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The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…
We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main…
We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the…
Establishing unambiguously the existence of speculative bubbles is an on-going controversy complicated by the need of defining a model of fundamental prices. Here, we present a novel empirical method which bypasses all the difficulties of…
A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
We study a dynamical Ising model of agents' opinions (buy or sell) with coupling coefficients reassessed continuously in time according to how past external news (magnetic field) have explained realized market returns. By combining herding,…
Simultaneous reproduction of all financial stylized facts is so difficult that most existing stochastic process-based and agent-based models are unable to achieve the goal. In this study, by extending the decision-making structure of…
We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which…
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments…
We present a dynamical theory of asset price bubbles that exhibits the appearance of bubbles and their subsequent crashes. We show that when speculative trends dominate over fundamental beliefs, bubbles form, leading to the growth of asset…
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction…
In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of…
Competition between varying ideas, people and institutions fuels the dynamics of socio-economic systems. Numerous analyses of the empirical data extracted from different financial markets have established a consistent set of stylized facts…
We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise…
We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of…
We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are…
Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective…
In the theory of financial markets, a stylized fact is a qualitative summary of a pattern in financial market data that is observed across multiple assets, asset classes and time horizons. In this article, we test a set of eleven stylized…
We present a detailed study of the statistical properties of an Agent Based Model and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the…