Structural model for fluctuations in financial markets

In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market which takes the form of an interacting generalization of the geometric Brownian motion model. It is formally equivalent to a model describing the stochastic dynamics of a system of analog neurons, which is expected to exhibit glassy properties and thus many metastable states in a large portion of its parameter space. We perform a generating functional analysis, introducing a slow driving of the dynamics to mimic the effect of slowly varying macroeconomic conditions. Distributions of asset returns over various time separations are evaluated analytically and are found to be fat-tailed in a manner broadly in line with empirical observations. Our model also allows us to identify collective, interaction-mediated properties of pricing distributions and it predicts pricing distributions which are significantly broader than their noninteracting counterparts, if interactions between prices in the model contain a ferromagnetic bias. Using simulations, we are able to substantiate one of the main hypotheses underlying the original modeling, viz., that the phenomenon of volatility clustering can be rationalized in terms of an interplay between the dynamics within metastable states and the dynamics of occasional transitions between them.