  In this paper we provide a comprehensive analysis of a structural model for
the dynamics of prices of assets traded in a market originally proposed in [1].
The model 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 analogue neurons, which is expected to
exhibit glassy properties and thus many meta-stable 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 macro-economic 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 to
identify collective, interaction mediated properties of pricing distributions
and it predicts pricing distributions which are significantly broader than
their non-interacting counterparts, if interactions between prices in the model
contain a ferro-magnetic bias. Using simulations, we are able to substantiate
one of the main hypotheses underlying the original modelling, viz. that the
phenomenon of volatility clustering can be rationalised in terms of an
interplay between the dynamics within meta-stable states and the dynamics of
occasional transitions between them.
