APPROXIMATING EXPECTED VALUE OF AN OPTION WITH NON-LIPSCHITZ PAYOFF IN FRACTIONAL HESTON-TYPE MODEL

Yuliya Mishura () and Anton Yurchenko-Tytarenko
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 05, 1-36

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.

Keywords: Fractional Heston model; fractional Brownian motion; option pricing (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500314

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