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In this paper, the meshless smoothed particle hydrodynamic (SPH) method is applied for solving the Black–Scholes model for European and American options, which are governed by a generalized Black–Scholes partial differential equation. We use the [Formula: see text]-method and SPH for discretizing the governing equation in time variable and option pricing, respectively. To validate our SPH method, we compare it with the analytical solution and also the finite difference method. The numerical tests demonstrate the accuracy and robustness of our method.

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