摘要：In this paper, we introduce a new numerical method for pricing American-style options, which has long been considered as a very challenging problem in financial engineering. Based on the HODIE (high order via differential identity expansion) finite difference scheme, we discretize the spatial variable on a piecewise uniform mesh, and meanwhile, use the implicit Euler method to discretize the time variable. Under such a discretization, we show that the resulting matrix is an M-matrix, which ensures the stability of the current scheme in the maximum-norm sense. By applying the discrete maximum principle, an error estimate of the current scheme is theoretically obtained first and then tested numerically. It is shown that our method is first order and second order convergent in the time and spatial directions, respectively. The results of various numerical experiments show that this new approach is quite accurate, and can be easily extended to price other kinds of American-style options.
关键词：American options ; Linear complementarity problem ; HODIE scheme ; Implicit Euler scheme ; Convergence analysis
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