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Importance sampling for jump processes and applications to finance

Author

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  • Laetitia Badouraly Kassim

    (SAM - Statistique Apprentissage Machine - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique)

  • Jérôme Lelong

    (SAM - Statistique Apprentissage Machine - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique)

  • Imane Loumrhari

    (SAM - Statistique Apprentissage Machine - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique)

Abstract

Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the standard exponential tilting for the Brownian motion. The free parameters of our framework are optimized using sample average approximation techniques. We illustrate the efficiency of our method on the valuation of financial derivatives in several jump models.

Suggested Citation

  • Laetitia Badouraly Kassim & Jérôme Lelong & Imane Loumrhari, 2015. "Importance sampling for jump processes and applications to finance," Post-Print hal-00842362, HAL.
    • Handle: RePEc:hal:journl:hal-00842362
    DOI: 10.21314/JCF.2015.292
    Note: View the original document on HAL open archive server: https://hal.science/hal-00842362
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    References listed on IDEAS

    as
    1. Arouna Bouhari, 2004. "Adaptative Monte Carlo Method, A Variance Reduction Technique," Monte Carlo Methods and Applications, De Gruyter, vol. 10(1), pages 1-24, March.
    2. Kiessling Jonas & Tempone Raúl, 2011. "Diffusion approximation of Lévy processes with a view towards finance," Monte Carlo Methods and Applications, De Gruyter, vol. 17(1), pages 11-45, January.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Lelong, Jérôme, 2008. "Almost sure convergence of randomly truncated stochastic algorithms under verifiable conditions," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2632-2636, November.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Genin, Adrien & Tankov, Peter, 2020. "Optimal importance sampling for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 20-46.
    2. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.

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