The Annals of Applied Probability

Integration by parts formula for locally smooth laws and applications to sensitivity computations

Vlad Bally, Marie-Pierre Bavouzet, and Marouen Messaoud

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 17, Number 1 (2007), 33-66.

Dates
First available in Project Euclid: 13 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1171377176

Digital Object Identifier
doi:10.1214/105051606000000592

Mathematical Reviews number (MathSciNet)
MR2292579

Zentralblatt MATH identifier
1139.60025

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60J75: Jump processes
Secondary: 65C05: Monte Carlo methods

Keywords
Malliavin calculus pure jump diffusions sensitivity analysis Monte Carlo algorithm European call and digital options

Citation

Bally, Vlad; Bavouzet, Marie-Pierre; Messaoud, Marouen. Integration by parts formula for locally smooth laws and applications to sensitivity computations. Ann. Appl. Probab. 17 (2007), no. 1, 33--66. doi:10.1214/105051606000000592. https://projecteuclid.org/euclid.aoap/1171377176


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