A reaction–diffusion model for market fluctuations – A relation between price change and traded volumes
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 t...
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Published in | Physics letters. A Vol. 382; no. 6; pp. 367 - 371 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
13.02.2018
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0375-9601 1873-2429 |
DOI: | 10.1016/j.physleta.2017.12.024 |