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Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options

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Date
2006
Dewey
Probabilités et mathématiques appliquées
Sujet
Monte Carlo; Malliavin calculus; quantization; American options
Journal issue
Computational Economics
Volume
27
Number
4
Publication date
2006
Article pages
497-531
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10614-005-9005-3
URI
https://basepub.dauphine.fr/handle/123456789/13602
Collections
  • CEREMADE : Publications
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Author
Mrad, Moez
Touzi, Nizar
Zeghal, Amina
Type
Article accepté pour publication ou publié
Abstract (EN)
We use the Malliavin integration by parts formula in order to provide a family of representations of the joint density (which does not involve Dirac measures) of (X_θ, X θ + δ), where X is a d-dimensional Markov diffusion (d ≥ 1), θ > 0 and δ > 0. Following Bouchard et al. (2004), the different representations are determined by a pair of localizing functions. We discuss the problem of variance reduction within the family of separable localizing functions: We characterize a pair of exponential functions as the unique integrated-variance minimizer among this class of separable localizing functions. We test our method on the d-dimensional Brownian motion and provide an application to the problem of American options valuation by the quantization tree method introduced by Bally et al. (2002).

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