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A nonlinear partial integro-differential equation from mathematical finance

Author

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  • Frédéric Abergel

    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

  • Rémi Tachet

    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

Abstract

We study a nonlinear partial integrodifferential equation arising in the calibration of stochastic volatility models to a market of vanilla options.

Suggested Citation

  • Frédéric Abergel & Rémi Tachet, 2010. "A nonlinear partial integro-differential equation from mathematical finance," Post-Print hal-00611962, HAL.
    • Handle: RePEc:hal:journl:hal-00611962
    DOI: 10.3934/dcds.2010.27.907
    Note: View the original document on HAL open archive server: https://hal.science/hal-00611962
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    File URL: https://hal.science/hal-00611962/document
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    Citations

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    Cited by:

    1. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    2. Ivan Guo & Gregoire Loeper, 2018. "Path Dependent Optimal Transport and Model Calibration on Exotic Derivatives," Papers 1812.03526, arXiv.org, revised Sep 2020.
    3. Fairouz Tchier & Ioannis Dassios & Ferdous Tawfiq & Lakhdar Ragoub, 2021. "On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions," Mathematics, MDPI, vol. 9(3), pages 1-14, February.
    4. Acciaio, Beatrice & Guyon, Julien, 2020. "Short communication: inversion of convex ordering: local volatility does not maximise the price of VIX futures," LSE Research Online Documents on Economics 102984, London School of Economics and Political Science, LSE Library.
    5. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01686114, HAL.
    6. Martin Larsson & Shukun Long, 2024. "Markovian projections for It\^o semimartingales with jumps," Papers 2403.15980, arXiv.org.
    7. Mao Fabrice Djete, 2022. "Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models," Papers 2208.09986, arXiv.org, revised Oct 2024.
    8. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    9. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01399542, HAL.
    10. Ivan Guo & Grégoire Loeper & Shiyi Wang, 2022. "Calibration of local‐stochastic volatility models by optimal transport," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 46-77, January.
    11. Beatrice Acciaio & Julien Guyon, 2019. "Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures," Papers 1910.05750, arXiv.org.
    12. Christoph Reisinger & Maria Olympia Tsianni, 2023. "Convergence of the Euler--Maruyama particle scheme for a regularised McKean--Vlasov equation arising from the calibration of local-stochastic volatility models," Papers 2302.00434, arXiv.org, revised Aug 2023.

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