Irregular grid methods for pricing high-dimensional American options

S.J. Berridge

Research output: ThesisDoctoral Thesis

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Abstract

This thesis proposes and studies numerical methods for pricing high-dimensional American options; important examples being basket options, Bermudan swaptions and real options. Four new methods are presented and analysed, both in terms of their application to various test problems, and in terms of their theoretical stability and convergence properties. A method using matrix roots (Chapter 2) and a method using local consistency conditions (Chapter 4) are found to be stable and to give accurate solutions, in up to ten dimensions for the latter case. A method which uses local quadratic functions to approximate the value function (Chapter 3) is found to be vulnerable to instabilities in two dimensions, and thus not suitable for high-dimensional problems. A proof of convergence related to these methods is provided in Chapter 6. Finally, a method based on interpolation of the value function (Chapter 5) is found to be effective in pricing Bermudan swaptions.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Tilburg University
Supervisors/Advisors
  • Schumacher, Hans, Promotor
Award date18 Jun 2004
Place of PublicationTilburg
Publisher
Print ISBNs905668132X
Publication statusPublished - 2004

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  • Cite this

    Berridge, S. J. (2004). Irregular grid methods for pricing high-dimensional American options. CentER, Center for Economic Research.