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

Griebel, Michael; Kuo, Frances; Sloan, Ian

doi:10.1090/mcom/3171

The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth
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by Michael Griebel, Frances Y. Kuo and Ian H. Sloan;

Math. Comp. 86 (2017), 1855-1876

DOI: https://doi.org/10.1090/mcom/3171

Published electronically: October 7, 2016

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Abstract:

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.

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