Mathematical Finance Seminar

May 2, 2002 , 5:30 PM to 7:00 PM

H. E. Stanley, Boston University

Understanding Large Movements in Stock Market Activity

After a very short introduction to some of the most recent results obtained in the field of econophysics we consider the problem of ``rare events'' of the stock market price dynamics. It is becoming widely appreciated that even extremely large movements in stock market activity may not be ``outliers'' but rather may conform to newly-uncovered empirical laws, such as the (i) power law distribution of returns with exponent 3, outside the Levy-stable regime, (ii) power law distribution of trading volume with exponent 1.5 [1]. We discuss these new empirical laws, and also discuss how one interdisciplinary ``economist/physicist'' collaboration is beginning to gain theoretical insight and understanding of these new empirical laws using concepts drawn from both the economics and physical sciences [2-5].
The research reported was done primarily in collaboration with X. Gabaix MIT Economics Dept), P. Gopikrishnan (now at Goldman Sachs), and V. Plerou (Boston University) and has been supported by NSF and BP.

[1] R. N. Mantegna and H. E. Stanley, Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000).
[2] V. Plerou, P. Gopikrishnan, X. Gabaix, and H. E. Stanley, ``Quantifying Stock Price Response to Demand Fluctuations'' cond-mat 0106657 (preprint).
[3] V. Plerou, P. Gopikrishnan, and H. E. Stanley, ``Critical Threshold for Symmetry Breaking in Stock Demand'' (preprint) cond-mat/0111349.
[4] X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, ``A Simple Theory of Asset Market Fluctuations, Motivated by the Cubic and Half Cubic Laws of Trading Activity in the Stock Market'' (preprint).
[5] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, T. Guhr, and H. E. Stanley, ``A Random Matrix approach to Financial Cross-Correlations'' Phys. Rev. E (in press) cond-mat/0108023.