Two-dimensional Shannon wavelet inverse Fourier technique for pricing European options

G. Colldeforns-Papiol, L. Ortiz-Gracia, C. W. Oosterlee

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

The SWIFT method for pricing European-style options on one underlying asset was recently published and presented as an accurate, robust and highly efficient technique. The purpose of this paper is to extend the method to higher dimensions by pricing exotic option contracts, called rainbow options, whose payoff depends on multiple assets. The multidimensional extension inherits the properties of the one-dimensional method, being the exponential convergence one of them. Thanks to the nature of local Shannon wavelets basis, we do not need to rely on a-priori truncation of the integration range, we have an error bound estimate and we use fast Fourier transform (FFT) algorithms to speed up computations. We test the method for similar examples with state-of-the-art methods found in the literature, and we compare our results with analytical expressions when available.

Original languageEnglish
Pages (from-to)115-138
Number of pages24
JournalApplied Numerical Mathematics
Volume117
DOIs
Publication statusPublished - 2017

Keywords

  • Basket options
  • Cardinal sine function
  • European options
  • Fourier transform inversion
  • Lévy process
  • Option pricing
  • Shannon wavelets
  • Spread options
  • Two-colour rainbow options

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