Econophysics: Empirical facts and agent-based models

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words “Economics” and “Physics”, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes. We give a brief introduction in the first part and begin with discussing interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics in the second part. Then the third part is dedicated to empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged “stylized facts” describing the distribution of the returns of financial assets: fat-tails, volatility clustering, etc. Then we show that some of these properties are directly linked to the way “time” is taken into account, and present some new remarks on this account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrations in this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Contributions to the study of correlations of assets such as random matrix theory and graph theory are finally presented in this part. The fourth part of our review deals with models in Econophysics through the point of view of agent-based modeling. Using previous work originally presented in the fields of behavioural finance and market microstructure theory, econophysicists have developed agent-based models of orderdriven markets that are extensively reviewed here. We then turn to models of wealth distribution where an agent-based approach also prevails: kinetic theory models, and continue with game theory models and review the now classic minority games. We end this review by providing an outlook on possible directions of research.