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Series representation of the pricing formula for the European option driven by space-time fractional diffusion

Jean-Philippe Aguilar, Cyril Coste and Jan Korbel

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Abstract: In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. The series formula can be obtained from the Mellin-Barnes representation of the option price with help of residue summation in $\mathbb{C}^2$. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

Date: 2017-12, Revised 2018-10
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Published in Fractional calculus and applied analysis 21(4), 2018, 981-1004

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