Asynchronous Simulations of a Limit Order Book

(Awarded the Manchester University 2007 Best Thesis prize)

Abstract

We investigate by means of computer simulations the intraday dynamics of stock markets, and show the primary role played by liquidity in the price formation mechanism. Liquidity dynamics are not only responsible for the statistical properties of price changes, but they also play a key role in determining the level at which market prices stabilise.

To model liquidity effectively, we need to move beyond traditional equilibrium models of price formation and represent the actual market mechanism responsible for matching demand and supply during continuous trading sessions, where trades occur out of equilibrium. We present a model and a computer implementation of a double auction market mechanism in which arbitrarily complex agents can issue or cancel orders asynchronously. We show that the main statistical properties of price changes exhibited by real markets can be recovered with a zero-intelligence model of agents. In this context, these stylized facts find their origin in the subtle interplay between limit orders, which supply liquidity, and market and cancellation orders, which remove it.

We test the Efficient Market Hypothesis in the context of our double auction: in the presence of a common knowledge fundamental value, market prices converge to their fundamentals, but uninformed traders are not necessarily priced out of the market by arbitrageurs. In the light of the recently proposed Self-Referential Market Hypothesis, we then relax the assumptions of fully informed rational arbitrageurs and common knowledge fundamental value, replacing them with an innovative model of self-referential agents. We show that in such self-referential markets, liquidity and informational efficiency are intrinsically linked, and that what is commonly viewed as a ``fundamental'' value is nothing more than a social construction emerging from investors' requirement for price stability.

PhD supervisors:

1. 3Prof. of Artificial Intelligence David S. Brée
   

2. 3Prof. of Theoretical Physics Sorin Solomon
   

PhD committee:

1. 3Prof. of Economics Stan Metcalfe (FRSA)
   

2. 3Prof. of Finance Olivier Brandouy

1. PhD thesis
   

2. Abstract
   

3. Presentation