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

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.

24 pages, 2 figures This paper is now published (in revised form), and is available online at http://www.degruyter.com/view/j/fca, so always cite it with the journal's coordinates