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An Adaptive MFD Method for the Obstacle Problem Read chapter Read first chapter

2013 | OriginalPaper | Chapter

A Reduced Basis Method for the Simulation of American Options

Authors : B. Haasdonk, J. Salomon, B. Wohlmuth

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

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Abstract

We present a reduced basis method for the simulation of American option pricing. To tackle this model numerically, we formulate the problem in terms of a time dependent variational inequality. Characteristic ingredients are a POD-greedy and an angle-greedy procedure for the construction of the primal and dual reduced spaces. Numerical examples are provided, illustrating the approximation quality and convergence of our approach.

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previous chapter On the Reliability of Error Indication Methods for Problems with Uncertain Data
next chapter SAVU: A Statistical Approach for Uncertain Data in Dynamics of Axially Moving Materials
Literature
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Y. Achdou and O. Pironneau. Computational methods for option pricing. Frontiers in applied mathematics. Society for Industrial and Applied Mathematics, 2005.
2.
Annalisa Buffa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, and Gabriel Turinici. A priori convergence of the greedy algorithm for the parametrized reduced basis. To be published ESAIM-Math. Model. Numer. Anal., 2011.
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Rama Cont, Nicolas Lantos, and Olivier Pironneau. A reduced basis for option pricing. SIAM Journal on Financial Mathematics, 2:287–316, 2011.MathSciNetMATHCrossRef
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C. Geiger and C. Kanzow. Theorie und Numerik restringierter Optimierungsaufgaben. Springer-Lehrbuch Masterclass. Springer, 2002.MATHCrossRef
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R. Glowinski. Numerical Methods for Nonlinear Variational Problems. Scientific Computation. Springer, 2008.MATH
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Bernard Haasdonk. Convergence rates of the POD-greedy method. jun 2011. SimTech Preprint 2011-23, University of Stuttgart, submitted.
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Bernard Haasdonk and Mario Ohlberger. Reduced basis method for finite volume approximations of parametrized linear evolution equations. M2AN, Math. Model. Numer. Anal, 42(2):277–302, 2008.
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Bernard Haasdonk, Julien Salomon, and Barbara Wohlmuth. A reduced basis method for parametrized variational inequalities. submitted, 2011. SimTech Preprint 2011-16, University of Stuttgart.
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C. Hager, S. Hüeber, and B. Wohlmuth. Numerical techniques for the valuation of basket options and its greeks. J. Comput. Fin., 13(4):1–31, 2010.
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G. Rozza. Shape design by optimal flow control and reduced basis techniques: applications to bypass configurations in haemodynamics. PhD thesis, EPFL, Lausanne, 2005.
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K. Veroy, C. Prud’homme, D. V. Rovas, and A. T. Patera. A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations. In In Proceedings of 16th AIAA computational fluid dynamics conference, 2003. Paper 2003-3847.
Metadata
Title
A Reduced Basis Method for the Simulation of American Options
Authors
B. Haasdonk
J. Salomon
B. Wohlmuth
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Numerical Mathematics and Advanced Applications 2011

Print ISBN: 978-3-642-33133-6

Electronic ISBN: 978-3-642-33134-3

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33134-3_85

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