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Applications of Malliavin calculus to Monte Carlo methods in finance

Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis; Touzi, Nizar (1999), Applications of Malliavin calculus to Monte Carlo methods in finance, Finance and Stochastics, 3, 4, p. 391-412. http://dx.doi.org/10.1007/s007800050068

Type
Article accepté pour publication ou publié
Date
1999
Journal name
Finance and Stochastics
Volume
3
Number
4
Publisher
Springer
Pages
391-412
Publication identifier
http://dx.doi.org/10.1007/s007800050068
Metadata
Show full item record
Author(s)
Fournié, Eric
Lasry, Jean-Michel
Lebuchoux, Jérôme
Lions, Pierre-Louis
Touzi, Nizar
Abstract (EN)
This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the {\it integration-by-parts} formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin calculus. The Greeks formulae, both with respect to initial conditions and for smooth perturbations of the local volatility, are provided for general discontinuous path-dependent payoff functionals of multidimensional diffusion processes. We illustrate the results by applying the formula to exotic European options in the framework of the Black and Scholes model. Our method is compared to the Monte Carlo finite difference approach and turns out to be very efficient in the case of discontinuous payoff functionals.
Subjects / Keywords
Monte Carlo methods; Malliavin calculus; hedge ratios and Greeks
JEL
C63 - Computational Techniques; Simulation Modeling
G13 - Contingent Pricing; Futures Pricing

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