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Affine Rough Models

Author

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  • Martin Keller-Ressel
  • Martin Larsson
  • Sergio Pulido

Abstract

The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential-affine transform formulas.

Suggested Citation

  • Martin Keller-Ressel & Martin Larsson & Sergio Pulido, 2018. "Affine Rough Models," Papers 1812.08486, arXiv.org.
    • Handle: RePEc:arx:papers:1812.08486
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    File URL: http://arxiv.org/pdf/1812.08486
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    References listed on IDEAS

    as
    1. Jim Gatheral & Martin Keller-Ressel, 2018. "Affine forward variance models," Papers 1801.06416, arXiv.org, revised Oct 2018.
    2. Philipp Harms & David Stefanovits, 2015. "Affine representations of fractional processes with applications in mathematical finance," Papers 1510.04061, arXiv.org, revised Feb 2018.
    3. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    4. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    7. F. Comte & L. Coutin & E. Renault, 2012. "Affine fractional stochastic volatility models," Annals of Finance, Springer, vol. 8(2), pages 337-378, May.
    8. Masaaki Fukasawa, 2017. "Short-time at-the-money skew and rough fractional volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 189-198, February.
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    Citations

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    Cited by:

    1. Bingyan Han & Hoi Ying Wong, 2019. "Merton's portfolio problem under Volterra Heston model," Papers 1905.05371, arXiv.org, revised Nov 2019.
    2. Ackermann, Julia & Kruse, Thomas & Overbeck, Ludger, 2022. "Inhomogeneous affine Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 250-279.
    3. Christian Bayer & Fabian Andsem Harang & Paolo Pigato, 2020. "Log-modulated rough stochastic volatility models," Papers 2008.03204, arXiv.org, revised May 2021.
    4. Etienne Chevalier & Sergio Pulido & Elizabeth Zúñiga, 2021. "American options in the Volterra Heston model," Working Papers hal-03178306, HAL.
    5. Bingyan Han & Hoi Ying Wong, 2019. "Mean-variance portfolio selection under Volterra Heston model," Papers 1904.12442, arXiv.org, revised Jan 2020.
    6. Han, Bingyan & Wong, Hoi Ying, 2021. "Merton’s portfolio problem under Volterra Heston model," Finance Research Letters, Elsevier, vol. 39(C).
    7. Benjamin James Duthie, 2019. "Portfolio optimisation under rough Heston models," Papers 1909.02972, arXiv.org.
    8. Bondi, Alessandro & Livieri, Giulia & Pulido, Sergio, 2024. "Affine Volterra processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 168(C).

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