Convergence of Crank-Nicolson scheme combined with wavelet discretization for the Black-Scholes equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F18%3A00005615" target="_blank" >RIV/46747885:24510/18:00005615 - isvavai.cz</a>
Result on the web
<a href="https://ieeexplore.ieee.org/document/8326852" target="_blank" >https://ieeexplore.ieee.org/document/8326852</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/MCSI.2017.53" target="_blank" >10.1109/MCSI.2017.53</a>

Result language
angličtina
Original language name
Convergence of Crank-Nicolson scheme combined with wavelet discretization for the Black-Scholes equation
Original language description
This paper is concerned with numerical solution of the Black-Scholes equation. We apply the Crank-Nicolson scheme for time discretization and Hermite cubic spline wavelets with four vanishing moments for space discretization. The advantages of this approach are higher order accuracy, a small number of iterations needed to resolve the problem with desired accuracy and a high potential in adaptive methods due to the four vanishing wavelet moments. Due to the data irregularities in the model, Crank-Nicolson scheme is often used together with Rannacher startup procedure to achieve second order convergence for approximations of the first derivatives. We numerically show that optimal convergence rate for the proposed scheme is obtained without using startup procedure. Moreover, it is necessary to apply only small number of GMRES iterations to achieve this results.
Czech name
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Czech description
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Project
<a href="/en/project/GA16-09541S" target="_blank" >GA16-09541S: Robust numerical schemes for pricing of selected options under various market conditions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
2017 Fourth International Conference on Mathematics and Computers in Sciences and in Industry (MCSI)
ISBN
978-1-5386-2820-1
ISSN
—
e-ISSN
—
Number of pages
4
Pages from-to
289-292
Publisher name
IEEE
Place of publication
NEW YORK
Event location
Corfu, GREECE
Event date
Jan 1, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000452189900047

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