A reaction–diffusion model for market fluctuations – A relation between price change and traded volumes

• Published in: Physics letters. A Vol. 382; no. 6; pp. 367 - 371
• Main Authors: Yuvan, Steven, Bier, Martin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 13.02.2018
• Subjects: Bond market; Econophysics; Market fluctuations; Reaction–diffusion model; Traded volumes; Zero-intelligence model; Econophysics; Traded volumes; Reaction–diffusion model; Zero-intelligence model; Market fluctuations; Bond market
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2017.12.024

Two decades ago Bak et al. (1997) [3] proposed a reaction–diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation. •Price changes and traded volumes of financial instruments are followed and explained.•Price change and traded volume appear to be related through a square root relation.•A simple stochastic model appears to reproduce the observed data.•The square root relation follows from a continuum approximation of the model.•The square root relation is very robust when modifications to the model are made.