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- Title
Modeling of financial processes with a space-time fractional diffusion equation of varying order.
- Authors
Korbel, Jan; Luchko, Yuri
- 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.
- Subjects
CAPUTO fractional derivatives; LEVY processes; HEAT equation; STANDARD &; Poor's 500 Index; MATHEMATICAL models of option
- Publication
Fractional Calculus & Applied Analysis, 2016, Vol 19, Issue 6, p1414
- ISSN
1311-0454
- Publication type
Article
- DOI
10.1515/fca-2016-0073