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
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.
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-75009ScopusID: 2-s2.0-84858679675OAI: oai:DiVA.org:kth-75009DiVA: diva2:490302
QC 201202102012-02-042012-02-042012-02-10Bibliographically approved