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

TL;DR

This paper derives a rapidly convergent double-series representation for European call option prices driven by space-time fractional diffusion, using Mellin-Barnes integrals and residue calculus, enhancing computational efficiency.

Contribution

It introduces a novel series formula for fractional diffusion-based option pricing, derived from Mellin-Barnes representation and residue summation, providing a new analytical tool.

Findings

Series formula converges rapidly, improving computational efficiency.

Derived series representation for risk-neutral factors via Esscher transform.

Provides a new analytical approach for fractional diffusion option pricing.

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.