A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models

Rama Cont () and Ekaterina Voltchkova ()
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Rama Cont: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Ekaterina Voltchkova: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Lévy process or, more generally, a time-inhomogeneous jump-diffusion process. We discuss localization to a finite domain and provide an estimate for the localization error under an integrability condition on the Lévy measure. We propose an explicit-implicit finite difference scheme which can be used to price European and barrier options in such models. We study stability and convergence of the scheme proposed and, under additional conditions, provide estimates on the rate of convergence. Numerical tests are performed with smooth and nonsmooth initial conditions.

Keywords: parabolic integro-differential equations; finite difference methods; Lé; vy process; jump-diffusion models; option pricing; viscosity solutions (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (80)

Published in SIAM Journal on Numerical Analysis, 2005, 43 (4), pp.1596-1626. ⟨10.1137/S0036142903436186⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00445645

DOI: 10.1137/S0036142903436186

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