Lillo F, Mantegna R N
Istituto Nazionale per la Fisica della Materia, Unità di Palermo, Viale delle Scienze, I-90128 Palermo, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016119. doi: 10.1103/PhysRevE.68.016119. Epub 2003 Jul 23.
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power-law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models.
我们通过研究指数收益率绝对值超过给定阈值的次数，来探讨金融市场在崩盘后瞬间的弛豫动力学。我们发现，超过选定阈值的事件数量呈幂律演化（这种行为在地球物理学中被称为大森定律）这一实证观察结果，与以下两种情况同时出现相符：（i）具有幂律渐近行为的收益率概率密度函数；（ii）其典型尺度的幂律弛豫衰减。我们的实证观察结果无法在简单且广泛应用的随机波动率模型框架内得到解释。
