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

摘要

AbstractTwo decades ago Bak et al. (1997) 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.Highlights?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 ro