Quadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Models

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dc.contributor.authorČerná, Dana
dc.date.accessioned2019-09-18T09:51:42Z
dc.date.available2019-09-18T09:51:42Z
dc.date.issued2019-09-18
dc.date.issued2019-08
dc.description.abstractThis 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 i-j>2 are orthogonal. Thus, matrices arising from discretization by the Galerkin method with this basis have O1 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 O1 nonzero entries in each column. Numerical experiments are provided for European options under the Merton model.cs
dc.format.extent21 strancs
dc.identifier.doi10.3390/sym11080999
dc.identifier.urihttps://dspace.tul.cz/handle/15240/153596
dc.identifier.urihttps://www.mdpi.com/2073-8994/11/8/999
dc.language.isocscs
dc.publisherMDPI
dc.relation.ispartofSYMMETRY-BASEL
dc.subjectquadratic splinecs
dc.subjectwaveletcs
dc.subjecthomogeneous boundary conditionscs
dc.subjectvanishing momentscs
dc.subjectsparse matrixcs
dc.subjectjump-diffusion modelcs
dc.subjectMerton modelcs
dc.titleQuadratic Spline Wavelets for Sparse Discretization of Jump-Diffusion Modelscs
local.accessopen access
local.article.number999
local.identifier.publikace7357
local.relation.issue8
local.relation.volume11
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