Local and implied volatilities with the Mixed-Modified-Fractional-Dupire Model

Eric Djeutcha and Jules Sadefo-Kamdem
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Eric Djeutcha: UMa - University of Maroua
Jules Sadefo-Kamdem: MRE - Montpellier Recherche en Economie - UM - Université de Montpellier
Authors registered in the RePEc Author Service: Jules SADEFO KAMDEM

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Abstract: In this paper, we use the Mellin transform to obtain the analytical formulas of European option (call or put) values, when the evolution of the underlying asset return is governed by a mixed modified fractional stochastic process. As an extension of the Dupire Model [12], we also introduce the so-called 'Mixed-Modified-Fractional-Dupire model', by giving the expression of it's local volatility and it's sensitivity in relation to the Hurst coefficient H. Finally, in the same vein, we highlight an analytical relationship between local volatility and implied volatility.

Keywords: Hurst coefficient; Option pricing; Surface volatility; Mellin transform; Local volatility (search for similar items in EconPapers)
Date: 2021-08-26
Note: View the original document on HAL open archive server: https://hal.science/hal-03324320
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Published in Chaos, Solitons & Fractals, 2021, 152, pp.111328. ⟨10.1016/j.chaos.2021.111328⟩

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Journal Article: Local and implied volatilities with the mixed-modified-fractional-Dupire model (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03324320

DOI: 10.1016/j.chaos.2021.111328

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