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Discrete variance swap in a rough volatility economy

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  • Yiru Xi
  • Hoi Ying Wong

Abstract

The discrete variance swap is one of the most popular volatility derivatives traded on the over‐the‐counter market. This paper discusses its valuation in a rough volatility economy and the impact of roughness on the term structure of discrete variance swap prices. A semianalytic solution is obtained through stochastic convolution. Our numerical experiments show that the roughness of volatility has a significant impact on the concavity of the variance swap term structure.

Suggested Citation

  • Yiru Xi & Hoi Ying Wong, 2021. "Discrete variance swap in a rough volatility economy," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1640-1654, October.
  • Handle: RePEc:wly:jfutmk:v:41:y:2021:i:10:p:1640-1654
    DOI: 10.1002/fut.22242
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    References listed on IDEAS

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    1. José Da Fonseca & Wenjun Zhang, 2019. "Volatility of volatility is (also) rough," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(5), pages 600-611, May.
    2. Eduardo Abi Jaber, 2019. "Lifting the Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 19(12), pages 1995-2013, December.
    3. Weiyi Liu & Song‐Ping Zhu, 2019. "Pricing variance swaps under the Hawkes jump‐diffusion process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 635-655, June.
    4. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    5. Eduardo Abi Jaber, 2019. "Lifting the Heston model," Post-Print hal-01890751, HAL.
    6. 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.
    7. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    8. Pun, Chi Seng & Chung, Shing Fung & Wong, Hoi Ying, 2015. "Variance swap with mean reversion, multifactor stochastic volatility and jumps," European Journal of Operational Research, Elsevier, vol. 245(2), pages 571-580.
    9. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    10. Mesias Alfeus & Ludger Overbeck & Erik Schlögl, 2019. "Regime switching rough Heston model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(5), pages 538-552, May.
    11. Eduardo Abi Jaber, 2018. "Lifting the Heston model," Papers 1810.04868, arXiv.org, revised Nov 2019.
    12. Fangyuan Dong & Hoi Ying Wong, 2017. "Variance swaps under the threshold Ornstein–Uhlenbeck model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(5), pages 507-521, September.
    13. Wendong Zheng & Yue Kuen Kwok, 2014. "Closed Form Pricing Formulas For Discretely Sampled Generalized Variance Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 855-881, October.
    14. Tetsuya Takaishi, 2019. "Rough volatility of Bitcoin," Papers 1904.12346, arXiv.org.
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    Cited by:

    1. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.

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