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Scaling and memory in volatility return intervals in financial markets
Kazuko Yamasaki1, Lev Muchnik, Shlomo Havlin
1Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
Summary
We discovered that daily stock and currency market volatility return intervals exhibit a power-law distribution, indicating a clustering phenomenon. This finding reveals predictable patterns in market volatility, offering new insights into financial market dynamics.
Area of Science:
- Quantitative Finance
- Financial Market Analysis
- Statistical Modeling
Background:
- Market volatility is a key characteristic of financial markets.
- Understanding the temporal dynamics of volatility is crucial for risk management and trading strategies.
Purpose of the Study:
- To investigate the statistical properties of return intervals between daily volatilities exceeding a threshold.
- To identify and characterize any patterns or clustering in these volatility return intervals.
Main Methods:
- Analysis of daily price changes in seven stock and seven currency markets.
- Statistical examination of return intervals (tau) between volatilities above a threshold (q).
- Modeling the distribution function Pq(tau) and its scaling properties.
Main Results:
- The distribution function Pq(tau) follows a scaling law: Pq(tau) = tau(-1)f(tau/tau).
- The scaling function f(x) is consistent with a power-law form, f(x) ~ x(-gamma) with gamma ~ 2.
- A significant "clustering" phenomenon was identified: short or long return intervals tend to be followed by similar intervals.
Conclusions:
- Volatility return intervals in financial markets exhibit universal scaling properties.
- The observed clustering of volatility intervals is linked to underlying long-term correlations in market volatility.
- This study uncovers a new characteristic of market dynamics with potential implications for financial modeling.