On the Quantitative Properties of Some Market Models Involving Fractional Derivatives

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00355833" target="_blank" >RIV/68407700:21340/21:00355833 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3390/math9243198" target="_blank" >https://doi.org/10.3390/math9243198</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math9243198" target="_blank" >10.3390/math9243198</a>

Result language
angličtina
Original language name
On the Quantitative Properties of Some Market Models Involving Fractional Derivatives
Original language description
We review and discuss the properties of various models that are used to describe the behavior of stock returns and are related in a way or another to fractional pseudo-differential operators in the space variable; we compare their main features and discuss what behaviors they are able to capture. Then, we extend the discussion by showing how the pricing of contingent claims can be integrated into the framework of a model featuring a fractional derivative in both time and space, recall some recently obtained formulas in this context, and derive new ones for some commonly traded instruments and a model involving a Riesz temporal derivative and a particular case of Riesz-Feller space derivative. Finally, we provide formulas for implied volatility and first- and second-order market sensitivities in this model, discuss hedging and profit and loss policies, and compare with other fractional (Caputo) or non-fractional models.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-16066S" target="_blank" >GA19-16066S: Nonlinear interactions and information transfer in complex systems with extreme events</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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