Return volatility interval analysis of stock indexes during a financial crash

• Return volatility interval distribution has the largest power-law exponents in plummet stage.
• The developed markets show weak correlation to the volatility interval in soaring stage of a crash.
• Emerging markets have constant correlation behavior to the extreme volatility during the crash.

We investigate the interval between return volatilities above a certain threshold qq for 10 countries data sets during the 2008/2009 global financial crisis, and divide these data into several stages according to stock price tendencies: plunging stage (stage 1), fluctuating or rebounding stage (stage 2) and soaring stage (stage 3). For different thresholds qq, the cumulative distribution function always satisfies a power law tail distribution. We find the absolute value of the power-law exponent is lowest in stage 1 for various types of markets, and increases monotonically from stage 1 to stage 3 in emerging markets.The fractal dimension properties of the return volatility interval series provide some surprising results. We find that developed markets have strong persistence and transform to weaker correlation in the plunging and soaring stages. In contrast, emerging markets fail to exhibit such a transformation, but rather show a constant-correlation behavior with the recurrence of extreme return volatility in corresponding stages during a crash. We believe this long-memory property found in recurrence-interval series, especially for developed markets, plays an important role in volatility clustering.