Reaction–diffusion–branching models of stock price fluctuations

Lei-Han Tang and Guang-Shan Tian

Physica A: Statistical Mechanics and its Applications, 1999, vol. 264, issue 3, 543-550

Abstract: Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) 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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:264:y:1999:i:3:p:543-550

DOI: 10.1016/S0378-4371(98)00549-4

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