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Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

Author

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  • Yang, Ben-Zhang
  • Yue, Jia
  • Wang, Ming-Hui
  • Huang, Nan-Jing

Abstract

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using the Feynman–Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous model. Moreover, discrete and continuous sampled volatility swap pricing formulas are given by employing the transform technique and the relationship between two pricing formulas is discussed under mild conditions. Finally, some numerical simulations are reported to support the results presented in this paper.

Suggested Citation

  • Yang, Ben-Zhang & Yue, Jia & Wang, Ming-Hui & Huang, Nan-Jing, 2019. "Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 73-84.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:73-84
    DOI: 10.1016/j.amc.2019.02.063
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    Cited by:

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    2. Wang, Xingchun, 2021. "Valuation of options on the maximum of two prices with default risk under GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    3. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2019. "Robust portfolio optimization with multi-factor stochastic volatility," Papers 1910.06872, arXiv.org, revised Jun 2020.
    4. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Continuous time mean-variance-utility portfolio problem and its equilibrium strategy," Papers 2005.06782, arXiv.org, revised Nov 2020.
    5. Xu, De-xuan & Yang, Ben-zhang & Kang, Jian-hao & Huang, Nan-jing, 2021. "Variance and volatility swaps valuations with the stochastic liquidity risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    6. Xianfei Hui & Baiqing Sun & Hui Jiang & Yan Zhou, 2022. "Modeling dynamic volatility under uncertain environment with fuzziness and randomness," Papers 2204.12657, arXiv.org, revised Oct 2022.
    7. Ayub Ahmadi & Mahdieh Tahmasebi, 2024. "Pricing and delta computation in jump-diffusion models with stochastic intensity by Malliavin calculus," Papers 2405.00473, arXiv.org.
    8. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Mean-variance-utility portfolio selection with time and state dependent risk aversion," Papers 2007.06510, arXiv.org, revised Aug 2020.

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