Petersen Alexander M, Wang Fengzhong, Havlin Shlomo, Stanley H Eugene
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036114. doi: 10.1103/PhysRevE.82.036114. Epub 2010 Sep 27.
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 2 yr period of 2001-2002 at the 1 min time resolution. We find quantitative relations between the main shock magnitude M≡log{10} V(T{c}) and 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.
我们研究了219次市场冲击前后紧挨着的级联动态。我们将市场冲击(T_{c})的时间定义为市场波动率(V(T_{c}))出现超过预定阈值的峰值的时间。由“主震”引发的高波动率“余震”级联在数量上类似于地震和太阳耀斑，它们已由三条经验定律——大森定律、生产率定律和巴斯定律描述。我们在2001 - 2002年的两年期间以1分钟的时间分辨率分析了美国市场上交易最活跃的531只股票。我们发现了主震震级(M≡log_{10} V(T_{c}))与量化余震波动率衰减以及震前波动率的参数之间的定量关系。我们还发现，交易活跃度较高的股票比交易活跃度较低的股票对市场冲击的反应更强烈、更迅速。我们的研究结果刻画了在市场和个股层面上以(M)为条件的典型波动率响应。我们认为，这三条统计定量关系在期权定价和波动率交易中的应用具有潜在效用。
