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Representation formulas for Malliavin derivatives of diffusion processes

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Abstract.

We provide new representation formulas for Malliavin derivatives of diffusions, based on a transformation of the underlying processes. Both the univariate and the multivariate cases are considered. First order as well as higher order Malliavin derivatives are characterized. Numerical illustrations of the benefits of the transformation are provided.

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Authors and Affiliations

  1. Boston University School of Management, MA 02215, Boston, USA

    Jérôme Detemple

  2. CIRANO, H3A2A5, Montréal, Canada

    Jérôme Detemple, René Garcia & Marcel Rindisbacher

  3. Université de Montréal and CIREQ, H3C3J7, Montréal, Canada

    René Garcia

  4. J.L. Rotman School of Management, M5S3E6, Toronto, Canada

    Marcel Rindisbacher

Authors
  1. Jérôme Detemple
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  2. René Garcia
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  3. Marcel Rindisbacher
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Corresponding author

Correspondence to Jérôme Detemple.

Additional information

JEL Classification:

G11, G12, G13

Mathematics Subject Classification (2000):

60H07, 60J60, 65C05

Financial support from the Network of Centers of Excellence (MITACS) is gratefully acknowledged. The second author is grateful to Hydro-Québec and the Bank of Canada for financial support.

Correspondence to: René Garcia.

Manuscript received: February 2002; final version received: November 2004

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Detemple, J., Garcia, R. & Rindisbacher, M. Representation formulas for Malliavin derivatives of diffusion processes. Finance Stochast. 9, 349–367 (2005). https://doi.org/10.1007/s00780-004-0151-6

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  • DOI: https://doi.org/10.1007/s00780-004-0151-6

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