Scaling and memory in volatility return intervals in financial markets

Kazuko Yamasaki, Lev Muchnik, Shlomo Havlin*, Armin Bunde, H. Eugene Stanley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

220 Scopus citations

Abstract

For both stock and currency markets, we study the return intervals τ between the daily volatilities of the price changes that are above a certain threshold q. We find that the distribution function Pq(τ) scales with the mean return interval τ̄ as Pq(τ) = τ̄-1f(τ/τ̄). The scaling function f(x) is similar in form for all seven stocks and for all seven currency databases analyzed, and f(x) is consistent with a power-law form, f(x) ∼ x with γ ≈ 2. We also quantify how the conditional distribution Pq(τ/τ0) depends on the previous return interval TQ and find that small (or large) return intervals are more likely to be followed by small (or large) return intervals. This "clustering" of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long-term correlations known to be present in the volatility.

Original languageAmerican English
Pages (from-to)9424-9428
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Volume102
Issue number26
DOIs
StatePublished - 28 Jun 2005
Externally publishedYes

Keywords

  • Econophysics
  • Extreme values
  • Fluctuations
  • Long-term correlations
  • Long-term memory

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