European Option Pricing under the CGMY Model using the Discontinuous Galerkin Method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F22%3A00011946" target="_blank" >RIV/46747885:24510/22:00011946 - isvavai.cz</a>

Výsledek na webu

<a href="https://pubs.aip.org/aip/acp/article-abstract/2425/1/110005/2823442/European-option-pricing-under-the-CGMY-model-using" target="_blank" >https://pubs.aip.org/aip/acp/article-abstract/2425/1/110005/2823442/European-option-pricing-under-the-CGMY-model-using</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0081500" target="_blank" >10.1063/5.0081500</a>

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.

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

AIP Conference Proceedings

ISBN

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ISSN

0094-243X

e-ISSN

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Počet stran výsledku

4

Strana od-do

—

Název nakladatele

American Institute of Physics Inc.

Místo vydání

Melville, NY

Místo konání akce

Rhodes

Datum konání akce

1. 1. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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