The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth
The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth
Dokument öffnen (467KB)Datum der Veröffentlichung
2014Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11910
Inhalt
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.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1090/mcom/3171Reihe, Nummer
INS Preprints ; 1403Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.: The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth. In: INS Preprints, 1403.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11910
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11910
@unpublished{handle:20.500.11811/11910,
author = {{Michael Griebel} and {Frances Y. Kuo} and {Ian H. Sloan}},
title = {The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth},
publisher = {Institut für Numerische Simulation (INS)},
year = 2014,
INS Preprints},
volume = 1403,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11910}
}
author = {{Michael Griebel} and {Frances Y. Kuo} and {Ian H. Sloan}},
title = {The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth},
publisher = {Institut für Numerische Simulation (INS)},
year = 2014,
INS Preprints},
volume = 1403,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11910}
}
Die folgenden Nutzungsbestimmungen sind mit dieser Ressource verbunden:
