Economic Fluctuations and Diffusion

TL;DR

This paper draws an analogy between stock price fluctuations and physical diffusion, analyzing transaction data to understand how microscopic trading activity influences price changes and their statistical properties.

Contribution

It systematically relates trading activity and price variance to a diffusion analogy, revealing power-law distributions and correlations in stock price fluctuations.

Findings

Price movements resemble a complex diffusion process with fluctuating diffusion coefficients.

Distributions of transaction counts and local variances exhibit power-law tails.

Long-range correlations are found in transaction counts but not in local variances.

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 $N_{\Delta t}$.