2001/06/29 by Vasiliki Plerou, Parameswaran Gopikrishnan, Xavier Gabaix +1
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Nonlinear Dynamics and Pattern Formation #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #q-fin.TR
paper · pdf · doi:10.1103/physreve.66.027104
4 pages (multicol fomat, revtex)
arxiv created 2001/06/29 · openalex publication_date 2002/08/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We empirically address the question of how stock prices respond to changes in demand. We quantify the relations between price change G over a time interval \ensuremathΔt and two different measures of demand fluctuations: (a) \ensuremathΦ, defined as the difference between the number of buyer-initiated and seller-initiated trades, and (b) \ensuremathΩ, defined as the difference in number of shares traded in buyer- and seller-initiated trades. We find that the conditional expectation functions of price change for a given \ensuremathΦ or \ensuremathΩ, 〈G〉_\ensuremathΦ and 〈G〉_\ensuremathΩ (``market impact function''), display concave functional forms that seem universal for all stocks. For small \ensuremathΩ, we find a power-law behavior 〈G〉_\ensuremathΩ\ensuremath∼\ensuremathΩ1/8 with \ensuremathδ depending on \ensuremathΔt (\ensuremathδ\ensuremath≈3 for \ensuremathΔt=5 min, \ensuremathδ\ensuremath≈3/2 for \ensuremathΔt=15 min and \ensuremathδ\ensuremath≈1 for large \ensuremathΔt). We find that large price fluctuations occur when demand is very small---a fact that is reminiscent of large fluctuations that occur at critical points in spin systems, where the divergent nature of the response function leads to large fluctuations.