Fractional Black–Scholes model with regularized Prabhakar derivative

Shiva Eshaghi, Alireza Ansari, Reza Khoshsiar Ghaziani, and Mohammadreza Ahmadi Darani

Abstract: We introduce a fractional type Black–Scholes model in European options including the regularized Prabhakar derivative. We apply the reconstruction of variational iteration method to get the approximate analytical solutions for some models of generalized fractional Black–Scholes equations in terms of the generalized Mittag-Leffler functions.

Keywords: generalized fractional Black–Scholes equation, regularized Prabhakar derivative, generalized Mittag-leffler function, reconstruction of variational iteration method, Laplace transform

Classification (MSC2000): 62P05; 26A33

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