Economic Fluctuations and Diffusion

Vasiliki Plerou, Parameswaran Gopikrishnan, Luis. A. Nunes Amaral, Xavier Gabaix and H. Eugene Stanley

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Abstract: Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and 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 documenting every transaction for 1000 US stocks over the two-year period 1994-1995. We find that price movements are equivalent to a complex variant of diffusion, where the diffusion coefficient fluctuates drastically in time. We relate the analog of the diffusion coefficient 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 local variance $w^2_{\Delta t}$ of the price changes for all transactions in $\Delta t$, which is the analog of the local mean square displacement between collisions. We study the distributions of both $N_{\Delta t}$ and $w_{\Delta t}$, and find that they display power-law tails. Further, we find that $N_{\Delta t}$ displays long-range power-law correlations in time, whereas $w_{\Delta t}$ does not. Our results are consistent with the interpretation that the pronounced tails of the distribution of $G_{\Delta t} are due to $w_{\Delta t}$, and that the long-range correlations previously found for $| G_{\Delta t} |$ are due to $N_{\Delta t}$.

Date: 1999-12
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Citations: View citations in EconPapers (16)

Published in Phys. Rev. E. (Rapid Comm.) 62 (2000) R3023.

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