Reaction-Diffusion-Branching Models of Stock Price Fluctuations

TL;DR

This paper models stock price fluctuations using reaction-diffusion-branching processes, revealing subdiffusive short-term behavior and crossover to random-walk dynamics at longer times, aligning well with empirical data.

Contribution

It introduces a novel reaction-diffusion-branching framework for stock market modeling, providing analytical insights into price fluctuation dynamics and crossover phenomena.

Findings

Short-time market price variation is subdiffusive with H=1/4.

Bias and copying lead to crossover to H=1/2 at long times.

Calculated crossover and diffusion constants match simulation data.

Abstract

Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent $H=1/4$. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ($H=1/2$) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.