Price fluctuations and market activity

We empirically quantify the relation between trading activity-measured by the number of transactions N-and the price change G(t) for a given stock, over a time interval [t, t + Deltat]. We relate the time-dependent standard deviation of price changes-volatility-to two microscopic quantities: the number of transactions N(t) in Deltat and the variance W-2(t) of the price changes for all transactions in Deltat. We find that the long-ranged volatility correlations are largely due to those of N. We then argue that the tail-exponent of the distribution of N is insufficient to account for the tail-exponent of P{G > x}. Since N and W display only weak inter-dependency, our results show that the fat tails of the distribution P{G > x} arises from U; which has a distribution with power-law tail exponent consistent with our estimates for G. (C) 2001 Elsevier Science B.V. All rights reserved.