Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 423 (6937), 267-70

A Theory of Power-Law Distributions in Financial Market Fluctuations

Affiliations

A Theory of Power-Law Distributions in Financial Market Fluctuations

Xavier Gabaix et al. Nature.

Abstract

Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financial system, huge databases now exist that facilitate the analysis of large fluctuations and the characterization of their statistical behaviour. Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations in stock price, trading volume and the number of trades. Surprisingly, the exponents that characterize these power laws are similar for different types and sizes of markets, for different market trends and even for different countries--suggesting that a generic theoretical basis may underlie these phenomena. Here we propose a model, based on a plausible set of assumptions, which provides an explanation for these empirical power laws. Our model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants. Starting from an empirical characterization of the size distribution of those large market participants (mutual funds), we show that the power laws observed in financial data arise when the trading behaviour is performed in an optimal way. Our model additionally explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades.

Similar articles

  • Discovery of Power-Laws in Chemical Space
    RW Benz et al. J Chem Inf Model 48 (6), 1138-51. PMID 18522387.
    Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in ch …
  • Universal Behavior of Extreme Price Movements in Stock Markets
    MA Fuentes et al. PLoS One 4 (12), e8243. PMID 20041178.
    Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occu …
  • Multiple Returns for Some Regular and Mixing Maps
    N Haydn et al. Chaos 15 (3), 33109. PMID 16252983.
    We study the distributions of the number of visits for some noteworthy dynamical systems, considering whether limit laws exist by taking domains that shrink around points …
  • Scaling and Power-Laws in Ecological Systems
    PA Marquet et al. J Exp Biol 208 (Pt 9), 1749-69. PMID 15855405. - Review
    Scaling relationships (where body size features as the independent variable) and power-law distributions are commonly reported in ecological systems. In this review we an …
  • Can a Power Law Improve Prediction of Pain Recovery Trajectory?
    GC Hartmann et al. Pain Rep 3 (4), e657. PMID 30123854. - Review
    The overall goal of this review was to introduce new conceptual direction to improve understanding of chronic pain development using mathematical approaches successful fo …
See all similar articles

Cited by 46 PubMed Central articles

See all "Cited by" articles

LinkOut - more resources

Feedback