Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options
Mrad, Moez; Touzi, Nizar; Zeghal, Amina (2006), Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options, Computational Economics, 27, 4, p. 497-531. http://dx.doi.org/10.1007/s10614-005-9005-3
TypeArticle accepté pour publication ou publié
Journal nameComputational Economics
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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).
Subjects / KeywordsMonte Carlo; Malliavin calculus; quantization; American options
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Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis; Touzi, Nizar (1999) Article accepté pour publication ou publié