Abstract
The paper is concerned with the valuation of European option prices and Greeks under the Merton jump-diffusion model. This model is represented by the nonstationary integro-differential equation with a degenerate elliptic differential operator. The Galerkin method with cubic spline wavelets is employed for spatial discretization combined with the Crank-Nicolson scheme and Richardson extrapolation for time discretization. This method provides many advantages such as sparse and uniformly conditioned discretization matrices, high-order convergence, and a small number of parameters representing the solution with the desired accuracy. Numerical experiments are presented for European vanilla put option to illustrate the efficiency and applicability of the proposed scheme.
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