Displaying similar documents to “Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets”

Application of cubic box spline wavelets in the analysis of signal singularities

Waldemar Rakowski (2015)

International Journal of Applied Mathematics and Computer Science

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In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian) or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The paper deals with the construction and properties of wavelets in the form of cubic box splines...

Quantitative properties of quadratic spline wavelet bases in higher dimensions

Černá, Dana, Finěk, Václav, Šimůnková, Martina

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To use wavelets efficiently to solve numerically partial differential equations in higher dimensions, it is necessary to have at one’s disposal suitable wavelet bases. Ideal wavelets should have short supports and vanishing moments, be smooth and known in closed form, and a corresponding wavelet basis should be well-conditioned. In our contribution, we compare condition numbers of different quadratic spline wavelet bases in dimensions d = 1, 2 and 3 on tensor product domains (0,1)^d. ...

Wavelet method for option pricing under the two-asset Merton jump-diffusion model

Černá, Dana

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This paper examines the pricing of two-asset European options under the Merton model represented by a nonstationary integro-differential equation with two state variables. For its numerical solution, the wavelet-Galerkin method combined with the Crank-Nicolson scheme is used. A drawback of most classical methods is the full structure of discretization matrices. In comparison, the wavelet method enables the approximation of discretization matrices with sparse matrices. Sparsity is essential...

Wavelet bases for the biharmonic problem

Bímová, Daniela, Černá, Dana, Finěk, Václav

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In our contribution, we study different Riesz wavelet bases in Sobolev spaces based on cubic splines satisfying homogeneous Dirichlet boundary conditions of the second order. These bases are consequently applied to the numerical solution of the biharmonic problem and their quantitative properties are compared.

Estimation of a smoothness parameter by spline wavelets

Magdalena Meller, Natalia Jarzębkowska (2013)

Applicationes Mathematicae

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We consider the smoothness parameter of a function f ∈ L²(ℝ) in terms of Besov spaces B 2 , ∞ s ( ℝ ) , s * ( f ) = s u p s > 0 : f ∈ B 2 , ∞ s ( ℝ ) . The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0 < s*(f) < 1/2. Using p-regular (p ≥ 1) spline wavelets with exponential decay we extend them to density functions with 0 < s*(f) < p+1/2. Applying the Franklin-Strömberg wavelet p = 1, we prove that the...