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Affine Volterra processes with jumps

Author

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  • Bondi, Alessandro
  • Livieri, Giulia
  • Pulido, Sergio

Abstract

The theory of affine processes has been recently extended to continuous stochastic Volterra equations. These so-called affine Volterra processes overcome modeling shortcomings of affine processes by incorporating path-dependent features and trajectories with regularity different from the paths of Brownian motion. More specifically, singular kernels yield rough affine processes. This paper extends the theory by considering affine stochastic Volterra equations with jumps. This extension is not straightforward because the jump structure and possible singularities of the kernel may induce explosions of the trajectories. This study also provides exponential affine formulas for the conditional Fourier–Laplace transform of marked Hawkes processes.

Suggested Citation

  • Bondi, Alessandro & Livieri, Giulia & Pulido, Sergio, 2024. "Affine Volterra processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:spapps:v:168:y:2024:i:c:s0304414923002363
    DOI: 10.1016/j.spa.2023.104264
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    References listed on IDEAS

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    1. Abi Jaber, Eduardo & El Euch, Omar, 2019. "Markovian structure of the Volterra Heston model," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 63-72.
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    7. Eduardo Abi Jaber, 2021. "Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels," Post-Print hal-02412741, HAL.
    8. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
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    10. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    11. Eduardo Abi Jaber & Omar El Euch, 2019. "Markovian structure of the Volterra Heston model," Post-Print hal-01716696, HAL.
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    Cited by:

    1. Aur'elien Alfonsi & Guillaume Szulda, 2024. "On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients," Papers 2402.19203, arXiv.org.
    2. Boyi Li & Weixuan Xia, 2024. "Crypto Inverse-Power Options and Fractional Stochastic Volatility," Papers 2403.16006, arXiv.org.

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