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Moment explosions in the rough Heston model

Author

Listed:
  • Stefan Gerhold

    (TU Wien)

  • Christoph Gerstenecker

    (TU Wien)

  • Arpad Pinter

    (TU Wien)

Abstract

We show that the moment explosion time in the rough Heston model, introduced by El Euch and Rosenbaum in 2016, is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions). We show that the critical moments are finite for all maturities. For negative correlation, we apply our algorithm for the moment explosion time to compute the lower critical moment.

Suggested Citation

  • Stefan Gerhold & Christoph Gerstenecker & Arpad Pinter, 2019. "Moment explosions in the rough Heston model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 575-608, December.
    • Handle: RePEc:spr:decfin:v:42:y:2019:i:2:d:10.1007_s10203-019-00267-6
    DOI: 10.1007/s10203-019-00267-6
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Giorgia Callegaro & Martino Grasselli & Gilles Paèes, 2021. "Fast Hybrid Schemes for Fractional Riccati Equations (Rough Is Not So Tough)," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 221-254, February.
    2. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    3. Mohamed Ben Alaya & Martin Friesen & Jonas Kremer, 2024. "Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process," Papers 2409.04496, arXiv.org.
    4. Martin Forde & Stefan Gerhold & Benjamin Smith, 2021. "Small‐time, large‐time, and H→0 asymptotics for the Rough Heston model," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 203-241, January.
    5. Martin Friesen & Peng Jin, 2022. "Volterra square-root process: Stationarity and regularity of the law," Papers 2203.08677, arXiv.org, revised Oct 2022.

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    More about this item

    Keywords

    Option pricing; Rough volatility; Rough Heston model; Moment explosion; Volterra integral equation;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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