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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA14-07983S" target="_blank" >GA14-07983S: Struktura vakua v kvantově polních teoriích</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fractional Calculus and Applied Analysis

ISSN

1311-0454

e-ISSN

—

Svazek periodika

19

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

1414-1433

Kód UT WoS článku

000394574400007

EID výsledku v databázi Scopus

2-s2.0-85007578492