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The Large-Maturity Smile For The Sabr And Cev-Heston Models

Author

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  • MARTIN FORDE

    (Department of Mathematics, King's College London, Strand, London, WC2R 2LS, United Kingdom)

  • ANDREY POGUDIN

    (Department of Mathematics, King's College London, Strand, London, WC2R 2LS, United Kingdom)

Abstract

Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β

Suggested Citation

  • Martin Forde & Andrey Pogudin, 2013. "The Large-Maturity Smile For The Sabr And Cev-Heston Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-20.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500477
    DOI: 10.1142/S0219024913500477
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    References listed on IDEAS

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    1. Antoine Jacquier & Aleksandar Mijatović, 2014. "Large Deviations for the Extended Heston Model: The Large-Time Case," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 263-280, September.
    2. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
    3. A. Gulisashvili, 2009. "Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes," Papers 0906.0394, arXiv.org.
    4. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
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    Citations

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    Cited by:

    1. Leif Döring & Blanka Horvath & Josef Teichmann, 2017. "Functional Analytic (Ir-)Regularity Properties Of Sabr-Type Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-48, May.
    2. Dan Pirjol & Lingjiong Zhu, 2020. "Asymptotics of the time-discretized log-normal SABR model: The implied volatility surface," Papers 2001.09850, arXiv.org, revised Mar 2020.
    3. Forde, Martin, 2014. "The large-maturity smile for the Stein–Stein model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 145-152.
    4. Blanka Horvath & Oleg Reichmann, 2018. "Dirichlet Forms and Finite Element Methods for the SABR Model," Papers 1801.02719, arXiv.org.
    5. Nian Yao & Zhiqiu Li & Zhichao Ling & Junfeng Lin, 2020. "Asymptotic Smiles for an Affine Jump-Diffusion Model," Papers 2003.00334, arXiv.org, revised May 2020.
    6. Stephen Taylor & Scott Glasgow & James Taylor & Jan Vecer, 2016. "Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 847-867, September.
    7. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Euler-Discretized Hull-White Stochastic Volatility Model," Papers 1707.00899, arXiv.org.
    8. Dan Pirjol & Lingjiong Zhu, 2018. "Asymptotics for the Euler-Discretized Hull-White Stochastic Volatility Model," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 289-331, March.

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