Volatility Before and After Market Shocks: Empirical Scaling Laws

Summary

The study examines volatility cascades around market shocks, treating each shock as a volatility peak above a preset threshold. It compares the resulting high-volatility episodes with empirical patterns known as the Omori, productivity, and Bath laws, and analyzes both elevated volatility preceding a shock and the decay of volatility afterward. Shock magnitude is defined using the logarithm of volatility at the peak.

The analysis covers 219 identified shocks in 531 heavily traded U.S. stocks during 2001–2002, using one-minute observations. The authors report relationships between shock magnitude and measures of pre-shock and post-shock volatility, and find that more actively traded stocks respond more strongly and rapidly. They suggest relevance to option pricing and volatility trading. These are conditional statistical findings from a historical sample; the excerpt does not establish causal mechanisms or demonstrate that the relationships remain stable in other periods or markets.

Key ideas

• Market shocks are identified as volatility peaks that exceed a predetermined threshold.
• The study examines volatility patterns before and after shocks through three empirical scaling laws.
• It reports links between shock magnitude and the behavior of volatility around the event.
• More actively traded stocks are reported to react more strongly and quickly.
• The evidence comes from a historical sample of U.S. stocks at one-minute resolution.

Tags

# Market dynamics immediately before and after financial shocks: quantifying the Omori, productivity and Bath laws


# Market dynamics immediately before and after financial shocks: quantifying the Omori, productivity and Bath laws









We study the cascading dynamics immediately before and immediately after 219 market shocks. We define the time of a market shock T_{c} to be the time for which the market volatility V(T_{c}) has a peak that exceeds a predetermined threshold. The cascade of high volatility "aftershocks" triggered by the "main shock" is quantitatively similar to earthquakes and solar flares, which have been described by three empirical laws --- the Omori law, the productivity law, and the Bath law. We analyze the most traded 531 stocks in U.S. markets during the two-year period 2001-2002 at the 1-minute time resolution. We find quantitative relations between (i) the "main shock" magnitude M \equiv \log V(T_{c}) occurring at the time T_{c} of each of the 219 "volatility quakes" analyzed, and (ii) the parameters quantifying the decay of volatility aftershocks as well as the volatility preshocks. We also find that stocks with larger trading activity react more strongly and more quickly to market shocks than stocks with smaller trading activity. Our findings characterize the typical volatility response conditional on M, both at the market and the individual stock scale. We argue that there is potential utility in these three statistical quantitative relations with applications in option pricing and volatility trading.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.