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+Δt]. We relate the time-dependent standard deviation of price changes—volatility—to two microscopic quantities: the number of transactions N(t) in Δt and the variance W2(t) of the price changes for all transactions in Δt. 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 W, which has a distribution with power-law tail exponent consistent with our estimates for G.