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

By Vlad Bally, M. Bavouzet, Marouen Messaoud. 2007

55 citations recorded by the source corpus.

We consider random variables of the form $F=f(V_1,...,V_n)$ where $f$ is a smooth function and $V_i,i\in\mathbbN$ are random variables with absolutely continuous law $p_i(y).$ We assume that $p_i,i=1,...,n$ are piecewise differentiable and we develop a differential calculus of Malliavin type based on $\partial\lnp_i.$ This allows us to establish an integration by parts formula $E(\partial_i\phi(F)G)=E(\phi(F)H_i(F,G))$ where $H_i(F,G)$ 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 Levy process.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/839ffbffa5da9a328ea2d3fb452db26182cea1a6

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In Management Science and Operations Research

Citations in the corpus

Bismut–Elworthy–Li-Type Formulae for Stochastic Differential Equations with Jumps (2010, methodology): “There are some approaches to tackle the problem on the sensitivities: the Girsanov transform approach [14] for Lévy processes initiated by Bismut [3], the martingale methods [5] similarly to [8] in the case of diffusion processes, and an application of the Malliavin calculus on the Wiener–Poisson sp”
Malliavin Monte Carlo Greeks for jump diffusions (2006, background): “Bavouzet and Massaoud (2005) and Bally et al. (2005) reduce the problem to a setting in which only ‘finite-dimensional’ Malliavin calculus is required. ElKhatib and Privault (2004) consider a market driven by jumps alone.”