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In this paper, we consider the adaptive multigrid method for solving the Black- Scholes equation to improve the efficiency of the option pricing. Adaptive meshing is generally regarded as an indispensable tool because of reduction of the computational costs. The Black- Scholes equation is discretized using a Crank-Nicolson scheme on block-structured adaptively refined rectangular meshes. And the resulting discrete equations are solved by a fast solver such as a multigrid method. Numerical simulations are performed to confirm the efficiency of the adaptive multigrid technique. In particular, through the comparison of computational results on adaptively refined mesh and uniform mesh, we show that adaptively refined mesh solver is superior to a standard method.

AN ADAPTIVE MULTIGRID TECHNIQUE FOR OPTION PRICING UNDER THE BLACK-SCHOLES MODEL