Price fluctuations, market activity and trading volume

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

Research output: Contribution to journalArticlepeer-review

86 Scopus citations

Abstract

We investigate the relation between trading activity—measured by the number of trades NΔt—and the price change GΔt 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 NΔt in Δt and the variance (Formula Presented) of the price changes for all transactions in Δt. We find that NΔt displays power-law decaying time correlations whereas WΔt displays only weak time correlations, indicating that the long-range correlations previously found in |GΔt| are largely due to those of NΔt. Further, we analyse the distribution P{NΔt > x} and find an asymptotic behaviour consistent with a power-law decay. We then argue that the tail-exponent of P{NΔt > x} is insufficient to account for the tail-exponent of P{GΔt > x}. Since NΔt and WΔt display only weak interdependence, we argue that the fat tails of the distribution P{GΔt > x} arise from WΔt, which has a distribution with power-law tail exponent consistent with our estimates for GΔt. Further, we analyse the statistical properties of the number of shares QΔt traded in Δt, and find that the distribution of QΔt is consistent with a Lévy-stable distribution. We also quantify the relationship between QΔt and NΔt, which provides one explanation for the previously observed volume–volatility co-movement.

Original languageEnglish (US)
Pages (from-to)262-269
Number of pages8
JournalQuantitative Finance
Volume1
Issue number2
DOIs
StatePublished - 2001

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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