A two-grid penalty method for American options
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In this paper we consider the pricing of American options, governed by a partial differential complementarity problem. The differential problem is first approximated by a semi-linear PDE using two distinct penalty approaches which are well known in computational finance. We then initiate the two-grid algorithm by solving the nonlinear problem on a coarse grid and further the linearized in the interpolated coarse-grid solution problem on a fine grid. By means of the maximum principle the algorithm is shown to be of fourth order convergence rate in space. Numerical experiments verify the presented two-grid approach where we draw some interesting conclusions.
KeywordsPenalty method Finite difference Two-grid Newton method Maximum principle
Mathematics Subject Classification35R35 65M06
Authors would like to thank the anonymous reviewers for their valuable and constructive comments that greatly contributed to improve the quality of the paper.
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