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Are there Dragon Kings in the Stock Market?

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  • Jiong Liu
  • M. Dashti Moghaddam
  • R. A. Serota

Abstract

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.

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  • Jiong Liu & M. Dashti Moghaddam & R. A. Serota, 2023. "Are there Dragon Kings in the Stock Market?," Papers 2307.03693, arXiv.org.
    • Handle: RePEc:arx:papers:2307.03693
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    References listed on IDEAS

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    1. M. Dashti Moghaddam & Jiong Liu & R. A. Serota, 2021. "Implied and realized volatility: A study of distributions and the distribution of difference," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2581-2594, April.
    2. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distribution of Historic Market Data ¨C Implied and Realized Volatility," Applied Economics and Finance, Redfame publishing, vol. 6(5), pages 104-130, September.
    3. Didier SORNETTE, 2009. "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
    4. Zhiyuan Liu & M. Dashti Moghaddam & R. A. Serota, 2019. "Distributions of historic market data – stock returns," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(3), pages 1-10, March.
    5. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
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