Are there Dragon Kings in the Stock Market?
股票市场中是否存在“龙王”极端事件？AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究股票指数实现波动率及其极端尾部分布，对应波动率与尾部风险。
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股票市场中是否存在“龙王”极端事件？
- 研究问题
- 标普 500 的极端实现波动率是否符合幂律尾部，还是表现为相对该尾部显著向上或向下偏离的异常事件？
- 方法与思路
- 作者分析约五十年的实现波动率，比较不同平均窗口，拟合 mGB、GB2 分布及对数坐标尾部直线，并使用置信区间和 p 值判断偏离。
- 材料陈述的贡献
- 摘要称尾部中潜在“龙王”最终转为向下偏离的“负龙王”，且随平均窗口扩大更明显，并比较有限终点与幂律尾部分布。
- 阅读关注点
- 应核对尾部阈值和平均窗口的选择、分布拟合不确定性、时间依赖与多重检验处理，以及“潜在龙王”的统计定义。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实。摘要未提供显著性数值或稳健性结果，极端事件归类依赖所选基准分布和检验方法。
原文摘要
We undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of realized volatility (RV) of the S&P500 index and its distribution function. As expected, the largest values of RV coincide with the largest economic upheavals of the period: Savings and Loan Crisis, Tech Bubble, Financial Crisis and Covid Pandemic. We address the question of whether these values belong to one of the three categories: Black Swans (BS), that is they lie on scale-free, power-law tails of the distribution; Dragon Kings (DK), defined as statistically significant upward deviations from BS; or Negative Dragons Kings (nDK), defined as statistically significant downward deviations from BS. In analyzing the tails of the distribution with RV > 40, we observe the appearance of "potential" DK which eventually terminate in an abrupt plunge to nDK. This phenomenon becomes more pronounced with the increase of the number of days over which the average RV is calculated -- here from daily, n=1, to "monthly," n=21. We fit the entire distribution with a modified Generalized Beta (mGB) distribution function, which terminates at a finite value of the variable but exhibits a long power-law stretch prior to that, as well as Generalized Beta Prime (GB2) distribution function, which has a power-law tail. We also fit the tails directly with a straight line on a log-log scale. In order to ascertain BS, DK or nDK behavior, all fits include their confidence intervals and p-values are evaluated for the data points to check if they can come from the respective distributions.