Efficient hierarchical approximation of high-dimensional option pricing problems

Christoph Reisinger*, Gabriel Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to show how an efficient discretization can be achieved by hierarchical approximation as well as asymptotic expansions of the underlying continuous problem. The relation to a number of state-of-the-art methods is highlighted.

Original languageEnglish (US)
Pages (from-to)440-458
Number of pages19
JournalSIAM Journal on Scientific Computing
Volume29
Issue number1
DOIs
StatePublished - Dec 1 2007

Keywords

  • Asymptotic expansions
  • Dimension reduction
  • Multigrid methods
  • Option pricing
  • Sparse grids

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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