A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models - HAL Access content directly
Journal articles SIAM Journal on Numerical Analysis Year : 2005

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

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.
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halshs-00445645, version 1 (10-01-2010)

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Rama Cont, Ekaterina Voltchkova. A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models. SIAM Journal on Numerical Analysis, 2005, 43 (4), pp.1596-1626. ⟨10.1137/S0036142903436186⟩. ⟨halshs-00445645⟩
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