Prices are macro-observables! Stylized facts from evolutionary finance

Abstract

Prices are macro-observables of a financial market that result from the trading actions of a huge number of individual investors. Major stylized facts of empirical asset returns concern (i) non-Gaussian distribution of empirical asset returns and (ii) volatility clustering, i.e., the slow decay of auto- correlations of absolute returns. We propose a model for the aggregate dynamics of the market which is generated by the coupling of a ‘slow’ and a ‘fast’ dynamical component, where the ‘fast’ component can be seen as a perturbation of the ‘slow’ one. Statistical properties of price changes in this model are estimated by simulation; sample size is 4 × 106. It is shown that increasing the decoupling of these two dynamical levels generates a crossover in the distribution of log returns from a concave Gaussian-like distribution to a convex, truncated Levy-like one. For a sufficiently large degree of dynamic decoupling, the return trails exhibit pronounced volatility clustering.