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The Alpha‐Heston stochastic volatility model

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  • Ying Jiao
  • Chunhua Ma
  • Simone Scotti
  • Chao Zhou

Abstract

We introduce an affine extension of the Heston model, called the α‐Heston model, where the instantaneous variance process contains a jump part driven by α‐stable processes with α∈(1,2]. In this framework, we examine the implied volatility and its asymptotic behavior for both asset and VIX options. Furthermore, we study the jump clustering phenomenon observed on the market. We provide a jump cluster decomposition for the variance process where each cluster is induced by a “mother jump” representing a triggering shock followed by “secondary jumps” characterizing the contagion impact.

Suggested Citation

  • Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2021. "The Alpha‐Heston stochastic volatility model," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 943-978, July.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:3:p:943-978
    DOI: 10.1111/mafi.12306
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    References listed on IDEAS

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    Cited by:

    1. Alessandro Bondi & Sergio Pulido & Simone Scotti, 2022. "The rough Hawkes Heston stochastic volatility model," Working Papers hal-03827332, HAL.
    2. Gaïgi, M’hamed & Ly Vath, Vathana & Scotti, Simone, 2022. "Optimal harvesting under marine reserves and uncertain environment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1181-1194.
    3. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2021. "CBI-time-changed L\'evy processes for multi-currency modeling," Papers 2112.02440, arXiv.org, revised Jul 2022.
    4. Alessandro Bondi & Sergio Pulido & Simone Scotti, 2022. "The rough Hawkes Heston stochastic volatility model," Papers 2210.12393, arXiv.org.
    5. 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.
    6. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2022. "CBI-time-changed Lévy processes," Working Papers 05/2022, University of Verona, Department of Economics.

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