Series representation of the pricing formula for the European option driven by space-time fractional diffusion-Reference-Cited by-同舟云学术

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

Published:2018-08-01 Issue:4 Volume:21 Page:981-1004
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Aguilar Jean-Philippe¹,Coste Cyril²,Korbel Jan³⁴⁵

Affiliation:

1. BRED Banque Populaire , Modeling Department 18 quai de la Râpée , Paris , 75012 , France

2. MAIF , 200 avenue Salvador Allende , Niort , France

3. Section for the Science of Complex Systems , CeMSIIS Medical University of Vienna , Spitalgasse 23, A-1090 , Vienna , Austria

4. Complexity Science Hub Vienna , Josefstädterstrasse 39, 1080 , Vienna , Austria

5. Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague Břehová 7, 115 19 , Prague , Czech Republic

Abstract

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. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in ℂ2. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2018-0054/pdf

Reference44 articles.

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3. J.-P. Aguilar and J. Korbel, Option pricing models driven by the space-time fractional diffusion: series representation and applications. Fractal Fract. 2 (2018), Paper ID 15; 10.3390/fractalfract2010015.

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