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A general framework for a joint calibration of VIX and VXX options

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  • Martino Grasselli
  • Andrea Mazzoran
  • Andrea Pallavicini

Abstract

We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in commodity smile modelling, we present a multi-factor stochastic-local volatility model that is able to jointly calibrate plain vanilla options both on VIX futures and VXX notes, thus going beyond the failure of purely stochastic or simply local volatility models. We discuss numerical results on real market data by highlighting the impact of model parameters on implied volatilities.

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  • Martino Grasselli & Andrea Mazzoran & Andrea Pallavicini, 2020. "A general framework for a joint calibration of VIX and VXX options," Papers 2012.08353, arXiv.org, revised Jun 2021.
    • Handle: RePEc:arx:papers:2012.08353
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    1. Emanuele Nastasi & Andrea Pallavicini & Giulio Sartorelli, 2020. "Smile Modeling In Commodity Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-28, May.
    2. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    3. Sebastian A. Gehricke & Jin E. Zhang, 2020. "The implied volatility smirk in the VXX options market," Applied Economics, Taylor & Francis Journals, vol. 52(8), pages 769-788, February.
    4. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    5. Schwert, G William, 1990. "Stock Returns and Real Activity: A Century of Evidence," Journal of Finance, American Finance Association, vol. 45(4), pages 1237-1257, September.
    6. Rama Cont & Thomas Kokholm, 2013. "A Consistent Pricing Model For Index Options And Volatility Derivatives," Post-Print hal-00801536, HAL.
    7. Jim Gatheral & Paul Jusselin & Mathieu Rosenbaum, 2020. "The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem," Papers 2001.01789, arXiv.org.
    8. Anthonie W. Van Der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2014. "The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-30.
    9. G. William Schwert, 2011. "Stock Volatility during the Recent Financial Crisis," European Financial Management, European Financial Management Association, vol. 17(5), pages 789-805, November.
    10. Bao, Qunfang & Li, Shenghong & Gong, Donggeng, 2012. "Pricing VXX option with default risk and positive volatility skew," European Journal of Operational Research, Elsevier, vol. 223(1), pages 246-255.
    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    12. Julien Guyon, 2020. "Inversion of convex ordering in the VIX market," Quantitative Finance, Taylor & Francis Journals, vol. 20(10), pages 1597-1623, October.
    13. Gabriel Drimus & Walter Farkas, 2013. "Local volatility of volatility for the VIX market," Review of Derivatives Research, Springer, vol. 16(3), pages 267-293, October.
    14. Lin, Yueh-Neng, 2013. "VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4432-4446.
    15. Nicola Moreni & Andrea Pallavicini, 2017. "Derivative Pricing With Collateralization And Fx Market Dislocations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-27, September.
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