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Statistics Of Vix Futures And Applications To Trading Volatility Exchange-Traded Products

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  • M. AVELLANEDA

    (Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York 10012-1185, NY, USA)

  • A. PAPANICOLAOU

    (Department of Finance and Risk Engineering, NYU Tandon School of Engineering, 6 MetroTech Center, Brooklyn 11201, NY, USA)

Abstract

We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is contango with VIX ≈ 12% and a long-term futures price V∞≈ 20%. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic. To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of SR = 0.5 or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are observed sporadically in the volatility futures market.

Suggested Citation

  • M. Avellaneda & A. Papanicolaou, 2019. "Statistics Of Vix Futures And Applications To Trading Volatility Exchange-Traded Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-30, February.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:01:n:s0219024918500619
    DOI: 10.1142/S0219024918500619
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    3. Christian Bayer & Jim Gatheral & Morten Karlsmark, 2013. "Fast Ninomiya--Victoir calibration of the double-mean-reverting model," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1813-1829, November.
    4. Laurent Laloux & Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Random Matrix Theory And Financial Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 391-397.
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    Cited by:

    1. Rama Cont, 2023. "In memoriam: Marco Avellaneda (1955–2022)," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 3-15, January.
    2. Ying-Li Wang & Cheng-Long Xu & Ping He, 2023. "A Markovian empirical model for the VIX index and the pricing of the corresponding derivatives," Papers 2309.08175, arXiv.org.
    3. M. Avellaneda & T. N. Li & A. Papanicolaou & G. Wang, 2021. "Trading Signals In VIX Futures," Papers 2103.02016, arXiv.org, revised Nov 2021.
    4. Andrew Papanicolaou, 2022. "Consistent time‐homogeneous modeling of SPX and VIX derivatives," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 907-940, July.

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