Option valuation under the VG process by a DG method

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/46747885:24510/21:00009601

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Option valuation under the VG process by a DG method

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Option valuation under the VG process by a DG method

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50200 - Economics and Business

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)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

66

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

30

Strana od-do

857-886

Kód UT WoS článku

000720636800004

EID výsledku v databázi Scopus

2-s2.0-85119500519