Option valuation under the VG process by a DG method

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F21%3A10248356" target="_blank" >RIV/61989100:27510/21:10248356 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24510/21:00009601
Result on the web
<a href="https://link.springer.com/article/10.21136/AM.2021.0345-20" target="_blank" >https://link.springer.com/article/10.21136/AM.2021.0345-20</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2021.0345-20" target="_blank" >10.21136/AM.2021.0345-20</a>

Result language
angličtina
Original language name
Option valuation under the VG process by a DG method
Original language description
The paper presents a discontinuous Galerkin method for solving partial integrodifferential equations arising from the European as well as American option pricing when the underlying asset follows an exponential variance gamma process. For practical purposes of numerical solving we introduce the modified option pricing problem resulting from a localization to a bounded domain and an approximation of small jumps, and we discuss the related error estimates. Then we employ a robust numerical procedure based on piecewise polynomial generally discontinuous approximations in the spatial domain. This technique enables a simple treatment of the American early exercise constraint by a direct encompassing it as an additional nonlinear source term to the governing equation. Special attention is paid to the proper discretization of non-local jump integral components, which is based on splitting integrals with respect to the domain according to the size of the jumps. Moreover, to preserve sparsity of resulting linear algebraic systems the pricing equation is integrated in the temporal variable by a semi-implicit Euler scheme. Finally, the numerical results demonstrate the capability of the numerical scheme presented within the reference benchmarks.
Czech name
—
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
50200 - Economics and Business

Project
<a href="/en/project/GA18-13951S" target="_blank" >GA18-13951S: New approaches to financial time series modelling based on soft computing</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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