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Fractional Calculus and Applied Analysis

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Volume 19, Issue 6


Modeling of financial processes with a space-time fractional diffusion equation of varying order

Jan Korbel
  • Department of Physics, Zhejiang University Hangzhou 310027, P.R. China
  • Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague Břehová 7, Prague – 11519, Czech Republic
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/ Yuri Luchko
Published Online: 2016-12-16 | DOI: https://doi.org/10.1515/fca-2016-0073


In this paper, a new model for financial processes in form of a space-time fractional diffusion equation of varying order is introduced, analyzed, and applied for some financial data. While the orders of the spatial and temporal derivatives of this equation can vary on different time intervals, their ratio remains constant and thus the global scaling properties of its solutions are conserved. In this way, the model covers both a possible complex short-term behavior of the financial processes and their long-term dynamics determined by its characteristic time-independent scaling exponent. As an application, we consider the option pricing and describe how it can be modeled by the space-time fractional diffusion equation of varying order. In particular, the real option prices of index S&P 500 traded in November 2008 are analyzed in the framework of our model and the results are compared with the predictions made by other option pricing models.

MSC 2010: 26A33; 34A08; 91B84; 91G20

Key Words and Phrases: Caputo fractional derivative; Riesz-Feller fractional derivative; space-time fractional diffusion equation; financial modeling; option pricing

A paper presented at Workshop “FaF”, Lorentz Center - Leiden, The Netherlands, May 17-20, 2016


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About the article

Received: 2016-09-30

Published Online: 2016-12-16

Published in Print: 2016-12-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 19, Issue 6, Pages 1414–1433, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2016-0073.

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