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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