Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets

Černá, Dana. "Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 47-56. <http://eudml.org/doc/299004>.

@inProceedings{Černá2023,
abstract = {This paper addresses the two-asset Merton model for option pricing represented by non-stationary integro-differential equations with two state variables. The drawback of most classical methods for solving these types of equations is that the matrices arising from discretization are full and ill-conditioned. In this paper, we first transform the equation using logarithmic prices, drift removal, and localization. Then, we apply the Galerkin method with a recently proposed orthogonal cubic spline-wavelet basis combined with the Crank-Nicolson scheme. We show that the proposed method has many benefits. First, as is well-known, the wavelet-Galerkin method leads to sparse matrices, which can be solved efficiently using iterative methods. Furthermore, since the basis functions are cubic splines, the method is higher-order convergent. Due to the orthogonality of the basis functions, the matrices are well-conditioned even without preconditioning, computation is simplified, and the required number of iterations is less than for non-orthogonal cubic spline-wavelet bases. Numerical experiments are presented for European-style options on the maximum of two assets.},
author = {Černá, Dana},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {wavelet-Galerkin method; Crank-Nicolson scheme; orthogonal spline wavelets},
location = {Prague},
pages = {47-56},
publisher = {Institute of Mathematics CAS},
title = {Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets},
url = {http://eudml.org/doc/299004},
year = {2023},
}

TY - CLSWK
AU - Černá, Dana
TI - Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 47
EP - 56
AB - This paper addresses the two-asset Merton model for option pricing represented by non-stationary integro-differential equations with two state variables. The drawback of most classical methods for solving these types of equations is that the matrices arising from discretization are full and ill-conditioned. In this paper, we first transform the equation using logarithmic prices, drift removal, and localization. Then, we apply the Galerkin method with a recently proposed orthogonal cubic spline-wavelet basis combined with the Crank-Nicolson scheme. We show that the proposed method has many benefits. First, as is well-known, the wavelet-Galerkin method leads to sparse matrices, which can be solved efficiently using iterative methods. Furthermore, since the basis functions are cubic splines, the method is higher-order convergent. Due to the orthogonality of the basis functions, the matrices are well-conditioned even without preconditioning, computation is simplified, and the required number of iterations is less than for non-orthogonal cubic spline-wavelet bases. Numerical experiments are presented for European-style options on the maximum of two assets.
KW - wavelet-Galerkin method; Crank-Nicolson scheme; orthogonal spline wavelets
UR - http://eudml.org/doc/299004
ER -