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Analytically Pricing Variance Swaps Under the Hawkes Jump‐Diffusion Process With Liquidity Risks

Author

Listed:
  • Ke Wang
  • Xun‐xiang Guo
  • Yang‐yang Wang
  • Hong‐yu Zhang

Abstract

We investigate variance swap pricing by incorporating a self‐exciting Hawkes process into a stochastic liquidity risk model. Within this framework, we derive closed‐form pricing formulas for discretely sampled variance swaps using two different methods. Through asymptotic analysis, we demonstrate that the discretely sampled pricing formulas converge to their continuously sampled counterparts as the sampling interval approaches zero. Numerical results further highlight the significant impact of jump clustering on the strike prices of variance swaps.

Suggested Citation

  • Ke Wang & Xun‐xiang Guo & Yang‐yang Wang & Hong‐yu Zhang, 2025. "Analytically Pricing Variance Swaps Under the Hawkes Jump‐Diffusion Process With Liquidity Risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(9), pages 1388-1408, September.
    • Handle: RePEc:wly:jfutmk:v:45:y:2025:i:9:p:1388-1408
    DOI: 10.1002/fut.22603
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    References listed on IDEAS

    as
    1. Carole Bernard & Zhenyu Cui, 2014. "Prices and Asymptotics for Discrete Variance Swaps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(2), pages 140-173, April.
    2. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    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. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    5. Thomas Little & Vijay Pant, 2002. "A Finite Difference Method For The Valuation Of Variance Swaps," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III), chapter 12, pages 275-295, World Scientific Publishing Co. Pte. Ltd..
    6. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    7. 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.
    8. Wu, Bin & Chen, Pengzhan & Ye, Wuyi, 2024. "Variance swaps with mean reversion and multi-factor variance," European Journal of Operational Research, Elsevier, vol. 315(1), pages 191-212.
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