Price fluctuations and market activity

We empirically quantify the relation between trading activity-measured by t he number of transactions N-and the price change G(t) for a given stock, ov er a time interval [t, t + Deltat]. We relate the time-dependent standard d eviation of price changes-volatility-to two microscopic quantities: the num ber of transactions N(t) in Deltat and the variance W-2(t) of the price cha nges for all transactions in Deltat. We find that the long-ranged volatilit y correlations are largely due to those of N. We then argue that the tail-e xponent of the distribution of N is insufficient to account for the tail-ex ponent of P{G > x}. Since N and W display only weak inter-dependency, our r esults 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 e stimates for G. (C) 2001 Elsevier Science B.V. All rights reserved.