Motion in random fields - an application to stock market data

TL;DR

This paper introduces a novel model for stock price fluctuations inspired by the motion of tracers in Gaussian random fields, capturing key empirical features like non-Gaussian short-term returns and super-diffusive volatility.

Contribution

The paper proposes a new stochastic model for stock prices based on physical analogies, providing analytical and numerical insights into its behavior and comparison with empirical data.

Findings

Model reproduces non-Gaussian short-term return distributions

Captures super-diffusive volatility and rapid decay of return correlations

Long-term return distribution tends towards Gaussian

Abstract

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-scale field show characteristics similar to those found in empirical studies of stock market data. Specifically, short-term returns have a non-Gaussian distribution, with super-diffusive volatility, and a fast-decaying correlation function. The correlation function of the absolute value of returns decays as a power-law, and the returns distribution converges towards Gaussian over long times. Some important characteristics of empirical data are not, however, reproduced by the model, notably the scaling of tails of the cumulative distribution function of returns.