Jiong Liu, M. Dashti Moghaddam, R. A. Serota
arXiv 7 Jul 2023 · Finance — Statistical Finance · publishedFoundations (2024) · 3 citations (OpenAlex)
arXiv:2307.03693 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J. Liu, R. A. Serota, Rethinking generalized beta family of distribu… (2023) Aticle: 24 | 1.000 | 12 | 3 | 100% |
| 2 | V. F. Pisarenko, D. Sornette, Robust statistical tests of dragon-kin… (2012) 95–115 | 1.000 | 7 | 3 | 100% |
| 3 | J. Janczura, R. Weron, Black swans or dragon-kings? a simple test fo… (2012) 79–93 | 0.843 | 3 | 3 | 100% |
| 4 | M. Dashti Moghaddam, J. Liu, R. Serota, Implied and realized volatil… (2021) 2581–2594 | 0.811 | 4 | 2 | 100% |
| 5 | M. Dashti Moghaddam, R. Serota, Combined mutiplicative-heston model… (2021) 125263 | 0.644 | 2 | 2 | 100% |
| 6 | J. B. McDonald, Y. J. Xu, A generlazition of the beta distribution w… (1996) 133–152 | 0.644 | 2 | 2 | 100% |
| 7 | M. Dashti Moghaddam, Z. Liu, R. Serota, Distributions of historic ma… (2019) 104–130 | 0.511 | 2 | 1 | 100% |
| 8 | CBOE VIX Index, https://www.cboe.com/tradable_products/vix/ (previou… | 0.405 | 1 | 1 | 100% |
| 9 | VIX Options and Futures Historical Data, http://www.cboe.com/product… | 0.405 | 1 | 1 | 100% |
| 10 | B. J. Chrstensen, N. R. Prabhala, The relation between implied and r… (1998) 125–150 | 0.405 | 1 | 1 | 100% |
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