Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem
Result description
In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.
Keywords
Discontinuous Galerkin methodBlack-Scholes equationspace semidiscretizationnonsymmetric stabilization of diffusion termsupwindinga priori error estimatesexperimental order of convergence
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Analysis of the Discontinuous Galerkin Method Applied to the European Option Pricing Problem
Original language description
In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), AIP Conference Proceedings 1570
ISBN
9780735411982
ISSN
0094-243X
e-ISSN
—
Number of pages
8
Pages from-to
227-234
Publisher name
AMER INST PHYSICS
Place of publication
Melville, NY, USA
Event location
Sozopol, Bulgaria
Event date
Jun 8, 2013
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000346051300025
Result type
D - Article in proceedings
CEP
BA - General mathematics
Year of implementation
2013