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Vix Versus Vxx: A Joint Analytical Framework

Author

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  • MARTINO GRASSELLI

    (Department of Mathematics, University of Padova, Via Trieste 63, Padova, Italy2Léonard de Vinci Pôle Universitaire, Research Center, 92916 Paris La Défense, France)

  • LAKSHITHE WAGALATH

    (IESEG School of Management, 3 rue de la Digue, 59000 Lille, France4LEM-CNRS 9221, 3 rue de la Digue, 59000 Lille, France)

Abstract

We propose a framework for modeling in a consistent manner the VIX index and the VXX, an exchange-traded note written on the VIX. Our study enables to link the properties of VXX to those of the VIX in a tractable way. In particular, we quantify the systematic loss observed empirically for VXX when the VIX futures term-structure is in contango and we derive option prices, implied volatilities and skews of VXX from those of VIX in infinitesimal developments. We also perform a calibration on real data which highlights the flexibility of our model in fitting the futures and the vanilla options market of VIX and VXX. Our framework can be used to model other exchange-traded notes on the VIX as well as any market where exchange-traded notes have been introduced on a reference index, hence providing tools to better anticipate and quantify systematic behavior of an exchange-traded note with respect to the underlying index.

Suggested Citation

  • Martino Grasselli & Lakshithe Wagalath, 2020. "Vix Versus Vxx: A Joint Analytical Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(05), pages 1-39, August.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:05:n:s0219024920500338
    DOI: 10.1142/S0219024920500338
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    Cited by:

    1. Tong, Zhigang & Liu, Allen, 2022. "Pricing variance swaps under subordinated Jacobi stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    2. Xiaoyu Tan & Chengxiang Wang & Wei Lin & Jin E. Zhang & Shenghong Li & Xuejun Zhao & Zili Zhang, 2021. "The term structure of the VXX option smirk: Pricing VXX option with a two‐factor model and asymmetry jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 439-457, April.
    3. Wei Lin & Jin E. Zhang, 2022. "Pricing VXX options by modeling VIX directly," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 888-922, May.

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