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Diffusion approximation of Lévy processes with a view towards finance
2011 (English)In: Monte Carlo Methods, Vol. 17, no 1, 11-45 p.Article in journal (Refereed) Published
Abstract [en]

Let the (log-)prices of a collection of securities be given by a d –dimensional L´evy process Xt having infinite activity and a smooth density. The value of a European contract with pay off g(x) maturing at T is determined by E[g(XT )]. Let ¯XT be a finite activity approximation to XT , where diffusion is introduced to approximate jumps smaller than a given truncation level ! > 0. The main result of this work is a derivation of an error expansion for the resulting model error, E[g(XT )g( ¯XT )], with computable leading order term. Our estimate depends both on the choice of truncation level ! and the contract payo ff g, and it is valid even when g is not continuous. Numerical experiments confirm that the error estimate is indeed a good approximation of the model error. Using similar techniques we indicate how to construct an adaptive truncation type approximation. Numerical experiments indicate that a substantial amount of work is to be gained from such adaptive approximation. Finally, we extend the previous model error estimates to the case of Barrier options, which have a particular path dependent structure.

Place, publisher, year, edition, pages
2011. Vol. 17, no 1, 11-45 p.
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-75009ScopusID: 2-s2.0-84858679675OAI: diva2:490302
QC 20120210Available from: 2012-02-04 Created: 2012-02-04 Last updated: 2012-02-10Bibliographically approved

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Kiessling, JonasTempone, Raúl
Computer and Information Science

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