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Lifting the Heston model

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  • Eduardo Abi Jaber

    (CEREMADE)

Abstract
How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as extreme cases the classical Heston model (when n = 1), and the rough Heston model (when n goes to infinity). We show that the lifted model enjoys the best of both worlds: Markovianity and satisfactory fits of implied volatility smiles for short maturities with very few parameters. Further, our approach speeds up the calibration time and opens the door to time-efficient simulation schemes.

Suggested Citation

  • Eduardo Abi Jaber, 2018. "Lifting the Heston model," Papers 1810.04868, arXiv.org, revised Nov 2019.
    • Handle: RePEc:arx:papers:1810.04868
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    References listed on IDEAS

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    1. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    2. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    3. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    4. Eduardo Abi Jaber & Omar El Euch, 2018. "Markovian structure of the Volterra Heston model," Working Papers hal-01716696, HAL.
    5. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    6. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    7. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    8. Eduardo Abi Jaber & Omar El Euch, 2018. "Multi-factor approximation of rough volatility models," Working Papers hal-01697117, HAL.
    9. Aurélien Alfonsi, 2015. "Affine Diffusions and Related Processes: Simulation, Theory and Applications," Post-Print hal-03127212, HAL.
    10. 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.
    11. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    12. 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.
    13. Philippe Carmona & Laure Coutin & G. Montseny, 2000. "Approximation of Some Gaussian Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 161-171, January.
    14. Eduardo Abi Jaber & Omar El Euch, 2018. "Multi-factor approximation of rough volatility models," Papers 1801.10359, arXiv.org, revised Apr 2018.
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