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In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails, and of the relevant correlation functions. We also propose a systematic methodology for estimating the parameters, and we describe the empirical analysis of the Standard & Poor 500 index daily returns, confirming the ability of the model to capture many of the established stylized fact as well as the scaling properties of empirical distributions over different time horizons.
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 most import
We introduce a minimal Agent Based Model with two classes of agents, fundamentalists (stabilizing) and chartists (destabilizing) and we focus on the essential features which can generate the stylized facts. This leads to a detailed understanding of t
In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compar
In this work we essentially reinterpreted the Sieczka-Ho{l}yst (SH) model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbor
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hy