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The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth

: Griebel, M.; Kuo, F.Y.; Sloan, I.H.

Fulltext ()

Mathematics of computation 86 (2017), No.306, pp.1855-1876
ISSN: 0025-5718
ISSN: 1088-6842
Journal Article, Electronic Publication
Fraunhofer SCAI ()

The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We study ANOVA decomposition of a function of infinitely many variables arising from the Brownian bridge formulation of the continuous option pricing problem. We show that all resulting ANOVA terms can be smooth in this infinite-dimensional case, despite the non-smoothness of the underlying payoff function. This result may explain why quasi-Monte Carlo methods or sparse grid quadrature techniques work for such option pricing problems.