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

  • Jan Korbel EMAIL logo and Yuri Luchko
Published/Copyright: December 16, 2016

Abstract

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

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


Acknowledgements

The first named author acknowledges support from the Czech Science Foundation, Grant No. GA14-07983S.

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Received: 2016-9-30
Published Online: 2016-12-16
Published in Print: 2016-12-1

© 2016 Diogenes Co., Sofia

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