Finite Element Methods for Parabolic Problems

Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph

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

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Cited by 4 publications

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“…Finite element (FE) methods provide a viable alternative to FD, but seem for the moment less popular with practioners; see however (Achdou and Pironneau, 2010) and also (Hilber et al, 2013) for a recent comprehensive textbook treatment with applications to computational finance. (Matache et al, 2005a) implement and analyse a FE scheme with a wavelet basis and prove convergence of order 1 in space and at most 1 in time for the American option pricing problem, including for Lévy processes of unbounded variation.…”

Section: Introductionmentioning

confidence: 99%

A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

Brummelhuis

Chan

2013

Applied Mathematical Finance

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We use Radial Basis Function (RBF) interpolation to price options in exponential Lévy models by numerically solving the fundamental pricing PIDE. Our RBF scheme can handle arbitrary singularities of the Lévy measure in 0 without introducing further approximations, making it simpler to implement than competing methods. In numerical experiments using processes from the CGMY-KoBoL class, the scheme is found to be second order convergent in the number of interpolation points, including for processes of unbounded variation.

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Section: Introductionmentioning

confidence: 99%