Economic fluctuations and anomalous diffusion

We quantify the relation between trading activity - measured by the number of transactions N-Delta t-and the price change G(Delta t) for a given stock , over a time interval [t, t+Delta t]. To this end, we analyze a database d ocumenting every transaction for 1000 U.S. stocks for the two-year period 1 994-1995; We find that price movements are equivalent to a complex variant of classic diffusion, where the diffusion constant fluctuates drastically i n time. We relate the analog for stock price fluctuations of the diffusion constant-known in economics as the volatility-to two microscopic quantities : (i) the number of transactions N-Delta t in Delta t, which is the analog of the number of collisions and (ii) the variance W-Delta t(2) of the price changes for all transactions in Delta t, which is the analog of the local mean square displacement between collisions. Our results are consistent wit h the interpretation that the power-law tails of P(G(Delta t)) are due to P (W-Delta t), and the long-range correlations in \G(Delta t)\ are due to N-D elta t.