A Structural Model for Fluctuations in Financial Markets

TL;DR

This paper introduces a structural model for asset price fluctuations that incorporates interactions and meta-stable states, explaining fat-tailed return distributions and volatility clustering observed in financial markets.

Contribution

It extends geometric Brownian motion to include interactions, analyzes the model using generating functional methods, and links meta-stable states to volatility clustering.

Findings

Distributions of returns are fat-tailed, matching empirical data.

Interactions broaden the distribution of asset prices, especially with ferro-magnetic bias.

Volatility clustering arises from transitions between meta-stable states.

Abstract

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.