Chapter 7 Conclusion - Gilles Daniel

Chapter 7
Conclusion
“The effect of noise on the world, and our views of the world, are
profound. [...] Most generally, noise makes it very difficult to test
either practical or academic theories about the way that financial or
economic markets work. We are forced to act largely in the dark.”
Fisher Black, Noise [Bla86]
This chapter brings the thesis to a conclusion. We begin by summarising
the key points of this work, what guided us in this direction and what can be
learned from our models and experiments. We then review our contributions and
academic achievements, and suggest some direct applications for practitioners.
7.1 On the origins of this thesis
This thesis has been mainly concerned with the role played by liquidity in the
dynamics of price formation in stock markets. We started by acknowledging
that since its very creation, the field of academic Finance has largely dismissed
as irrelevant the way markets are organised and operate, favouring instead the
parsimonious and analytically tractable efficient market models. From this normative
perspective, markets operate at equilibrium between the aggregate supply
and demand generated by informed and rational traders, so that the prices they
produce constantly reflect any type of information and constitute the best possible
estimator of the fundamental value of shares. One of the reasons explaining
the early success of this approach, aside from providing closed form solutions
and feeding free market advocates with useful theoretical arguments, is that this
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so-called fundamental value is so difficult to estimate in real life that one can
never falsify the hypothesis that market prices actually reflect it closely. In fact,
only indirect evidence on its predictions could be provided, for instance on the
apparent random nature of price changes or the inability of fund managers to
consistently outperform the market. However, it was shown that market prices
are far too volatile to be simply explained by the arrival of new information, and
some research started being conducted on the role of market microstructure and
the incidence of traders’ psychology on their decision making process. Market
Microstructure and Behavioral Finance are nowadays two research fields widely
recognised for their contribution to a deeper understanding of financial markets.
With the wider availability of data, more stylised facts exhibited by real markets
were identified, and the research endeavour to explain these properties left unexplained
by the efficient market models shifted from exogenous information-based
models to the study of endogenous dynamics that could generate comparable price
changes. In particular, some statistical models have recently been presented in
the field of EconoPhysics that relate the dynamics of the order flow to the price
dynamics.
In order to capitalise on these recent advances in the fields of Market Microstructure,
Behavioral Finance and EconoPhysics, we participated in a project
having an artificial stock market implementing a double auction mechanism, the
most pervasive matching mechanism found among real markets. Special attention
was paid to the design of the market architecture, and the model was agent-based
so as to allow for the easy modelling of various trading strategies. The aims were
multiple. Firstly, to verify whether classical models of price formation, that
assume that markets operate at equilibrium following a simple price clearing condition,
would survive or alternatively break down when tested in a more realistic
market environment. Secondly, to relate the dynamics of the order flow to the
microscopic behaviour of the traders responsible for it, with the hope of eventually
being able to provide first principle explanations of the dynamics of the
order flow and of global price formation. Finally, to test the impact of different
trading strategies on these price dynamics. In the process of experimenting with
this market simulator, we realised the importance of timing for trading strategies:
two strategies identical on every point except on their timing will not have the
same price impact (and hence probably not the same performance), even if they
produce the same net aggregate demand. This is because the price dynamics are

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affected not only by the aggregate level of supply and demand, but more importantly
by the timing in which orders arrive, are stored in the book or generate
a trade which moves the price; in a word, by the liquidity of the market. This
became the main thesis of this work.
7.2 Contributions and achievements
In this dissertation, we have presented a model and computer implementation of
zero-intelligence agents which is able to generate a realistic order flow – except
for the long memory in orders signs, incompatible with random agents – which in
turn produces realistic price dynamics, and is able to recover qualitatively and to
a certain extent quantitatively the main stylised facts exhibited by real markets.
We found that these non-trivial statistical properties are the result of the subtle
interplay between limit orders, which provide liquidity, and market and cancellation
orders, which remove it. To our knowledge, such a micro-founded agent-based
model presenting first principle explanations to the emergence of global price dynamics
is presently unique. Its significance is the following: first, it highlights
the need for considering carefully the impact of the market microstructure on
the price dynamics, and to recognise the usefulness and validity of disequilibrium
models of price dynamics. Second, since this zero-intelligence model recovers the
main stylised facts with no assumption on agents’ behaviour or trading strategy,
it can compete with models assuming a simplified price clearing condition and
requiring specific assumptions on the part of the agents themselves to produce
realistic price dynamics. Each type of model can certainly contribute in different
ways to a deeper understanding of the true underlying process. Finally, like many
others before, this model is able to reproduce price dynamics, and therefore suggest
possible explanations, with no need for the arrival of external information.
Once again, we are not claiming that new information is irrelevant in explaining
price changes, but rather that most price changes are effectively the result of
uninformed demand shift, and further that their properties can be explained in
terms of liquidity dynamics at the micro level.
A limited contribution, probably relevant mainly to the field of Agent-based

