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Error Bounds for Small Jumps of Lévy Processes

Part of: Stochastic processes Partial differential equations, boundary value problems Markov processes

Published online by Cambridge University Press:  04 January 2016

E. H. A. Dia
E. H. A. Dia*
Affiliation:
Université Paris-Est
*
∗ Postal address: Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR CNRS 8050, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée, France. Email address: dia.eha@gmail.com
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Abstract

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The pricing of options in exponential Lévy models amounts to the computation of expectations of functionals of Lévy processes. In many situations, Monte Carlo methods are used. However, the simulation of a Lévy process with infinite Lévy measure generally requires either truncating or replacing the small jumps by a Brownian motion with the same variance. We will derive bounds for the errors generated by these two types of approximation.

Keywords

approximation of small jumpsLévy processSkorokhod embeddingSpitzer identity

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 65N15: Error bounds
Secondary: 60J75: Jump processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 1 , March 2013 , pp. 86 - 105
Copyright
© Applied Probability Trust 

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