conclusion and Opinion:
Market makers have come a long way from the humble times of the “commissioner des
treasures”, the market has evolved to become a fast and dynamic world and hence so should
the market maker behind it. A lot of breakthroughs for market makers came over the years, the
LMSR seemed to be the most efficient method to deal with the task at hand. The algorithm
allowed for full atomization of the market making process and thus freeing personal for more
profit generating. Our examination of Brahma et al’s (2012) paper showed us that an alternative
to LMSR exists in the form of BMM. In summary, the BMM algorithm provides a more suitable
alternative to LMSR mainly because it on average will not generate a loss and can provide
faster and more accurate quotes in a simulated market environment.
BMM however does suffer from one fatal flaw which is that it only concentrates on one
variable to predict the market; the actions taken by traders cannot alone fully explain the price
movement of the asset they are trading. Introducing machine learning in to BMM should be the
next step in the evolution of market makers; with that the algorithm can better deduce the future
price and limit any losses.
As with everything else in our social evolution as a financial market will continue to
evolve as we discover more innovative solutions to the problems we face. Most recently high
frequency computing has catapulted us well in to the future were machines are taking over the
simplest of tasks; machine learning and artificial intelligence might be the obvious next step
for market makers but it will not be the last.

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6. Bibliography
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BIS Markets Committee , 2016. Electronic trading in fixed income markets, Basel: Banl
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Brahma, A. et al., 2012. A Bayesian Market Maker, s.l.: ACM Trans..
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Madureira, L. & Underwood, S., 2008. Information, Sell-Side Research, and Market
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Nielsen, D., Gyntelberg, J. & Sangill, T., 2012. Liquidity in government versus covered
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Othman, A., SANDHOLM, T., PENNOCK, D. & REEVES, D., 2010. A practical
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