A two-grid penalty method for American options

Journal Article · Sun Jul 15 00:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0457-6· OSTI ID:22769307

Chernogorova, Tatiana P. ^[1]; Valkov, Radoslav L. ^[2]

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1. Sofia University, Department of Numerical Methods and Algorithms (Bulgaria)
2. University of Antwerp, Department of Mathematics and Computer Science (Belgium)

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.

• OSTI ID: 22769307
• Journal Information: Computational and Applied Mathematics, Vol. 37, Issue 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
APPROXIMATIONS
CONVERGENCE
MATHEMATICAL SOLUTIONS
NEWTON METHOD
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS