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Pricing variance swaps under the Hawkes jump‐diffusion process

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  • Weiyi Liu
  • Song‐Ping Zhu

Abstract

This paper presents an analytical approach for pricing variance swaps with discrete sampling times when the underlying asset follows a Hawkes jump‐diffusion process characterized with both stochastic volatility and clustered jumps. A significantly simplified method, with which there is no need to solve partial differential equations, is used to derive a closed‐form pricing formula. A distinguished feature is that many recently published formulas can be shown to be special cases of the one presented here. Some numerical examples are provided with results demonstrating that jump clustering indeed has a significant impact on the price of variance swaps.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:6:p:635-655
    DOI: 10.1002/fut.21997
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    Cited by:

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    3. Luis A. Souto Arias & Pasquale Cirillo & Cornelis W. Oosterlee, 2022. "A new self-exciting jump-diffusion process for option pricing," Papers 2205.13321, arXiv.org, revised Feb 2023.
    4. Xinglin Yang & Ji Chen, 2021. "VIX term structure: The role of jump propagation risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 785-810, June.
    5. Sha Lin & Xin‐Jiang He, 2024. "Closed‐Form Formulae for Variance and Volatility Swaps Under Stochastic Volatility With Stochastic Liquidity Risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1447-1461, August.
    6. Jing, Bo & Li, Shenghong & Ma, Yong, 2021. "Consistent pricing of VIX options with the Hawkes jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    7. Xin-Jiang He & Sha Lin, 2024. "A probabilistic approach for the valuation of variance swaps under stochastic volatility with jump clustering and regime switching," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-23, December.
    8. Guanghua Lian & Robert J. Elliott & Petko Kalev & Zhaojun Yang, 2022. "Approximate pricing of American exchange options with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(6), pages 983-1001, June.
    9. 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.

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