Advances in Applied Probability

Error bounds for small jumps of Lvy processes

E. H. A. Dia

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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.

Article information

Adv. in Appl. Probab., Volume 45, Number 1 (2013), 86-105.

First available in Project Euclid: 15 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes 65N15: Error bounds
Secondary: 60J75: Jump processes

approximation of small jumps Lévy process Skorokhod embedding Spitzer identity


Dia, E. H. A. Error bounds for small jumps of Lvy processes. Adv. in Appl. Probab. 45 (2013), no. 1, 86--105. doi:10.1239/aap/1363354104.

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