This paper focuses on pricing two-asset European options under the Merton model admitting jumps in the price of under-lying assets. This model is represented by a nonstationary integro-differential equation with two state variables. First, we transform the equation to logarithmic prices, approximate the domain and the integral term, and set appropriate boundary conditions. Then, we study the wavelet-Galerkin method combined with the Crank-Nicolson scheme for discretization. The significant advantage of the method is a sparse structure of resulting matrices, which is not achieved for many standard methods due to the integral term. Other advantages are uniformly bounded condition numbers of the matrices, high-order accuracy of the scheme, and a small number of parameters representing the solution. To illustrate the efficiency of the method, we provide numerical experiments.
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1 September 2023
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2021
20–26 September 2021
Rhodes, Greece
Research Article|
September 01 2023
Wavelet-Galerkin method for pricing two-asset European options under merton model
Dana Černá
Dana Černá
a)
Department of Mathematics and Didactics of Mathematics, Technical University in Liberec
, Studentská 2, Liberec, 46117, Czech Republic
a)Corresponding author: dana.cerna@tul.cz
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a)Corresponding author: dana.cerna@tul.cz
AIP Conf. Proc. 2849, 090002 (2023)
Citation
Dana Černá; Wavelet-Galerkin method for pricing two-asset European options under merton model. AIP Conf. Proc. 1 September 2023; 2849 (1): 090002. https://doi.org/10.1063/5.0162134
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