Moduleco 1. -  Simulation of markets, social networks and population dynamics 1.3. A Lux-like model of financial market.

The models of  Thomas Lux (1997, 1998, Lux & Marchesi, 1999, 2000) are multi-agent (without individual agents !) simulations of financial markets. Lux purpose is to replicate the statistic stylized facts observed in real markets, namely :

1. Fat tails (series are leptokurtic)
2. Volatility clustering (large fluctuations are followed by large fluctuations) and even...
3.  The hyperbolic decay of the volatility autocorrelation ( the so-called long memory property).

These features of financial data imply that the probability distribution function is highly non-gaussian. This simulation shows that with gaussian information arrivals, and a market composed of heterogeneous agents who switch between different strategies, the price exhibits the characteristics of real data.

The Model

This kind of model is used by an increasing number of authors, see, e.g. Youssefmir and Huberman [1997] and Kirman [1993] among others. In a complex environment, adaptive agents continuously switch between different strategies, influenced in their decisions by the interactions with other investors. The population of investors is divided into two groups, chartists (using past data to infer future price) and fundamentalists (they trade only on information). The chartist group is also divided in two sub-groups, the "optimistics", who extrapolate the price trend (positive feedback trading) and the "pessimistics" who believe that the price will revert (negative feedback trading, the so-called "contrarian" strategy). In this setting, agents compare profits obtained with these different strategies. As the chartist profits depends on a opinion index, mimetism is introduced. This leads to large waves of optimism and pessimism. Readers may refer to the different articles of Lux to understand the transition probabilities between different strategies of trading.

Note : in Moduleco, the right-part graph represents the evolution of the market price (which is arbitrarily fixed to 100 at the beginning, and is equal to the fundamental price) and the fractions of different groups, namely, blue for fundamentalists, green for optimistics and red for pessimistics.

note writing by Nicolas Boitout, Sebastien Chivoret, Thierry Delahaut

• Kirman A. [1993], ' Ants, rationality and recruitment', Quarterly Journal of Economics, Volume 108 
• Lux T. [1997], 'The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions, Journal of Economic Behavior & Organization, Volume 33
• Lux. T [1998], 'Time variation of second moments from a noise trader/infection model, Journal of Economic Dynamics and Control, Volume 22, Issue 1 
• Lux T., M. Marchesi [1999], 'Scaling and criticality in a stochastic multi-agent model of financial market', Nature vol. 397 pp 498 - 500 
• Lux T., M. Marchesi [2000], 'Volatility clustering in financial markets: a microsimulation of interacting agents, International Journal of Theoretical and Applied Finance
• Youssefmir M., B. A. Huberman [1997],'Clustered volatility in multiagent dynamics', Journal of Economic Behavior & Organization, Volume 32, Issue 1

Denis.Phan@enst-bretagne.fr ;   Antoine Beugnard@enst-bretagne.fr