Eur. Phys. J. B 55, 123-133 (2007)
https://doi.org/10.1140/epjb/e2006-00356-9

Statistical regularities in the return intervals of volatility

¹ Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA
² Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany
³ Department of Environmental Sciences, Tokyo University of Information Sciences, Chiba, 265-8501, Japan
⁴ Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel

Corresponding author: ^a fzwang@bu.edu

Received: 30 May 2006
Revised: 28 July 2006
Published online: 4 October 2006

Abstract

We discuss recent results concerning statistical regularities in the return intervals of volatility in financial markets. In particular, we show how the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series. We find scaling in the distribution of return intervals for thresholds ranging over a factor of 25, from 0.6 to 15 standard deviations, and also for various time windows from one minute up to 390 min (an entire trading day). Moreover, these results are universal for different stocks, commodities, interest rates as well as currencies. We also analyze the memory in the return intervals which relates to the memory in the volatility and find two scaling regimes, ℓ<ℓ^* with α₁=0.64±0.02 and ℓ> ℓ^* with α₂=0.92±0.04; these exponent values are similar to results of Liu et al. for the volatility. As an application, we use the scaling and memory properties of the return intervals to suggest a possibly useful method for estimating risk.