Finite Element Methods for Parabolic Problems

Norbert Hilber, Oleg Reichmann, Christoph Schwab and Christoph Winter
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Norbert Hilber: Zurich University of Applied Sciences
Oleg Reichmann: Swiss Federal Institute of Technology (ETH)
Christoph Schwab: Swiss Federal Institute of Technology (ETH)
Christoph Winter: Allianz Deutschland AG

Chapter Chapter 3 in Computational Methods for Quantitative Finance, 2013, pp 27-45 from Springer

Abstract: 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.

Keywords: Option Price; Weak Derivative; Riesz Representation Theorem; Parabolic PDEs; Element Shape Function (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-35401-4_3

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DOI: 10.1007/978-3-642-35401-4_3

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