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Stratified sampling and quasi-Monte Carlo simulation of Lévy processes

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  • Leobacher G.

    (E-mail: gunther.leobacher@jku.at)

Abstract

We provide a method for the generation of paths of Lévy processes which allows for more efficient simulation than crude step-by-step generation. We show how, using our method, one can apply stratified sampling and quasi-Monte Carlo methods to obtain better numerical schemes analog to the Brownian case. As a numerical example we consider the problem of pricing an asian option in the so-called hyperbolic market model.

Suggested Citation

  • Leobacher G., 2006. "Stratified sampling and quasi-Monte Carlo simulation of Lévy processes," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 231-238, October.
    • Handle: RePEc:bpj:mcmeap:v:12:y:2006:i:3:p:231-238:n:2
    DOI: 10.1515/156939606778705155
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    Citations

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    Cited by:

    1. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    2. Imai, Junichi & Tan, Ken Seng, 2025. "Dimension reduction for Quasi-Monte Carlo methods via quadratic regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 371-390.
    3. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    4. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
    5. Genin, Adrien & Tankov, Peter, 2020. "Optimal importance sampling for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 20-46.
    6. Gunther Leobacher, 2017. "A short introduction to quasi-Monte Carlo option pricing," Papers 1707.04293, arXiv.org, revised Jul 2017.
    7. Baldeaux Jan, 2008. "Quasi-Monte Carlo methods for the Kou model," Monte Carlo Methods and Applications, De Gruyter, vol. 14(4), pages 281-302, January.

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