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State spaces of multifactor approximations of nonnegative Volterra processes

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  • Eduardo Abi Jaber
  • Christian Bayer
  • Simon Breneis

Abstract

We show that the state spaces of multifactor Markovian processes, coming from approximations of nonnegative Volterra processes, are given by explicit linear transformation of the nonnegative orthant. We demonstrate the usefulness of this result for applications, including simulation schemes and PDE methods for nonnegative Volterra processes.

Suggested Citation

  • Eduardo Abi Jaber & Christian Bayer & Simon Breneis, 2024. "State spaces of multifactor approximations of nonnegative Volterra processes," Papers 2412.17526, arXiv.org.
    • Handle: RePEc:arx:papers:2412.17526
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    File URL: http://arxiv.org/pdf/2412.17526
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    References listed on IDEAS

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    1. Thierry Bochud & Damien Challet, 2007. "Optimal approximations of power laws with exponentials: application to volatility models with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 585-589.
    2. Gytenis Lileika & Vigirdas Mackevičius, 2021. "Second-Order Weak Approximations of CKLS and CEV Processes by Discrete Random Variables," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    3. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
    4. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
    5. Christian Bayer & Simon Breneis, 2023. "Markovian approximations of stochastic Volterra equations with the fractional kernel," Quantitative Finance, Taylor & Francis Journals, vol. 23(1), pages 53-70, January.
    6. Christian Bayer & Simon Breneis, 2024. "Efficient option pricing in the rough Heston model using weak simulation schemes," Quantitative Finance, Taylor & Francis Journals, vol. 24(9), pages 1247-1261, September.
    7. Christian Bayer & Simon Breneis, 2023. "Weak Markovian Approximations of Rough Heston," Papers 2309.07023, arXiv.org.
    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.
    9. Etienne Chevalier & Sergio Pulido & Elizabeth Z'u~niga, 2021. "American options in the Volterra Heston model," Papers 2103.11734, arXiv.org, revised May 2022.
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    Cited by:

    1. Eduardo Abi Jaber & Soukaina Bruneau & Nathan De Carvalho & Dimitri Sotnikov & Laurent Tur, 2025. "Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration," Papers 2501.05975, arXiv.org.

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