The Mathematical Institute, University of Oxford, Eprints Archive

On multigrid for anisotropic equations and variational inequalities: pricing multi-dimensional European and American options

Reisinger, Christoph and Wittum, Gabriel (2004) On multigrid for anisotropic equations and variational inequalities: pricing multi-dimensional European and American options. Computing and Visualization in Science, 7 (3-4). pp. 189-197. ISSN 1433-0369

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Official URL: http://www.springerlink.com/(5uazodz5tojxczrsatfk4...

Abstract

Partial differential operators in finance often originate in bounded linear stochastic processes. As a consequence, diffusion over these boundaries is zero and the corresponding coefficients vanish. The choice of parameters and stretched grids lead to additional anisotropies in the discrete equations or inequalities. In this study various block smoothers are tested in numerical experiments for equations of Black–Scholes-type (European options) in several dimensions. For linear complementarity problems, as they arise from optimal stopping time problems (American options), the choice of grid transfer is also crucial to preserve complementarity conditions on all grid levels. We adapt the transfer operators at the free boundary in a suitable way and compare with other strategies including cascadic approaches and full approximation schemes.

Item Type:Article
Subjects:O - Z > Partial differential equations
H - N > Numerical analysis
Research Groups:Oxford Centre for Industrial and Applied Mathematics
Mathematical and Computational Finance Group
ID Code:237
Deposited By:Christoph Reisinger
Deposited On:07 Jun 2006
Last Modified:20 Jul 2009 14:19

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