Quadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Models

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Quadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Models

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Quadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Models

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Symmetry

ISSN

2073-8994

e-ISSN

—

Svazek periodika

11

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

21

Strana od-do

—

Kód UT WoS článku

000483559300110

EID výsledku v databázi Scopus

2-s2.0-85070494450