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

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  • Eric Djeutcha

    (UMa - University of Maroua)

  • Jules Sadefo-Kamdem

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

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.

Suggested Citation

  • Eric Djeutcha & Jules Sadefo-Kamdem, 2021. "Local and implied volatilities with the Mixed-Modified-Fractional-Dupire Model," Post-Print hal-03324320, HAL.
    • Handle: RePEc:hal:journl:hal-03324320
    DOI: 10.1016/j.chaos.2021.111328
    Note: View the original document on HAL open archive server: https://hal.science/hal-03324320
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    References listed on IDEAS

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