Quantifying fluctuations in market liquidity: analysis of the bid-ask spread.

Quantifying the statistical features of the bid-ask spread offers the possibility of understanding some aspects of market liquidity. Using quote data for the 116 most frequently traded stocks on the New York Stock Exchange over the two-year period 1994-1995, we analyze the fluctuations of the average bid-ask spread S over a time interval deltat. We find that S is characterized by a distribution that decays as a power law P[S>x] approximately x(-zeta(S) ), with an exponent zeta(S) approximately = 3 for all 116 stocks analyzed.

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.

Random matrix approach to cross correlations in financial data.

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"--a random correlation matrix constructed from mutually uncorrelated time series.