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On Lévy processes, Malliavin calculus and market models with jumps

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Abstract.

Recent work by Nualart and Schoutens (2000), where a kind of chaotic property for Lévy processes has been proved, has enabled us to develop a Malliavin calculus for Lévy processes. For simple Lévy processes some useful formulas for computing Malliavin derivatives are deduced. Applications for option hedging in a jump–diffusion model are given.

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Authors and Affiliations

  1. Departamento de Matemáticas, CINVESTAV-IPN, Apartado Postal 14-740, 07000 México, D.F., México (e-mail: jleon@math.cinvestav.mx) , , , , , , MX

    Jorge A. León

  2. Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain (e-mail: jllsole@mat.uab.es, utzet@mat.uab.es, vives@mat.uab.es) , , , , , , ES

    Josep L. Solé, Frederic Utzet & Josep Vives

Authors
  1. Jorge A. León
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  2. Josep L. Solé
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  3. Frederic Utzet
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  4. Josep Vives
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Manuscript received: November 2000; final version received: May 2001

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León, J., Solé, J., Utzet, F. et al. On Lévy processes, Malliavin calculus and market models with jumps. Finance Stochast 6, 197–225 (2002). https://doi.org/10.1007/s007800100055

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  • DOI: https://doi.org/10.1007/s007800100055

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