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Implementable coupling of Lévy process and Brownian motion

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  • Fomichov, Vladimir
  • González Cázares, Jorge
  • Ivanovs, Jevgenijs

Abstract

We provide a simple algorithm for construction of Brownian paths approximating those of a Lévy process on a finite time interval. It requires knowledge of the Lévy process trajectory on a chosen regular grid and the law of its endpoint, or the ability to simulate from that. This algorithm is based on reordering of Brownian increments, and it can be applied in a recursive manner. We establish an upper bound on the mean squared maximal distance between the paths and determine a suitable mesh size in various asymptotic regimes. The analysis proceeds by reduction to the comonotonic coupling of increments. Applications to model risk and multilevel Monte Carlo are discussed in detail, and numerical examples are provided.

Suggested Citation

  • Fomichov, Vladimir & González Cázares, Jorge & Ivanovs, Jevgenijs, 2021. "Implementable coupling of Lévy process and Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 407-431.
    • Handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:407-431
    DOI: 10.1016/j.spa.2021.09.008
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    References listed on IDEAS

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    1. Ferreiro-Castilla, A. & Kyprianou, A.E. & Scheichl, R. & Suryanarayana, G., 2014. "Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 985-1010.
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    8. Böttcher, Björn & Schilling, René L. & Wang, Jian, 2011. "Constructions of coupling processes for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1201-1216, June.
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    10. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c, 2021. "Monte Carlo algorithm for the extrema of tempered stable processes," Papers 2103.15310, arXiv.org, revised Dec 2022.
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    Cited by:

    1. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.

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