Integration by parts formula for locally smooth laws and applications to sensitivity computations
Bally, Vlad ; Bavouzet, Marie-Pierre ; Messaoud, Marouen
Ann. Appl. Probab., Tome 17 (2007) no. 1, p. 33-66 / Harvested from Project Euclid
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We consider random variables of the form F=f(V1, …, Vn), where f is a smooth function and Vi, i∈ℕ, are random variables with absolutely continuous law pi(y) dy. We assume that pi, i=1, …, n, are piecewise differentiable and we develop a differential calculus of Malliavin type based on ∂lnpi. This allows us to establish an integration by parts formula E(∂iϕ(F)G)=E(ϕ(F)Hi(F, G)), where Hi(F, G) is a random variable constructed using the differential operators acting on F and G. We use this formula in order to give numerical algorithms for sensitivity computations in a model driven by a Lévy process.
Publié le : 2007-02-14
Classification:  Malliavin calculus,  pure jump diffusions,  sensitivity analysis,  Monte Carlo algorithm,  European call and digital options,  60H07,  60J75,  65C05 
@article{1171377176,
     author = {Bally, Vlad and Bavouzet, Marie-Pierre and Messaoud, Marouen},
     title = {Integration by parts formula for locally smooth laws and applications to sensitivity computations},
     journal = {Ann. Appl. Probab.},
     volume = {17},
     number = {1},
     year = {2007},
     pages = { 33-66},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1171377176}
}

Bally, Vlad; Bavouzet, Marie-Pierre; Messaoud, Marouen. Integration by parts formula for locally smooth laws and applications to sensitivity computations. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp.  33-66. http://gdmltest.u-ga.fr/item/1171377176/