Quadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Models

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F19%3A00007357" target="_blank" >RIV/46747885:24510/19:00007357 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2073-8994/11/8/999" target="_blank" >https://www.mdpi.com/2073-8994/11/8/999</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym11080999" target="_blank" >10.3390/sym11080999</a>

Result language

angličtina

Original language name

Quadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Models

Original language description

This paper is concerned with a construction of new quadratic spline wavelets on a bounded interval satisfying homogeneous Dirichlet boundary conditions. The inner wavelets are translations and dilations of four generators. Two of them are symmetrical and two anti-symmetrical. The wavelets have three vanishing moments and the basis is well-conditioned. Furthermore, wavelets at levels i and j where ORi−j OR>2 are orthogonal. Thus, matrices arising from discretization by the Galerkin method with this basis have O(1) nonzero entries in each column for various types of differential equations, which is not the case for most other wavelet bases. To illustrate applicability, the constructed bases are used for option pricing under jump–diffusion models, which are represented by partial integro-differential equations. Due to the orthogonality property and decay of entries of matrices corresponding to the integral term, the Crank–Nicolson method with Richardson extrapolation combined with the wavelet–Galerkin method also leads to matrices that can be approximated by matrices with O(1) nonzero entries in each column. Numerical experiments are provided for European options under the Merton model.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Name of the periodical

Symmetry

ISSN

2073-8994

e-ISSN

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Volume of the periodical

11

Issue of the periodical within the volume

8

Country of publishing house

CH - SWITZERLAND

Number of pages

21

Pages from-to

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UT code for WoS article

000483559300110

EID of the result in the Scopus database

2-s2.0-85070494450