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Economic fluctuations and anomalous diffusion

Plerou1, Gopikrishnan, Nunes Amaral LA

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215 and Department of Physics, Boston College, Chestnut Hill, Massachusetts 02164, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

We found stock price changes resemble diffusion with a fluctuating constant. Trading activity and transaction price variance explain this volatility and long-range correlations in stock price movements.

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Area of Science:

  • Quantitative Finance
  • Statistical Mechanics
  • Econophysics

Background:

  • Stock price fluctuations exhibit complex dynamics.
  • Understanding the relationship between trading activity and price changes is crucial for financial markets.

Purpose of the Study:

  • To quantify the relationship between trading activity (number of transactions) and stock price changes.
  • To model stock price movements using principles of diffusion and volatility.

Main Methods:

  • Analysis of a comprehensive transaction database for 1000 U.S. stocks (1994-1995).
  • Quantification of price changes G(Δt) and trading activity N(Δt) over time intervals Δt.
  • Relating volatility to the number of transactions and the variance of price changes.

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Main Results:

  • Stock price movements were found to be analogous to a complex diffusion process with a time-varying diffusion constant (volatility).
  • Volatility was directly linked to the number of transactions and the variance of price changes within a given interval.
  • Power-law tails in price change distributions were attributed to the distribution of price change variances, and long-range correlations to trading activity.

Conclusions:

  • The study provides a microscopic explanation for stock price dynamics, linking macroscopic properties like volatility and correlations to observable trading behaviors.
  • Findings suggest that trading activity and the variance of individual transaction price changes are key determinants of overall stock price behavior.