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Computational Economics, was to highlight the importance of the statistical equilibrium
price present in closed markets, which can act as a price attractor disturbing
the dynamics under study. A characterisation of the actual speed of convergence
of the price to this attractor was offered, in terms of agents’ risk aversion
profile, and indicators signalling such a convergence were presented, namely the
skewness and Gini coefficient of agents’ endowments.
We then shifted our attention back to the original question informational
efficiency of markets, and whether the market prices we observe reflect any fundamental
value. As we have seen before, this cannot be tested directly with
market data, due to the impossibility of assessing the fundamental value. However,
in an artificial market, one can at least test the internal consistency of
theoretical models. We proposed an innovative model of a self-referential market,
based on the theoretical framework of the Self-Referential Market Hypothesis,
which we see as an extension of the Efficient Market Hypothesis in markets for
which there is no common knowledge fundamental value – a description much
closer to real markets, in our opinion – and tested this model in two different
market conditions. Firstly, we started by assuming the existence of a common
knowledge fundamental value, defined externally to the market, so as to test the
predictions of the Efficient Market Hypothesis in the setting of our double auction
mechanism. In these conditions, our self-referential agents acted as fully
informed rational arbitrageurs and, as expected by the EMH, the market price
closely tracked the fundamental value. However, when the rational arbitrageurs
had the slightest uncertainty regarding the true level of the fundamental value,
the uninformed traders, implemented by zero-intelligence agents, were not driven
out of the market, as would have been expected.
Finally, we relaxed the assumption of a common knowledge fundamental value,
and observed that even in the absence of external information, self-referential
agents could coordinate their expectations around a given price level, which could
be stable for some time and appear as reflecting a consensus price on the fundamental
value of the stock. However, a simple volatility feedback was enough
to lead eventually to the endogenous destabilisation of this convention, followed
by a period of self-referential crisis and finally the emergence of a new convention,
thanks to the observation in the order book of salient points, price levels
at which the latent liquidity had accumulated. This mechanism could explain

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the apparent stability of market prices, which we interpret a posteriori as reflecting
certain economic realities, quickly followed by their destabilisation for no
apparent reason.
7.3 Applications and possible extensions
In the opening of this dissertation, we have identified two properties that well
functioning financial markets should possess: informational efficiency and liquidity.
Informational efficiency, the degree to which prices produced by markets
reflect the underlying economic reality of the assets traded, is required if we want
markets to provide reliable signals to investors, and therefore avoid the waste of
resources. Liquidity, on the other hand, is a property required by investors in
order to invest their capital in the first place: they want stable prices, indicative
of the effective price at which they could get in or out of the market. These
two properties appear as completely unrelated in mainstream equilibrium models,
since the first is accepted as a basic axiom and the second is relegated to the
rank of technical detail. However, we hope to have succeeded in this thesis in
showing that informational efficiency and liquidity might be intrinsically linked,
and, more generally, to help attract the attention of the academic community on
the need for developing disequilibrium models of price formation.
What are the policy implications for market designers and market participants
André Orléan claims that financial markets have lost their social role of
providing strong and reliable signals to the economy, to the profit of speculators
striving on the provision of liquidity. One thing is for sure, stock exchanges are
nowadays converging toward fully automated markets using the double auction
mechanism and competing for volumes and liquidity. Concommitently, real-time
access to tick-by-tick data allows for the elaboration of sophisticated trading
strategies executed by computer algorithms. Simulations can help apprehend
this changing reality: we are now working with an Electronic Communication
Network on the NASDAQ focusing on large volumes, and with a hedge fund
specialised in automated trading, in order to extend the functionalities of our
market simulator and use it as a sandbox for the testing of new market designs
and innovative trading strategies.