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Approximating Expected Value Of An Option With Non-Lipschitz Payoff In Fractional Heston-Type Model

Author

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  • YULIYA MISHURA

    (Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Akad. Glushkova Av. 4-e, Kyiv 03127, Ukraine)

  • ANTON YURCHENKO-TYTARENKO

    (Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Akad. Glushkova Av. 4-e, Kyiv 03127, Ukraine)

Abstract

In this paper, we consider option pricing in a framework of the fractional Heston-type model with H > 1/2. As it is impossible to obtain an explicit formula for the expectation 𝔼f(ST) in this case, where ST is the asset price at maturity time and f is a payoff function, we provide a discretization schemes Ŷn and Ŝn for volatility and price processes correspondingly and study convergence 𝔼f(ŜTn) → 𝔼f(S T) as the mesh of the partition tends to zero. The rate of convergence is calculated. As we allow f to be non-Lipschitz and/or to have discontinuities of the first kind which can cause errors if ST is replaced by ŜTn under the expectation straightforwardly, we use Malliavin calculus techniques to provide an alternative formula for 𝔼f(ST) with smooth functional under the expectation.

Suggested Citation

  • Yuliya Mishura & Anton Yurchenko-Tytarenko, 2020. "Approximating Expected Value Of An Option With Non-Lipschitz Payoff In Fractional Heston-Type Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(05), pages 1-36, August.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:05:n:s0219024920500314
    DOI: 10.1142/S0219024920500314
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    Citations

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    Cited by:

    1. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    2. Marc Mukendi Mpanda, 2022. "Malliavin differentiability of fractional Heston-type model and applications to option pricing," Papers 2207.10709, arXiv.org, revised Aug 2022.
    3. Giulia Di Nunno & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2022. "Option pricing in Sandwiched Volterra Volatility model," Papers 2209.10688, arXiv.org, revised Dec 2023.

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