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

Černá, Dana (2021)

Programs and Algorithms of Numerical Mathematics

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 for the...

WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation

Kwangil Kim, Kwanhung Ri, Wonho Han (2025)

Applications of Mathematics

A new fifth-order weighted essentially nonoscillatory (WENO) scheme is designed to approximate Hamilton-Jacobi equations. As employing a fifth-order linear approximation and three third-order ones on the same six-point stencil as before, a newly considered WENO-Z methodology is adapted to define nonlinear weights and the final WENO reconstruction results in a simple and clear convex combination. The scheme has formal fifth-order accuracy in smooth regions of the solution and nonoscillating behavior...

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