Abstract
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 i - j > 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.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Cited by
7 articles.
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1. Wavelet-Galerkin method for pricing two-asset European options under merton model;AIP Conference Proceedings;2023
2. Adaptive wavelet method for numerical solution of integro-differential equations;AIP Conference Proceedings;2023
3. Wavelet-Galerkin method for integro-differential equations;INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020;2022
4. Wavelet method for sensitivity analysis of European options under Merton jump-diffusion model;INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020;2022
5. A priori selected spline–wavelet basis for option pricing under Black–Scholes and Merton model;“TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev;2022