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

Černá, Dana. "Wavelet method for option pricing under the two-asset Merton jump-diffusion model." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2021. 30-39. <http://eudml.org/doc/296855>.

@inProceedings{Černá2021,
abstract = {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 efficient application of iterative methods in solving the resulting systems and the efficient computation of the matrices arising from the discretization of integral terms. To illustrate the efficiency of the method, we provide the results of numerical experiments concerning a European option on the maximum of two assets.},
author = {Černá, Dana},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {Merton model; wavelet-Galerkin method; integro-differential equation; spline wavelets; Crank-Nicolson scheme; sparse matrix; option pricing},
location = {Prague},
pages = {30-39},
publisher = {Institute of Mathematics CAS},
title = {Wavelet method for option pricing under the two-asset Merton jump-diffusion model},
url = {http://eudml.org/doc/296855},
year = {2021},
}

TY - CLSWK
AU - Černá, Dana
TI - Wavelet method for option pricing under the two-asset Merton jump-diffusion model
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2021
CY - Prague
PB - Institute of Mathematics CAS
SP - 30
EP - 39
AB - 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 efficient application of iterative methods in solving the resulting systems and the efficient computation of the matrices arising from the discretization of integral terms. To illustrate the efficiency of the method, we provide the results of numerical experiments concerning a European option on the maximum of two assets.
KW - Merton model; wavelet-Galerkin method; integro-differential equation; spline wavelets; Crank-Nicolson scheme; sparse matrix; option pricing
UR - http://eudml.org/doc/296855
ER -