INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS CONDENSED MATTER.pdf

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 17 (2005) S1259–S1268 doi:10.1088/0953-8984/17/14/015 Heterogeneity and feedback in an agent-based market model Franc?ois Ghoulmie1, Rama Cont2 and Jean-Pierre Nadal1 1 Laboratoire de Physique Statistique, Ecole Normale, Supe?rieure 24 rue Lhomond, 75231 Paris Cedex, France 2 CMAP-Ecole Polytechnique, F 91128 Palaiseau, France E-mail: ghoulmie@ Received 3 September 2004, in final form 17 November 2004 Published 24 March 2005 Online at /JPhysCM/17/S1259 Abstract We propose an agent-based model of a single-asset financial market, described in terms of a small number of parameters, which generates price returns with statistical properties similar to the stylized facts observed in financial time series. Our agent-based model generically leads to the absence of autocorrelation in returns, self-sustaining excess volatility, mean-reverting volatility, volatility clustering and endogenous bursts of market activity non- attributable to external noise. The parsimonious structure of the model allows the identification of feedback and heterogeneity as the key mechanisms leading to these effects. (Some figures in this article are in colour only in the electronic version) 1. Introduction The study of statistical properties of financial time series has revealed a wealth of universal stylized facts which seem to be common to a wide variety of markets, instruments and periods [6, 15]. Agent-based market models, which are based on a stylized description for the behaviour of agents, attempt to explain the origins of the observed behaviour of market prices in terms of simple behavioural rules of market participants: in this approach a financial market is modelled as a system of heterogeneous, interacting agents and several examples of such models have been shown to generate price behaviour with statistical properties similar to those observed in real markets [1, 4, 5, 13, 17, 19–21, 18, 12, 2