Adaptive wavelet based scheme for option pricing

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F19%3A00007363" target="_blank" >RIV/46747885:24510/19:00007363 - isvavai.cz</a>
Result on the web
<a href="https://ieeexplore.ieee.org/abstract/document/8769814" target="_blank" >https://ieeexplore.ieee.org/abstract/document/8769814</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Adaptive wavelet based scheme for option pricing
Original language description
This contribution deals with the numerical solution of the Black-Scholes equation. The Crank-Nicolson scheme is applied for time discretization and wavelets are applied for space discretization. Hermite cubic spline wavelets with four vanishing moments are adaptively used because they enable higher order approximations, are well-conditioned, have short supports, have a high potential in adaptive methods due to the four vanishing wavelet moments and mainly because arising stiffness matrices are sparse in wavelet coordinates. Due to irregularities of the initial data in the Black-Scholes model, the use of the second-order Crank-Nicolson scheme usually requires a certain amount of damping to compensate for the known weak stability of this scheme. We numerically show here that optimal convergence rate for a proposed adaptive wavelet discretization in space can be obtained without any damping and without any restriction on the time step. A numerical example is given for the Black-Scholes equation with real data from the Frankfurt Stock Exchange. We also compare numerical results for adaptive and non-adaptive wavelet discretization in space.
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
2018 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND COMPUTERS IN SCIENCES AND INDUSTRY (MCSI 2018)
ISBN
978-1-5386-7500-7
ISSN
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e-ISSN
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Number of pages
4
Pages from-to
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Publisher name
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Place of publication
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Event location
Corfu, GREECE
Event date
Jan 1, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000493389900022

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