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Fractal Fract 2018, 2(1), 15; https://doi.org/10.3390/fractalfract2010015

Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications

1
BRED Banque Populaire, Modeling Department, 18 quai de la Râpée, 75012 Paris, France
2
Section for the Science of Complex Systems, Center for Medical Statistics, Informatics, and Intelligent Systems (CeMSIIS), Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria
3
Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080 Vienna, Austria
4
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague 115 19, Czech Republic
*
Author to whom correspondence should be addressed.
Received: 27 February 2018 / Revised: 13 March 2018 / Accepted: 14 March 2018 / Published: 16 March 2018
(This article belongs to the Special Issue Fractional Calculus in Economics and Finance)
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Abstract

In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model parameters from the market data and estimation of implied volatility within the space-time fractional option pricing models. View Full-Text
Keywords: space-time fractional diffusion; European option pricing; Mellin transform; multidimensional complex analysis space-time fractional diffusion; European option pricing; Mellin transform; multidimensional complex analysis
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Aguilar, J.-P.; Korbel, J. Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications. Fractal Fract 2018, 2, 15.

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