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

Christoph Reisinger, Gabriel Wittum

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)189-197
Number of pages9
JournalComputing and Visualization in Science
Volume7
Issue number3-4
DOIs
StatePublished - Jan 1 2004

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

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