During any unique crisis, panic sell-off leads to a massive stock market crash that may continue for more than a day, termed as mainshock. The effect of a mainshock in the form of aftershocks can be felt throughout the recovery phase of stock price. As the market remains in stress during recovery, any small perturbation leads to a relatively smaller aftershock. The duration of the recovery phase has been estimated using structural break analysis. We have carried out statistical analyses of 1987 stock market crash, 2008 financial crisis and 2020 COVID-19 pandemic considering the actual crash times of the mainshock and aftershocks. Earlier, such analyses were done considering absolute one-day return, which cannot capture a crash properly. The results show that the mainshock and aftershock in the stock market follow the Gutenberg–Richter (GR) power law. Further, we obtained higher β value for the COVID-19 crash compared to the financial-crisis-2008 from the GR law. This implies that the recovery of stock price during COVID-19 may be faster than the financial-crisis-2008. The result is consistent with the present recovery of the market from the COVID-19 pandemic. The analysis shows that the high-magnitude aftershocks are rare, and low-magnitude aftershocks are frequent during the recovery phase. The analysis also shows that the inter-occurrence times of the aftershocks follow the generalized Pareto distribution, i.e. P(τi)∝1[1+λ(q−1)τi]1(q−1), where λ and q are constants and τi is the inter-occurrence time. This analysis may help investors to restructure their portfolio during a market crash.

中文翻译：

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重新审视股市崩盘余震的统计特性：基于 1987 年崩盘、2008 年金融危机和 COVID-19 大流行的分析

在任何独特的危机中，恐慌性抛售会导致可能持续一天以上的大规模股市崩盘，称为主震。在股票价格的整个恢复阶段都可以感受到以余震形式出现的主震的影响。由于市场在复苏期间仍处于压力之下，任何小的扰动都会导致相对较小的余震。恢复阶段的持续时间已使用结构断裂分析进行了估计。考虑到主震和余震的实际崩盘时间，我们对 1987 年股市崩盘、2008 年金融危机和 2020 年 COVID-19 大流行进行了统计分析。早些时候，此类分析是在考虑绝对一日回报的情况下进行的，这无法正确捕捉崩盘。结果表明，股票市场的主震和余震遵循古腾堡-里希特（GR）幂律。此外，我们获得了更高的β与 GR 法中的 2008 年金融危机相比，COVID-19 崩溃的价值。这意味着 COVID-19 期间股价的恢复可能比 2008 年金融危机时更快。这一结果与目前市场从 COVID-19 大流行中复苏的趋势一致。分析表明，在恢复阶段，大余震少见，小余震多发。分析还表明，余震的发生间隔时间服从广义帕累托分布，即磷(τ一世)∝1[1+λ(q-1)τ一世]1(q-1)， 在哪里λ和q是常数和τ一世是互现时间。这种分析可以帮助投资者在市场崩盘期间重组他们的投资组合。