European Option Pricing under the CGMY Model using the Discontinuous Galerkin Method
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F22%3A10250543" target="_blank" >RIV/61989100:27510/22:10250543 - isvavai.cz</a>
Výsledek na webu
<a href="https://aip.scitation.org/toc/apc/2425/1?windowStart=50&size=50" target="_blank" >https://aip.scitation.org/toc/apc/2425/1?windowStart=50&size=50</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0081500" target="_blank" >10.1063/5.0081500</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
European Option Pricing under the CGMY Model using the Discontinuous Galerkin Method
Popis výsledku v původním jazyce
We present the discontinuous Galerkin method applied to valuation of European options assuming that the underlying follows a CGMY process. This special case of an infinite activity Lévy process has purely discontinuous paths with finite and/or infinite variation with respect to the density of Lévy measure. The corresponding CGMY model was proposed as an extension of geometric Brownian motion to overcome some of the limitations of the Black-Scholes approach. The evolution of the option prices under this model can be expressed in the form of a partial integro-differential equation, which involves both integrals and derivatives of an unknown option value function. With a localization to a bounded spatial domain, the pricing equation is discretized by the discontinuous Galerkin method over a finite element mesh and it is integrated in temporal variable by a semi-implicit Euler scheme. The special attention is paid to the proper discretization of jump components. The whole procedure is accompanied with preliminary practical results compared to reference values. (C) 2022 American Institute of Physics Inc.. All rights reserved.
Název v anglickém jazyce
European Option Pricing under the CGMY Model using the Discontinuous Galerkin Method
Popis výsledku anglicky
We present the discontinuous Galerkin method applied to valuation of European options assuming that the underlying follows a CGMY process. This special case of an infinite activity Lévy process has purely discontinuous paths with finite and/or infinite variation with respect to the density of Lévy measure. The corresponding CGMY model was proposed as an extension of geometric Brownian motion to overcome some of the limitations of the Black-Scholes approach. The evolution of the option prices under this model can be expressed in the form of a partial integro-differential equation, which involves both integrals and derivatives of an unknown option value function. With a localization to a bounded spatial domain, the pricing equation is discretized by the discontinuous Galerkin method over a finite element mesh and it is integrated in temporal variable by a semi-implicit Euler scheme. The special attention is paid to the proper discretization of jump components. The whole procedure is accompanied with preliminary practical results compared to reference values. (C) 2022 American Institute of Physics Inc.. All rights reserved.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
50200 - Economics and Business
Návaznosti výsledku
Projekt
<a href="/cs/project/GA18-13951S" target="_blank" >GA18-13951S: Nové přístupy k modelování finančních časových řad pomocí soft-computingu</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
AIP Conference Proceedings. Volume 2505
ISBN
978-0-7354-4396-9
ISSN
0094-243X
e-ISSN
—
Počet stran výsledku
4
Strana od-do
—
Název nakladatele
AIP Publishing
Místo vydání
Melville
Místo konání akce
Sofie
Datum konání akce
7. 6. 2022
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
—