We present an overview of some representative Agent-Based Models in Economics. We discuss why and how agent-based models represent an important step in order to explain the dynamics and the statistical properties of financial markets beyond the Class
ical Theory of Economics. We perform a schematic analysis of several models with respect to some specific key categories such as agents strategies, price evolution, number of agents, etc. In the conclusive part of this review we address some open questions and future perspectives and highlight the conceptual importance of some usually neglected topics, such as non-stationarity and the self-organization of financial markets.
We show that the statistics of spreads in real order books is characterized by an intrinsic asymmetry due to discreteness effects for even or odd values of the spread. An analysis of data from the NYSE order book points out that traders strategies co
ntribute to this asymmetry. We also investigate this phenomenon in the framework of a microscopic model and, by introducing a non-uniform deposition mechanism for limit orders, we are able to quantitatively reproduce the asymmetry found in the experimental data. Simulations of our model also show a realistic dynamics with a sort of intermittent behavior characterized by long periods in which the order book is compact and liquid interrupted by volatile configurations. The order placement strategies produce a non-trivial behavior of the spread relaxation dynamics which is similar to the one observed in real markets.
We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity $g$) as a proxy for liquidity. This leads to a Price Im
pact Surface which depends on both volume $omega$ and $g$. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function $<phi(omega,g)>_gsimomega^delta$ with $deltaapprox 0.59$. Instead the dependence on the granularity is $phi(omega,g|omega)sim g^alpha$ with $alphaapprox-1$, showing a divergence of price fluctuations in the limit $gto 0$. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.
