Superconvergence of the finite element solutions of the Black–Scholes equation

A. Golbabai, L.V. Ballestra and D. Ahmadian

Finance Research Letters, 2013, vol. 10, issue 1, 17-26

Abstract: We investigate the performances of the finite element method in solving the Black–Scholes option pricing model. Such an analysis highlights that, if the finite element method is carried out properly, then the solutions obtained are superconvergent at the boundaries of the finite elements. In particular, this is shown to happen for quadratic and cubic finite elements, and for the pricing of European vanilla and barrier options. To the best of our knowledge, lattice-based approximations of the Black–Scholes model that exhibit nodal superconvergence have never been observed so far, and are somehow unexpected, as the solutions of the associated partial differential problems have various kinds of irregularities.

Keywords: Finite element method; Black–Schoels equation; Vanilla option; Barrier options; Gauss–Lobatto; Superconvergence (search for similar items in EconPapers)
JEL-codes: C02 C1 C63 G11 G12 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:finlet:v:10:y:2013:i:1:p:17-26

DOI: 10.1016/j.frl.2012.09.002

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