Advances in Applied Probability

Error bounds for small jumps of Lvy processes

E. H. A. Dia

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Abstract

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

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

Dates
First available in Project Euclid: 15 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1363354104

Digital Object Identifier
doi:10.1239/aap/1363354104

Mathematical Reviews number (MathSciNet)
MR3077542

Zentralblatt MATH identifier
1263.60044

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

Keywords
approximation of small jumps Lévy process Skorokhod embedding Spitzer identity

Citation

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. https://projecteuclid.org/euclid.aap/1363354104


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