A theory of power-law distributions in financial market fluctuations.

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.

Quantifying stock-price response to demand fluctuations.

We empirically address the question of how stock prices respond to changes in demand. We quantify the relations between price change G over a time interval Deltat and two different measures of demand fluctuations: (a) Phi, defined as the difference between the number of buyer-initiated and seller-initiated trades, and (b) Omega, defined as the difference in number of shares traded in buyer- and seller-initiated trades. We find that the conditional expectation functions of price change for a given Phi or Omega, (Phi) and (Omega) ("market impact function"), display concave functional forms that seem universal for all stocks.