Asynchronous Simulations of a Limit Order Book - Gilles Daniel

Asynchronous Simulations of
a Limit Order Book
Liquidity, price changes and price levels
in an artificial stock market
Gilles Daniel
Supervisors:
Prof. David S. Brée
Prof. Sorin Solomon
School of Computer Science
University of Manchester, UK
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Overview
(hypo)thesis
Liquidity dynamics drive price dynamics and set
equilibrium price levels endogenously
modus operandi
Computer simulations of:
- the double auction market mechanism
- the artificial agents responsible for the order flow
.. calibrated on empirical stylised facts
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Conditions for efficient allocation of capital
Informational efficiency
• Market prices must send accurate signals to drive capital into the
productive economy
Liquidity
• Quoted prices must be tradable (liquidity gives stocks there value)
• In the absence of news, we expect prices to be stable and continuous
otherwise investors would not bring there capital in the first place
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Research Questions
What moves stock prices
• Origins of the stylised facts observed at intra-day, daily, etc. level
• H0: traders' strategies Or rather the market microstructure
• We go down to the basic, atomic interactions: trades
• We find that high-frequency stylised facts can be recovered with a
disequilibrium model of Zero-Intelligence agents, and explained by
uninformed demand shifts
What sets price levels
• H0: Information only Or rather endogenous factors
• Do prices converge to, and reflect, a fund. value (EMH)
• Yes if this fundamental value is common knowledge
• Otherwise, conventions can emerge and get destabilised
endogenously (SRMH)
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What moves stock prices
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Stylised Facts (AOL dataset)
Price
Normalised returns
Normality plot
Inter-trade waiting times
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Stylised Facts (2)
P(r)
P(R>r)
ACF(r)
ACF(|r|)
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Agent-based Model of Price Formation
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Limit Order Book
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Asynchronous Processes
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Zero-Intelligence Agents
Order sign
sign = buy with prob. 0.5
sell with prob. 0.5
Order type
type =
Order size
cancellation with prob. c
market
limit
v = [v(b)|v(a)]
P(log v) ~ ()
with prob. m
with prob. 1- c
- m
for market orders
for limit orders
Limit Price
P(p) ~ U]b,a[
P() ~ -(1+
with prob. in
with prob. 1- in
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Simulation Runs
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Aggregate Order Flow received
Limit price Limit price >0
Order size
Inter-orders waiting times
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Spread
Spread s
P(S>s)
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Book shape
Bids
Offers
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Price dynamics
Price
Normalised returns
Order size
Inter-trades waiting times
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Price Dynamics (2)
P(r)
P(|R|>r)
ACF(r)
ACF(|r|)
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Conclusion on ZI model
A simple model of artificial stock market
implementing a double auction and
populated with ZI agents can reproduce
empirical stylised facts, with no need for
information.
The key is in the subtle interplay
between limit orders, which provide
liquidity, and market and cancellation
orders, which remove it.
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What sets price levels
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EMH setup: common knowledge
fundamental value
Price
Zoom
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With common knowledge fundamental
value (2)
Shares
Cash
Wealth
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With common knowledge fundamental
value (3)
Wealth ratio
Uninformed traders are not driven out of the market
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With common knowledge fundamental
value (4)
Wealth uninformed
Wealth arbitrageurs
Wealth ratio
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Conclusion on EMH setup
When the fundamental value is common
knowledge, the EMH holds (the market
price prices converges toward its f.v.),
but uninformed traders are not
necessarily driven out of the market by
arbitrageurs.
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Self-Referential Market Hypothesis
“Prices reflect the beliefs of those operating in the
markets – no more, no less.” A. Orléan
Keynes' Beauty Contest
levels of specularity
Salient points a la Schelling
volume v -> v*
Conventions (objective and strategic rationalities)
confidence c -> c*
volatility
-> * (learned)
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Without common knowledge f.v.
Prices
Normalised returns
Measured volatility
Confidence
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Conclusion on SRMH setup
When the fundamental value is not
common knowledge, it becomes rational
to take into account other traders'
opinion, which leads to the emergence,
stabilisation and collapse of conventions,
even in the absence of information and
communication, often interpreted a
posteriori as reflecting an economic
reality.
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Main message
Liquidity dynamics are not only
responsible for the statistical properties
of prices changes (stylised facts), but
they also play a key role in determining
the level at which market prices stabilise
(endogenous conventions).
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Consequence
The need for liquidity has superseded
the need for sending relevant signals
(informational efficiency) to the
Economy.
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Contributions
Attract the attention of the scientific
community on the relevance of
modelling the market microstructure.
Propose a disequilibrium model of price
formation:
- microfounded
- endogenous
- consistent with empirical data
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ACKNOWLEDGEMENTS
David S. Brée
Sorin Solomon
Enrico Scalas
Lev Muchnik
Teams in Manchester and Torino
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