A note on the treatment of boundary conditions for the vanilla
option pricing problem discretized by DG method

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A note on the treatment of boundary conditions for the vanilla option pricing problem discretized ...

Přehled o publikaci

D 2014

A note on the treatment of boundary conditions for the vanilla option pricing problem discretized by DG method

HOZMAN, Jiří a Tomáš TICHÝ

Základní údaje

Originální název

A note on the treatment of boundary conditions for the vanilla option pricing problem discretized by DG method

Autoři

HOZMAN, Jiří (203 Česká republika, garant, domácí) a Tomáš TICHÝ (203 Česká republika)

Vydání

Ostrava, MANAGING AND MODELLING OF FINANCIAL RISKS: 7TH INTERNATIONAL SCIENTIFIC CONFERENCE, PTS I-III, od s. 282-290, 9 s. 2014

Nakladatel

VSB-TECH UNIV OSTRAVA

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

50200 5.2 Economics and Business

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Odkazy

URL

Kód RIV

RIV/46747885:24510/14:#0001180

Organizace

Fakulta přírodovědně-humanitní a pedagogická – Technická univerzita v Liberci – Repozitář

ISBN

978-80-248-3631-7

UT WoS

000350605800034

Klíčová slova anglicky

Option; valuation; discontinuous Galerkin approach; boundary condition; implied volatility

Změněno: 7. 4. 2015 14:43, Jiří Hozman

Anotace

V originále

The valuation of a wide range of option contracts using the different financial models has acquired increasing popularity in modern financial theory and practice. This paper is dedicated to the plain vanilla option pricing problem, driven according to the one-dimensional Black-Scholes equation, and the main attention is paid to the treatment of boundary conditions. The whole system is discretized by the discontinuous Galerkin method combined with the implicit Euler scheme for the temporal discretization. Three concepts of boundary conditions are mentioned here such as Dirichlet, Neumann and transparent boundary condition. Moreover, their influence on the approximate solution together with the localization of an underlying asset and a strike price is studied. The preliminary numerical results are presented on real data of options on German DAX index obtained for 15SEPT2011 with implied volatilities and compared for the different treatments of boundary conditions to each other.

Citovat

HOZMAN, Jiří a Tomáš TICHÝ. A note on the treatment of boundary conditions for the vanilla option pricing problem discretized by DG method. In Culik, M. MANAGING AND MODELLING OF FINANCIAL RISKS: 7TH INTERNATIONAL SCIENTIFIC CONFERENCE, PTS I-III. Ostrava: VSB-TECH UNIV OSTRAVA, 2014, s. 282-290. ISBN 978-80-248-3631-7.

@inproceedings{18330,
   author = {Hozman, Jiří and Tichý, Tomáš},
   address = {Ostrava},
   booktitle = {MANAGING AND MODELLING OF FINANCIAL RISKS: 7TH INTERNATIONAL SCIENTIFIC CONFERENCE, PTS I-III},
   editor = {Culik, M},
   keywords = {Option; valuation; discontinuous Galerkin approach; boundary condition; implied volatility},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Ostrava},
   isbn = {978-80-248-3631-7},
   pages = {282-290},
   publisher = {VSB-TECH UNIV OSTRAVA},
   title = {A note on the treatment of boundary conditions for the vanilla option pricing problem discretized by DG method},
   url = {http://www.ekf.vsb.cz/export/sites/ekf/rmfr/cs/sbornik/Sbornik_parts/Sbornik_I.dil.pdf},
   year = {2014}
}

TY  - CONF
ID  - 18330
AU  - Hozman, Jiří - Tichý, Tomáš
PY  - 2014
TI  - A note on the treatment of boundary conditions for the vanilla option pricing problem discretized by DG method
PB  - VSB-TECH UNIV OSTRAVA
CY  - Ostrava
SN  - 9788024836317
KW  - Option
KW  - valuation
KW  - discontinuous Galerkin approach
KW  - boundary condition
KW  - implied volatility
UR  - http://www.ekf.vsb.cz/export/sites/ekf/rmfr/cs/sbornik/Sbornik_parts/Sbornik_I.dil.pdf
L2  - http://www.ekf.vsb.cz/export/sites/ekf/rmfr/cs/sbornik/Sbornik_parts/Sbornik_I.dil.pdf
N2  - The valuation of a wide range of option contracts using the different financial models has acquired increasing popularity in modern financial theory and practice. This paper is dedicated to the plain vanilla option pricing problem, driven according to the one-dimensional Black-Scholes equation, and the main attention is paid to the treatment of boundary conditions. The whole system is discretized by the discontinuous Galerkin method combined with the implicit Euler scheme for the temporal discretization. Three concepts of boundary conditions are mentioned here such as Dirichlet, Neumann and transparent boundary condition. Moreover, their influence on the approximate solution together with the localization of an underlying asset and a strike price is studied. The preliminary numerical results are presented on real data of options on German DAX index obtained for 15SEPT2011 with implied volatilities and compared for the different treatments of boundary conditions to each other.
ER  -

HOZMAN, Jiří a Tomáš TICHÝ. A note on the treatment of boundary conditions for the vanilla option pricing problem discretized by DG method. In Culik, M. \textit{MANAGING AND MODELLING OF FINANCIAL RISKS: 7TH INTERNATIONAL SCIENTIFIC CONFERENCE, PTS I-III}. Ostrava: VSB-TECH UNIV OSTRAVA, 2014, s.~282-290. ISBN~978-80-248-3631-7.