Scaling and memory in volatility return intervals in financial markets
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 [Formula] as [Formula]. 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-γ with γ ≈ 2. We also quantify how the conditional distribution Pq(τ|τ0) depends on the previous return interval τ0 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.
Author contributions: S.H. and H.E.S. designed research; K.Y., L.M., S.H., and H.E.S. performed research; A.B. contributed new reagents/analytic tools; A.B. analyzed data; and S.H. wrote the paper.Abbreviations: pdf, probability density function; S&P 500, Standard and Poor's 500 Index; USD, U.S. dollar; JPY, Japanese yen; SEK, Swedish krona.- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- June 2005
- DOI:
- 10.1073/pnas.0502613102
- Bibcode:
- 2005PNAS..102.9424Y
- Keywords:
-
- econophysics;
- fluctuations;
- extreme values;
- long-term correlations;
- long-term memory;
- Economic Sciences, Social Sciences