Economic Fluctuations and Diffusion

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

doi:10.1103/PhysRevE.62.R3023

paper

Economic Fluctuations and Diffusion

arXiv:cond-mat/9912051 · doi:10.1103/PhysRevE.62.R3023

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 $N_{Δ t}$ - and the price change $G_{Δ t}$ , for a given stock, over a time interval $[t, t + Δ t]$ . 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 $N_{Δ t}$ in $Δ t$ , which is the analog of the number of collisions and (ii) the local variance $w_{Δ t}^{2}$ of the price changes for all transactions in $Δ t$ , which is the analog of the local mean square displacement between collisions. We study the distributions of both $N_{Δ t}$ and $w_{Δ t}$ , and find that they display power-law tails. Further, we find that $N_{Δ t}$ displays long-range power-law correlations in time, whereas $w_{Δ t}$ does not. Our results are consistent with the interpretation that the pronounced tails of the distribution of $G_{Δ t} a r e d u e t o$ w_{Δt} $, an d t ha tt h e l o n g - r an g ecor r e l a t i o n s p r e v i o u s l y f o u n df or$ | G_{Δt} | $a r e d u e t o$ N_{Δt}$.

RevTex 2 column format. 6 pages, 36 references, 15 eps figures

Economic Fluctuations and Diffusion

Abstract

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