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Published in:
Notions of Mathematical Finance Read chapter Read first chapter

2013 | OriginalPaper | Chapter

3. Finite Element Methods for Parabolic Problems

Authors : Norbert Hilber, Oleg Reichmann, Christoph Schwab, Christoph Winter

Published in: Computational Methods for Quantitative Finance

Publisher: Springer Berlin Heidelberg

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Abstract

The finite element methods are an alternative to the finite difference discretization of partial differential equations. The advantage of finite elements is that they give convergent deterministic approximations of option prices under realistic, low smoothness assumptions on the payoff function as, e.g. for binary contracts. The basis for finite element discretization of the pricing PDE is a variational formulation of the equation. Therefore, we introduce the Sobolev spaces needed in the variational formulation and give an abstract setting for the parabolic PDEs.

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previous chapter Elements of Numerical Methods for PDEs
next chapter European Options in BS Markets
Footnotes
1
CFL is an acronym for Courant, Friedrich and Lewy who identified an analogous condition as being necessary for the stability of explicit timestepping schemes for first order, hyperbolic equations.
 
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V. Thomée. Galerkin finite element methods for parabolic problems, volume 25 of Springer Series in Computational Mathematics, 2nd edition. Springer, Berlin, 2006. MATH
Metadata
Title
Finite Element Methods for Parabolic Problems
Authors
Norbert Hilber
Oleg Reichmann
Christoph Schwab
Christoph Winter
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Computational Methods for Quantitative Finance

Print ISBN: 978-3-642-35400-7

Electronic ISBN: 978-3-642-35401-4

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-35401-4_3

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