ADAPTIVE FINITE ELEMENT METHODS FOR LOCAL VOLATILITY EUROPEAN OPTION PRICING

Alexandre Ern (), Stéphane Villeneuve () and Antonino Zanette ()
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Alexandre Ern: CERMICS, Ecole nationale des ponts et chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne la Vallée cedex 2, France
Stéphane Villeneuve: Université d'Evry Val d'Essonne, Equipe d'Analyse et de Probabilité, Boulevard F. Mitterand, 91 025 Evry cedex, France
Antonino Zanette: Dipartimento di Finanza dell'Impresa, e dei Mercati Finanziari, Università di Udine, via Tomadini 30/A, Udine, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2004, vol. 07, issue 06, 659-684

Abstract: We investigate finite element discretizations using functions that are discontinuous in time and continuous in space for European options with local volatility Black–Scholes models. We present ana posteriorierror estimate where a user-specified functional of the error is controlled by the inner product of the finite element residual with the solution of a dual problem that involves the density of the target functional as prescribed data. Examples of error functionals are discussed in the context of either option pricing or volatility calibration from market data. Thea posteriorierror estimator is then localized onto the space-time cells of the computational mesh and implemented in the framework of an adaptive mesh refinement/derefinement algorithm which provides some form of optimal compromise between accuracy requirements and computational costs. Numerical examples illustrate the efficiency of the proposed methodology.

Keywords: Computational finance; adaptive finite element; discontinuous Galerkin (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0219024904002669

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