Brownian markets

TL;DR

This paper models financial market dynamics using the generalized Langevin equation, revealing oscillatory decay in return correlations and classifying stocks based on their autocorrelation behaviors, aligning with empirical data.

Contribution

It introduces a novel application of the generalized Langevin equation to market dynamics, capturing memory effects and classifying stocks by autocorrelation characteristics.

Findings

Market return rates exhibit oscillatory-decaying autocorrelation with long tails.

Stocks can be categorized into heavy, neutral, and light based on their autocorrelation functions.

Model aligns well with empirical observations of market behavior.

Abstract

Financial market dynamics is rigorously studied via the exact generalized Langevin equation. Assuming market Brownian self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior with a long-time tail, similar to empirical observations. Individual stocks are also described via the generalized Langevin equation. They are classified by their relation to the market memory as heavy, neutral and light stocks, possessing different kinds of autocorrelation functions.