Plerou V, Gopikrishnan P, Gabaix X
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215 and Department of Physics, Boston College, Chestnut Hill, Massachusetts 02164, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Sep;62(3 Pt A):R3023-6. doi: 10.1103/physreve.62.r3023.
We quantify the relation between trading activity - measured by the number of transactions N(Deltat)-and the price change G(Deltat) for a given stock, over a time interval [t, t+Deltat]. To this end, we analyze a database documenting every transaction for 1000 U.S. stocks for the two-year period 1994-1995. We find that price movements are equivalent to a complex variant of classic diffusion, where the diffusion constant fluctuates drastically in time. We relate the analog for stock price fluctuations of the diffusion constant-known in economics as the volatility-to two microscopic quantities: (i) the number of transactions N(Deltat) in Deltat, which is the analog of the number of collisions and (ii) the variance W(2)(Deltat) of the price changes for all transactions in Deltat, which is the analog of the local mean square displacement between collisions. Our results are consistent with the interpretation that the power-law tails of P(G(Deltat)) are due to P(W(Deltat)), and the long-range correlations in |G(Deltat)| are due to N(Deltat).
我们对给定股票在时间间隔[t, t + Δt]内，以交易数量N(Δt)衡量的交易活动与价格变化G(Δt)之间的关系进行量化。为此，我们分析了一个记录1994 - 1995年两年间1000只美国股票每笔交易的数据库。我们发现价格变动等同于经典扩散的一种复杂变体，其中扩散常数随时间急剧波动。我们将扩散常数（在经济学中称为波动率）的股票价格波动类似物与两个微观量联系起来：(i) Δt内的交易数量N(Δt)，它类似于碰撞次数；(ii) Δt内所有交易价格变化的方差W²(Δt)，它类似于碰撞之间的局部均方位移。我们的结果与以下解释一致：P(G(Δt))的幂律尾部归因于P(W(Δt))，而|G(Δt)|中的长程相关性归因于N(Δt)。
