Title: Error analysis of asymptotic option prices in a jump-diffusion model

Authors: Lamia Benothman; Faouzi Trabelsi

Addresses: Department of Mathematics, Faculté des Sciences de Bizerte, Université de Carthage, Jarzouna 7021, Bizerte, Tunisia; Unité de Recherche 'Multifractales et Ondelettes' (UR11ES53), Faculté des Sciences de Monastir, Université de Monastir, Avenue de l'Environnement – Monastir – 5000, Tunisia ' Department of Mathematics, Institut Supérieur d'Informatique et de Mathématiques de Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Tunisia; Unité de Recherche 'Multifractales et Ondelettes' (UR11ES53), Faculté des Sciences de Monastir, Université de Monastir, Avenue de l'Environnement – Monastir – 5000, Tunisia

Abstract: This paper is concerned with an approximation of the jump-size distribution in a jump-diffusion model in the context of European and US option pricing in mathematical finance. With a binomial-like jump-size distribution with an arbitrarily chosen support, we show that the approximation error (relative to Gaussian jump-size distribution) tends to zero as the number of atoms increases.

Keywords: jump diffusion model; market models; Merton's model; binomial distribution; asymptotic analysis; European call; American call; convergence error; Taylor's formulas; option pricing; jump size distribution; modelling.

DOI: 10.1504/IJMMNO.2014.063266

International Journal of Mathematical Modelling and Numerical Optimisation, 2014 Vol.5 No.3, pp.171 - 190

Received: 26 Nov 2013
Accepted: 06 Feb 2014

Published online: 08 Jul 2014 *

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