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Wavelet Galerkin pricing of American options on Lévy driven assets

by A. M. Matache and P.-A. Nitsche and Ch. Schwab

(Report number 2003-06)

Abstract
The price of an American style contract on assets driven by Lévy processes with infinite jump activity is expressed as solution of a parabolic variational integro-differential inequality (PIDI). A Galerkin discretization in logarithmic price using a wavelet basis is presented with compression of the moment matrix of the jump part of the price process' Dynkin operator. An iterative solver with wavelet preconditioning for the resulting large matrix inequality problems is presented and its efficiency is demonstrated by numerical experiments.

Keywords: Lévy processes, integro-differential operators, variational inequalities, Galerkin discretization, bi-orthogonal wavelet basis, wavelet preconditioning

@Techreport{MNS03_318,
  author = {A. M. Matache and P.-A. Nitsche and Ch. Schwab},
  title = {Wavelet Galerkin pricing of American options on Lévy driven assets},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-06.pdf },
  year = {2003}
}

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