Market Dynamics Immediately Before and After Financial Shocks: Quantifying the Omori, Productivity and Bath Laws

Physical Review E, Vol. 82, 2010

16 Pages Posted: 24 Oct 2010

See all articles by Alexander Michael Petersen

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program

Fengzhong Wang

Boston University

Shlomo Havlin

Bar Ilan University

H. Eugene Stanley

Boston University - Center for Polymer Studies

Date Written: October 3, 2010

Abstract

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 the "main shock" magnitude M\equiv\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.

Keywords: Volatility Aftershocks, Market Shocks, Market Response Dynamics, News

JEL Classification: C22, G14, D82, D84

Suggested Citation

Petersen, Alexander Michael and Wang, Fengzhong and Havlin, Shlomo and Stanley, H. Eugene, Market Dynamics Immediately Before and After Financial Shocks: Quantifying the Omori, Productivity and Bath Laws (October 3, 2010). Physical Review E, Vol. 82, 2010, Available at SSRN: https://ssrn.com/abstract=1696608

Alexander Michael Petersen (Contact Author)

University of California Merced, Ernest and Julio Gallo Management Program ( email )

School of Engineering
Science & Engineering 2, Suite 315
Merced, CA 95343
United States

Fengzhong Wang

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States

Shlomo Havlin

Bar Ilan University ( email )

Ramat Gan
Ramat Gan, 52900
Israel

HOME PAGE: http://havlin.biu.ac.il/

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

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