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An importance sampling method based on the density transformation of Lévy processes

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  • Kawai Reiichiro

    (Postal address : Financial Engineering, Fixed Income Department, Daiwa Securities SMBC Co.Ltd., 1-14-5, Eitai, Koto-ku, Tokyo, 135-0034, Japan. Email address: reiichiro.kawai@daiwasmbc.co.jp.)

Abstract

In this paper, we develop an importance sampling method with the help of flexible control on the Lévy measure in the density transformation. The method has significant efficacy even on evaluating random variables with complex path-dependent structures. Numerical examples are presented to illustrate convergence acceleration through variance reduction with a view towards financial derivatives pricing.

Suggested Citation

  • Kawai Reiichiro, 2006. "An importance sampling method based on the density transformation of Lévy processes," Monte Carlo Methods and Applications, De Gruyter, vol. 12(2), pages 171-186, April.
    • Handle: RePEc:bpj:mcmeap:v:12:y:2006:i:2:p:171-186:n:1
    DOI: 10.1515/156939606777488833
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    References listed on IDEAS

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    1. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Bernard Lapeyre & J'er^ome Lelong, 2010. "A framework for adaptive Monte-Carlo procedures," Papers 1001.3551, arXiv.org, revised Jul 2010.
    2. 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.
    3. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.

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