Representation formulas for Malliavin derivatives of diffusion processes

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 o...

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Bibliographic Details
Published in:Finance and stochastics 2005-07, Vol.9 (3), p.349-367
Main Authors: Detemple, Jérôme, Garcia, René, Rindisbacher, Marcel
Format: Article
Language:English
Subjects:
Brownian motion
Calculus
Capital market
Derivatives
Differential equations
Diffusion
Econometric models
Error
Financial economics
Mathematics
Multivariate analysis
Ordinary differential equations
Pricing
Stochastic models
Stochastic processes
Studies
Volatility
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-004-0151-6