Importance sampling for jump processes and applications to finance

Laetitia Badouraly Kassim, Jérôme Lelong () and Imane Loumrhari
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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

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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.

Keywords: adaptive Monte Carlo methods.; sample average approximation; Importance sampling; adaptive Monte Carlo methods (search for similar items in EconPapers)
Date: 2015-12
Note: View the original document on HAL open archive server: https://hal.science/hal-00842362v1
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Citations: View citations in EconPapers (2)

Published in The Journal of Computational Finance, 2015, 19 (2), pp.109-139. ⟨10.21314/JCF.2015.292⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00842362

DOI: 10.21314/JCF.2015.292

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