Fluctuation behaviors of financial return volatility duration

• A new concept of the durations of daily financial return volatility is introduced.
• Probability distributions, memory effects and multifractal properties of volatility duration series are investigated.
• The proposed concept of the duration is a meaningful and beneficial trial for the stock volatility series analysis.
• Empirical research of the durations is performed for world’s seven representative stock indices.

It is of significantly crucial to understand the return volatility of financial markets because it helps to quantify the investment risk, optimize the portfolio, and provide a key input of option pricing models. The characteristics of isolated high volatility events above certain threshold in price fluctuations and the distributions of return intervals between these events arouse great interest in financial research. In the present work, we introduce a new concept of daily return volatility duration, which is defined as the shortest passage time when the future volatility intensity is above or below the current volatility intensity (without predefining a threshold). The statistical properties of the daily return volatility durations for seven representative stock indices from the world financial markets are investigated. Some useful and interesting empirical results of these volatility duration series about the probability distributions, memory effects and multifractal properties are obtained. These results also show that the proposed stock volatility series analysis is a meaningful and beneficial trial.