Modeling of financial processes with a space-time fractional diffusion equation of varying order
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F16%3A00306008" target="_blank" >RIV/68407700:21340/16:00306008 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/fca-2016-0073" target="_blank" >http://dx.doi.org/10.1515/fca-2016-0073</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/fca-2016-0073" target="_blank" >10.1515/fca-2016-0073</a>
Alternative languages
Result language
angličtina
Original language name
Modeling of financial processes with a space-time fractional diffusion equation of varying order
Original language description
In this paper, a new model for financial processes in form of a spacetime 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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-07983S" target="_blank" >GA14-07983S: Vacuum structure in Quantum Field Theories</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fractional Calculus and Applied Analysis
ISSN
1311-0454
e-ISSN
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Volume of the periodical
19
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
1414-1433
UT code for WoS article
000394574400007
EID of the result in the Scopus database
2-s2.0-85007578492