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Persistence and discontinuity in the VIX dynamics

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  • Ouandlous, Arav
  • Barkoulas, John T.
  • Alhaj-Yaseen, Yaseen

Abstract

We estimate the two Mandelbrotian parameters (“dual forms of wild variability”), namely, long-range dependence (Joseph effect) and discontinuity or fat tails (Noah effect) for the VIX stock market volatility measure. We find the VIX scalar series to be characterized by strong dependence (with nonstationary but mean-reverting dynamics) and fat tails with a power-law asymptotic behavior in the upper tail. The temporal stability analysis shows that the recent financial crisis, in particular, the collapse of Lehman Brothers in September 2008 and its aftereffects, had a pronounced impact on the behavior of the Mandelbrotian parameters. The presence of these statistical features in the VIX dynamics sheds valuable insight into the underlying data generating process for the VIX.

Suggested Citation

  • Ouandlous, Arav & Barkoulas, John T. & Alhaj-Yaseen, Yaseen, 2018. "Persistence and discontinuity in the VIX dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 333-344.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:333-344
    DOI: 10.1016/j.chaos.2018.04.013
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    as
    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    3. Rama Cont & Thomas Kokholm, 2013. "A Consistent Pricing Model For Index Options And Volatility Derivatives," Post-Print hal-00801536, HAL.
    4. Fernandes, Marcelo & Medeiros, Marcelo C. & Scharth, Marcel, 2014. "Modeling and predicting the CBOE market volatility index," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 1-10.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    6. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
    7. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 636-670.
    8. Charles J. Corrado & Thomas W. Miller, Jr., 2005. "The forecast quality of CBOE implied volatility indexes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(4), pages 339-373, April.
    9. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    10. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    11. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    12. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    13. Yin‐Wong Cheung, 1993. "Tests For Fractional Integration:A Monte Carlo Investigation," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(4), pages 331-345, July.
    14. Simon Lalancette & Jean†Guy Simonato, 2017. "The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation," European Financial Management, European Financial Management Association, vol. 23(2), pages 325-354, March.
    15. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    16. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    17. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    18. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
    19. Bekaert, Geert & Hoerova, Marie, 2014. "The VIX, the variance premium and stock market volatility," Journal of Econometrics, Elsevier, vol. 183(2), pages 181-192.
    20. Martens, Martin & van Dijk, Dick & de Pooter, Michiel, 2009. "Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic announcements," International Journal of Forecasting, Elsevier, vol. 25(2), pages 282-303.
    21. Torben G. Andersen & Oleg Bondarenko, 2007. "Construction and Interpretation of Model-Free Implied Volatility," NBER Working Papers 13449, National Bureau of Economic Research, Inc.
    22. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
    23. Victor Pontines, 2010. "Fat-tails and house prices in OECD countries," Applied Economics Letters, Taylor & Francis Journals, vol. 17(14), pages 1373-1377.
    24. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    25. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    26. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    27. Jacinto Marabel Romo, 2017. "Pricing volatility options under stochastic skew with application to the VIX index," The European Journal of Finance, Taylor & Francis Journals, vol. 23(4), pages 353-374, March.
    28. Ritirupa Samanta & Blake LeBaron, 2005. "Extreme Value Theory and Fat Tails in Equity Markets," Computing in Economics and Finance 2005 140, Society for Computational Economics.
    29. Stilian A. Stoev & George Michailidis, 2010. "On the estimation of the heavy‐tail exponent in time series using the max‐spectrum," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 224-253, May.
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